JPRS ID: 10157 TRANSLATION RADIATING PROPERTIES OF SHOCK WAVES IN GASES BY M.A. TSIKULIN ANYE G. POPOV

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JPRS L/ 10157
3 December 1981
Translation
RADIATING PROPERTIES OF SHOCK WAVES iN GASES
By
M.A. Tsikulin and Ye. G. Papov
i
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JPRS L/10157
3 December 1981
RADIATING PROPERTIES OF SHOCK WAVES IN GASES
Moscow IZLUCHATEL'NYYE SVOYSTVA UDARNYKH VOLN V GAZAKH in Russian 1977
[Book by M.A. Tsikulin and Ye. G. Popov, Izdatel'stvo "Nauka," 173 pages]
CONTENTS
Annotation 1
Foreword 1
Table of Contents 3
Chapter 1. Certain Problems of Radiating Gas Dynamics 5
1.1. Investigation of Strong Shock Waves in Gases 5
1.2. Problems of Moving I,arge Cosmic Bodies in the Atmosphere........... 14
1.3. Problems of Experimental Investigation 24
Chapter 2. Producing Strong Shock Waves in Gases 26
2.1. Exciting Shock Waves When Detonation Exd.ts Into the Gas............ 26
2.2. Producing Shock Waves by Detonating Gharges With a Cumulative
Channel 28
- 2.3. Produciag Strong Shock Waves by Compressing Gas Under
Canditions of Acute-Angled Geometry 33
2.4. Ottier Methods of Producing Strong Shock Waves 35
(fiapter 3. Method for Measuring the Intensity Temperature and Other Values... 37
3.1. Basic Concepts of the Radiation Theory 37
3.2. Measuring the Intensity Temperature by Photography 50
3.3. Method of Spectral Investigation of Radiation 56
- (hapter 4. Radiation Proper"ties of Shock Waves Determined by Results af
the Experiment 61
4.1. Intensity of Strong Shock Waves in Air 66
4.2. Intensity of Strong Shock Waves in Inert Gases 70
- a - [I - USSR - K FOUO)
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4.3. Resu;ts of Spectral Investigation of Radiation...........v........ 78
4.4. Instability of the Flat Front When Shock Waves Move in
Cliannels 93
Qiapter 5. Evaluation of the Influence of the Front Structure on Shnrlc
Wave :tadiation 10I
5.1. Effect of the Relaxation Layer 105
5.2. Radiation Heat Exchange at the Shock Wave Front 112
5.3. Radiation Shielding by Heated Iayer 120
5.4. Shielding of Radiation Front in Gas Pitxturea 133
Qiapter 6. Explosion Radiation Sources 141
6.1. Explosion Radiator for PhQtiometry Purposes............ 141
6.2. Installation of an Ultraviolet Shock............................... 143
- 6.3. Efficiency of Explosion Sources.................................... 151
6.4. Certain Results of Investigating the EfiEect of Radiation With
a Continuous Spectrum on a Hard Substance 165
_ BibliograFhy ....................................................o............ 177
- b -
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Annotation
This monograph contains exQerimenral investigations of the radiating properties of
large amplitude shock waves in gases. A review is given of inethods for obtaining
strong shock waves in rarified and dense gases and experimental results. Installa-
tions and the methods used to record the parameters of the shock waves are described.
Explosion sources as a method for obtaining powerful radiation with a contincsous
spectrum were especially considered. Results are cited of studies of the intensity
of the shock waves in the air and in the inert gas of various densities ( at
temperatures of up to 120,0000); their spectral investigation; measurement of the
angular distribution of the wave front; and the shielding and other phenomena
accompanying the radiation of strong shock waves. The possibilities of raising the
efficiency of the explosion sources further are considered. Examples are cited of
using the investigation results in astrophysics, physics o.f ineteor phenomena, gas
dynamics and plasma physics.
- The book is intended, for specialists in the area of shock wave physics, plasma
physics, astrophysics, and meteor physics, post-graduate students and students of
the indicated specialties.
Foreword
The book cites results of the experimental investigations of the radiating properties
of strong shock waves in dense gases which were carried out by the authors in the
Earth Physics Institute /IFZ/ imeni O. Yu. Shmidt of the USSR Academy of Sciences
during 1966-1969.
The experiments were organized primarily due to an increasing interest in the
dynamics of radiating gas. Investigations in this area, related to many phenomena,
for example, a strong explosion, the movement of cosmic bodies in the atmosphere,
the effect of laser_radiation on a substance, were moved forward considerably in
- recent years by the following Soviet scientists: Ya. B. Zel'dovich, Yti. P. Rayzer,
N. G. Basov, 0. N. Krokhin, L. M. Biberman, K. P. Stanyukovicho I. V. Nemchinov and
others.
1
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Various authors have established the basic possibility of using strong shock waves
in gases as a powerful high temperature radiator. By creating shock waves in dense
gases by means of condease explosive substance (VV), it is possible to obtain large
radia}ion flows in small installat'.ons. Especially efficient in this respect are
shock waves in heavy inert gases. The absence of expenditures for dissociation and
the large atomic weight of the latter facilitates the achievement af high temperatures
behind the shock front, and the transparency of the gas ahead cf the front to hard
ultraviolet leads to the radiation of considerably flows of energy by the wave.
The explosion of a W charge in an atmosphere of heavy inert g3s is used as a flash
lamp in hi,91speed photography /1-7/ . Recently, many investigators, in particular,
wanless /8_% proposed the use of such lamps for optical_pumping of quar.ta oscilZatcrs.
I. V. Nemchinov, M. A. Tsikulin and I. F. Zharikov / 9/ investigated by means of an
explosion source, the effect of powerful ultraviolet radiation on various materials,
their intensive evaporation and dispersion. A. N. Dromin and S. D. Savrov were able
to detonate an explosive substancc / 10 / by a light pulse from such a source.
Using an explosive source, A. A. Provalov and the coauthors / 11 / observed a
self-shielding phenomenon of the body surface from powerful radiation. The authors
/12-14_% proposed a high-temperature radiator of the explosion type, suitable for
photometry.
Radiation of shock wa,:es was encoUntered in solving im8ortant practical problems
related to strong explosions and the movement of cosmic bodies in the atmosphere.
IIy setting up experiments with strong shock waves, it was possible to expand the
investigation of optical properties of gases heated to a high temperature and
investigating the effect of powerful radiation flows on a solid substance (ablation
of solid bodies).
The shock wave remains an object of thorough experiments and theoretical investi-
gations that pr(jvides valuable information on dissociation, ionization and oth2r
elementary processes in heated gases. 'Much attention is being devoted to lumi-
nescence, carrying various information about these processes. A detailed analysis
of the volumetric gas radiation in numerous experiments in shock pipes can serve as
an example of this. Strong shock waves in fairly dense gases, which are
high-temperature surface xadiators, may be obtained by explosive substances. Such
shock waves present tl:e possibility of studying experimentally the processes in
dense plasma whose theoretic description causes many difficulties.
The carrying out of experimental investigations in the indicated direction requires
a fairly high level of the measurement techniques of high-speed phenomena. The
implementation of this wurk was made possible by the fact that the School for
Investigating Explosion Processes, headed by academician M. A. Sadovskiy, achieved
certain successes in understanding the essence of er.plosion phenomena, as well as
in the development of the recording methods and apparatus. Optical and electronic
devices developed at the IFZ for recording high-speed processers, used in our work,
make it possible to study fully the complex physical pyocess which is the propagation
of a strong shock wave in gas.
A certain relationship between the investigatior.s of explosion processes with such
an especially astronomic problem as the movement of space bodies in the atmosphere
of the earth, is due ta one and the same object of the investigations--the shock
wave, formed in the air when moving at supersonic speed. The well known papers by
K. P. Stanyukovich / 15, 16/, V. A. Bronshten / 17, 18/ and others, as well as the
- paper by one of the authors / 19 / proves the comir,on nature of these phenomena again.
Therefore, the authors hope that the results of laboratory experiments on investi-
gating the radiating properties of shock waves in gases, cited in this bQOk, will
find application in solving astronomic phenomena.
2
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The work developed in several directions. The first, although an auxiliary but
necessary direction, was in developing methods for obtaining strong shock waves.
As a result, it was faund possible ta obtain shock waves with velocities of up to
80 km/sec and temperatures greater than 1050K in gases with normal density (at
atmospheric pressure).
The second direction was studying the radiating properties of strong shock waves and
their relationship to the front structure. Here, along with experimentaZ results
such as nonstationary shielding of the radiation front at certain conditions,
, theoretical results were also obtained, in particular, a deduction was mad2 on the
important role of the nonequilibrium processes ahead of the shock wave front.
On the basis of the results of the first two directions, optimal installations were
- developed to obtain powerful radiation flows with a continuous spectrum. Fairly high
parameters were obtained: density of radiation flow at the target--15 to 20
Megawatt/cm2; radiation time--20 to 30 microsec; the integral energy at the target
reached 130 joules/cm2 for a total irradiated surface of up to 100cm2. Such
radiators were used in the laboratory to ablate bodies under the influence of
powerful radiating flows.
= The description of the results of the work in the indicated directions makes up the
content of the book. Some results of the work were reported in physics seminars
of Lhe Earth Physics Institute, the Problems of Mechanics Institute of the USSR
Academy of Sciences and scientific conferences of the Moscow Physio-Technological
- Institute and published in scientific journals.
, The Committee for Meteorites of the USSR Academy of Sciences showed great interest
, in the work. The authors were supported in their work by M. A. Sadovskiy, P. V.
Kevlishvili, V. N. Rodionov, I. V. Nemchinov, N. M. Kuznetsov, Yu. P. Rayzer and are
grateful to them.
The authors also express their gratitude to staff workers who helped in the work and
participated in carrying out a number of experiments: Yu. Zatsepina, A. A4 Provalova,
I. E. Markovich, I. I. Divnova, Yu. N. Kiseleva, F. A. Sorokina and I. I. Zotova.
M. A. Tsikulin and Ye. G. Popov
The manuscript of the book was still unfinished when my teacher, noted specialist
in the area of explosion physics, Mikhail Andreyevich Tsikulin, died. Staff workers
of the laboratory headed by M. A. Tsikulin, gathered up the uncoordinated material
of the manuscript and actively participated in completing the paper. However, we
apparently were not able to avoid imperfections in several chapters of the book.
In preparing the book for printing, V. A. Bronshten made a number of valuable comments
and additions, and also took upon himself the cares related to issuing the book.
Ye. G. Popov
Table of Contents
Foreword 3
Chapter 1
Certain problems of radiating gas dvnamics 7
l. Investigation of strong shock waves in gases 7
3
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2. Problems of moving large cosmic bodies in the
atmosphere 16
3. Problems of experimental investigation 22
Chapter 2.
Producing strong shock waves in gases 24
1. Exciting shock waves when detonation exits
- into the gas 24
2. Producing shock waves by detonating charges
with a cumulative channel 26
3. Producing strong shock waves by compressing
gas under conditions of acute-angled geometry 32
4. Other methods of producing strong 'shock waves 34
Chapter 3
Method for measuring the intensity temperature and other values 37
1. Basic concepts of the radiation theory 37
2. Measuring the intensity temperature by photography 49
3. Method of spectral investigation of radiation 57
4. Measuring the intensity temperature by photoelectric
radiation receivers 60
Chapter 4
Radiation properties of shock waves determined by results of the
experiment 62
l. Intensity of strong shock waves in air 67
2. Intensity of strong shock waves in inert gases 70
_ 3. Results of spectral investigation of radiation 75
4. Instability of the flat front when shock waves
move in channels 85
Chapter 5
- Evaluation of the influence of the front structure on
- shock wave radiation 95
1. Efiect of the relaxation layer 97
- 2. Radiation heat exchange at the shock wave front 102
3. Radiation shielding by heated layer 108
4. Shielding of radiation front in gas mixtures 118
' Chapter 6
Explosion radiation sources 124
1. Explosion radiator for photometry purposes 124
2. Installation of an ultraviolet shock 127
3. Efficiency of explosion sources 133
4. Certain results of investigating the effect of
radiation with a continuous spectrum on a hard
substance 143
Addendum
Adiabatic shock curves and internal energy of inert gases 153
Bibliography 167
COPYRIGHT: Izdatel'stvo "Nauka", 1977 4
2291
CSO: I 1 � .
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CERTAIN PROBIEi,S OF RADIATINCr GAS DYNAMICS
Moscow IZLUCHATEL'NYYE SVOYSTVA UDARNYKH VOLN V GAZAKH in Rusaian 1977 PP 7-16,
22-28
, [Chapter 1 from the book "iladiating Properties of Shock Waves in Gases"., by M. A.
Tsikulin and Ye. G. Popov, Izdatel'stvo "Nauka", 173 pages]
[Text] The specific success achieved recently in the dynamics of a radiatinq
gas is related to phenomena in which high energy concentratian is reached and
which leads to the state of a gas with very hi,gh temperature. Among these phenom-
ena, besides detonation of an explosive charge in the gas, should be included nu-
clear explosions, the effect of a focussed laser beam and a powerful electric
discharge.
The problems of producing a high-temperature ioni2ed gas--a hot plasma--led to in-
tensive research in this field. The niunber of papers published on plasma physics
is very great and continues to grow. We will not consider here the problems re-
lated to a razefied plasma (these problems are related mainly to the electrodynam-
ics of a rarefied and dense conducting medium) and we wilt not pose the aim of
providing a complete survey of the state of the dynamics of radiating gases. We
shall note only the main aspects in the results and the existing difficulties and
we shall consider the problems of motion of cosmic bodies in the atmosphere since
this is related to shock wave formation.
1. Investigation of Strong Shock Waves in Gases
The state of a high-temperature gas is still achieved under terrestrial conditions
only in the pulsed mode when the main moment is scattering of the initial formation
at high velocity. Shock waves of consicierable intensity occur with sufficiently
hiqh initial density of the gas in which scattering occurs and with sufficiently
large dimensions of the device and the shock-compressed gas b.a,hind the front be-
comes the subject of investigation. Therefore, investigations of a high-tempera-
ture radiating gas are mainly investigations ,f strong shock waves in gases.
Because of a number of features, shock compression of a gas became one of the most
important methods of achieving hiqh temperatures. Heating in a shock wave occurs
within a very short time comparable to the times of relaxation processes in the
- gas, which permits one to study the kinetice of these processes. During shock com-
pression, one can achieve very high temperatures much greater than during adiabatic
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compression to equilibriim pressure. And perhaps the most typical phenomenon that
indicates high temperatures have been reached (on the order of 10,000� and above)
is the glow of the gas in the shock wave. Detailed inWestigation of this glow was
begun in the 1950s when laboratory methads of producing strong shock waves began
to be employed. klethods of recording high-speed processes were improved adequately
by that time. Without resortinq to one or the other, the authors of earlier papers
could still resolve some principle problems. As early as 1934 Muraour and Levy
[201 pointed out that the glow observed during explosions is caused riot so much by
the thermal radiation of detonation products or their chemoluminescence as by the
radiation of the ambient air shock-heated by scattered products. In 1943 Ya. B.
Zel'dovich and 0. I. Leypunskiy [211 demonstrated the capa}aility of achieving high
temperatures during shock compression of a qas with high atomic weight. Firing at
a glowing flask filled with mercury vapors from a gun, they observed a bright flash
during passage of a bullet throuqh the vapors.
The front of investigations was expanded significantly with the appeazance of shock
tubes. In 1950 Ya. K. Gershanik, Ya. B. Zel'dovich and A. N. Rozlovskiy [22] em-
plnyed an installation into which atmospherie air flowed into a tube containing the
low-pressure mixture under investigations upon rapid removal of the plug. Instead
of a plug, they subsequently began to use a diaphragm, after rupture of which a
strongly compressed gas (hydrogen or helium) expanded and excited a shock wave in
the gas under investigation. From the gas-dynamics viewpoint, the burst der.ays
upon formation of a shock wave propagated toward the gas at lower pressure. A
rarefaction wave propagates in the opposite direction. A diagram of the processes
is given in Figure 1.
`1, QlIQ~ QlMf
a
P
b ,.e
P pi
G,
D
. ~
t~
d
Tt r
u
e, _
~
Figure 1. Operation of a Shoc;k Tube: a--diagram of tube prior to operation;
b--pressure profile before rupture of diaphragm; c-e--preseure
prof.iles, temperatures and velocities of gas at some moment after
rupture of diaphragm
[Key on following page]
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[Key continued from precedinq page]:
1. Diaphragm
2. Working gas
3. Gas to be investigated
The followinq is denoted here and further: p is pressure, D is the shock wave
velocity, u is mass velocity, T is qas temperature and c is the speed of sound.
The arrows indicate the direction of motion of the waves (the gas moves toward
lower pressure). T'he dashed line denot2s the contact burst--the baundary of the
gases initially on both sides of t.he diaphragm. A relationship between the pres-
-sure behind the shock wave and the initial gas pressure in the high-pressure cham-
ber is found from the condition of equal gas velo'-ity on the contact burst. Adia-
batic motion of the gas occurs on the rarefaction wave and the Riemann invariant
u+ 2c/Y(Y - 1) is retained. Then from the condition u3 = 0 we find
. r.-i - -
1i_( Ps 1 (1.1)
us
_ Y~ - i P~ I
The gas velocity behind the shock wave is
u1=co Z Pi/Po -i (1.2)
.
Having set u2 and ul equal and having dennted the internal gas energy by e=
_ c2/Y(Y- 1), we find the relationship of p3 and pl:
sv~
l
V I(Y+-- )I2Y2jealea (1
I~s=Pi{1-(P,/Po-11 l(Yi--i)/(Yt -1)1Pe/Po-~ l ~ .3)
The ratio of densities on the shock burst is pl/pp =(Y1 + 1)/(yl - 1) �or a strong
shock wave and the temperature behind the shock front is then equal to
1 (1.4)
Ti =To 71- Pi
Vt +1 Po
, The shock wave intensity pl/p0 and together with it the temperature behind the
shock front T1 may be very high with sufficiently high pressure c?Y4p on ths dia-
phragm P3/pp. A significant parameter in this case is the ratio of internal gas
energy in the high- and low-pressure chambers e3/ep. The higher this ratio, the
- higher the shock wave intensity and gas temperature. Haviag expressed the internal
gas energy e by temperature T, the molecular weight u and the adiabatic index Y,
we find
Vn -1 �oT,
e0 Y_ R'll" 1 (1.5)
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The higher the gas temperature in the high-preseure chamber and the greater the
- molecular weight in the low-pressure chamber, the stronger the effect will be.
In 1953 Hollyer et al [23] first observed the glow in a shock tube fi-lled with
xenon. The glow occurred at the momant the shock wave was reflected from the open
end of the tube and the glow spectrum changed from linear to continuous as the
shock wave amplitude increased.
Petschek et al [24] later observed the glow of argon in a shack tube which also
contained lines on a background of the continuous spectriun. Since then the volume
of research performed in shock tubes has increased continuoualy.
_ However, one should note the esaentially limited capabilities of a shock tube in
achieving high temperatures. We find the finite intensity of a shock wave from
formula (1.3) with infinitely large pressure drop on a diaphragm p3/pp This
= is related to the fact that the gas behind the rarefaction wave cannot be cooled
below absolute zero (gas condensation actually occure much earlier). For the case
of different gases (for example, ep � e3), from formula (1.3) for p3/pp we
fi.nd the maximum values of pressure and temperature behind the shock front:
pl+n Yt + 1 2y2 'e2
P, YT- fy,-1 e. ' (1.6)
7 Im ZV2 ra
T. Ya -1 rl
Using the most advantageous combinations of gases, one can find a more than 100-
fold temperature increase (Table 1).
Table 1
I He - Air I He-Re I HI-7Ce
ea1PO 4.3 33 ! 10
Tim/7'o 23 165 770
When one uses the reflection of a shock wave from the closed end of a tube, one can
increase the temperature additionally by a factor of (3yl - 1)/Y1, which is also
twofold greater at Y1 = 1.2. Thus, one can achieve an approximately 1,000-fold
temperature increase in a shock tube; however, the real number is tens of times
_ less due to gas ionization behind the sl:ock �ront.
New capabilities were discovered with the appearance of electric discharge shock
tubes. Z`he shock wave is formed in these tubes as a result of rapid expansion of
a gas heated by a powerful capacitor discharqe and also by acceleration of the
plasma formed by the magnetic fa.eld of the discharge. Z'he working principle of
the tube is shown in Figure 2. The bua along which current is fed to the discharge
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gap is laid along the outer surface of the tube, inside which the discharge occurs.
The plasma formed by the discharge, in addition to its own expansion, is ejected
by the magnetic field of the discharge current since the conductors with opposite
direction of current (in the bus and in the discharqe) are repelled. P3asma scat-
tering (at initial pressure of 0.7 ns! Hg in the tube) at velocaty up te 90 kmJs
was achieved in the first device nf this type and in this case the temperature
reached 120,000�K [25].
!
Figure 2. Diagram of Electric-Discharge Shock Tube
Modern electric-discharge tubes make it possible to produce shock waves with
velocities greater than 100 km/s and gas temperature of more thar. 105 �K behind the
front. Such high velocities and temperatures are achieved in strorgly rarefied
gases (the gas pressure in front of the wave does not exceed several mm Hg).
The dimensions of shock tubes and the density of the gas filling them are usually
such that the heated zone is optically thin and radiates in all directions. Care-
ful analysis of this radiation provi.ded much valuable data on dissociation, ioniz-
ation and other elementary processes in heated gases. A rich arsenal of procedures
and means was worked out, that includes along with methods of astrophysics (analy-
sis of the shape of spectral lines), new methods based on f:he use of electromag-
netic radiation in different regions of the spectrum and beams of neutral and
charged particles. A modern shock tube is a complex piece of equipment frequently
= created to investigate some single problem and outfitted with unique apparatus.
The experimental material obtained in shock tubes is enormous. The number of pub-
lished papt-rs is counted in the thousands and there are many survey articles and
books.
Shock waves in which the heated region with the optically dense became the subject
of investigations very rarely. All the features of radiation are determined in
this case by the narrow layer of gas adjacent to the wave front. It is for this
reason that one can talk about the radiatinq properties of a strictly shock wave
without relating them to the entire region of a shock-heated gas. These shock
waves occur, for example, upon entry of large cosmic bodies into the atmosphere
at high velocity and during nuclear exp?osions. Under laboratory conditions the
shock waves that radiate in a similar manner can be created in gases at atmospheric
pressure by means of powerful explosives. And although the 3pecifics of experi-
ments with explosives sustained the investigations, a number of interesting results
has been obtained on this route during the past few years.
The glow of shock waves with velocities of approximately 8 km/s, which can be pro-
duced comparatively simply upon the emergence of an explosive detonation to a
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boundary containir:g gas, has been studied in more detail. A bright glow was die-
covered in 1941 by Michel-Levy et al [261 upon the collision of two of these waves
in argon. The relative glow intensity distributi.on measured by them through the
spectrum was the same as that of a black body with temperature of 351000�K. Later
Stettbacher [27] made similar measurements fQr shock waves forne3 upon *he dis -
charge of a detonation from an explosive (tetranitromethane + toluene) into argon
and air. The color temperature of the wave front was 27,000�K in experiments with
argon and 10,500�K in experiments with air. Roth [28] very carefully measured
the glow intensity distribution through the spectrum. The shock wave in his exper-
iments was stimulated upon discharge of the detonation from an expZosive (trotyl +
+ hexogen and then trotylhexogen) into argon. The color temperature of the front
- was 29,000 + 1,000�K and was appreciably above the temperature of the shoc}c-heated
argon (24,000�K), calculated from shock relations. Tn 1965 Conger et al [7] at-
tempted to compare the intensity of visible and hear ultraviolet radiation (X = 230-
330 n.~n) during explosive of a pentolite charge in ar7on. fihe color temperature of
the front of 20,000�K, which was somewhat lower than the temperature of a shock-
- heated gas (23,500�K) obtained by calculation, corresponded to the intensity ratio.
The relativ.e glow intensity dis*xibution to the spectrum and the proximity of the
_ color temperature of the front to the calculated temperature of the gas behind the
front confirmed the opinion of investigators that the shock wave formed upon dis-
_ charge of detonation from the eacolosive glows like a black body. However, total
confidence in this appeared only after I. Sh. Model' [29] preaented the results of
, measuring the absolute glow intensity in 1957. The shock wave in his experiment:;
was stimulated upon discharge o:f the detonation from an explosive (trotyl + hexogen
_ and later trotylhexoqen) into air.* The absolute glow intensity measured behind a
red light filter was like that of a black body with temperature of 10,000�K and
this value coincided with the temperature of shock-heated air calculated from the
wave velocity known from experimsnt. Recording the increase af glow intensity
af ter discharge of the detonation from the explosive, I. Sh. Model' [29] and later
Roth [28] managed to show that opticala.y dense wave$ are formed in these experi-
ments. All concepts toward this calculation were previously based on estimates of
the absorption coefficient by the Kramers formula, the applicability of which to
a non-hydrogen-like dense plasma raised doubts.
The data presented in papers [13, 14, 30-321 also indicate the similarity of a
shock wave to absolutely black radiation.
The temperature and emissivity of a shock wave increase significantly with an in-
crease of amplttude. Thus, if the density of the luminous flux from the front is
- equal to 1.6�106 W/cm2 at shock wave velocity of 8]an/s in argon, it is then
- 1.6�107 W/cm2 at velocity of 16 km/s. This explains the interest in the stronger
shock waves than those which can be produced upon discharge of a detonation from
powerful explosives to a boundary with a gas.
We touch on the experiments with very strong shock waves, described by I. Sh.
Model', somewhat later.
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Figure 3. Temperature Profile of Strong Shock Wave With Regard to Radiation
(dashed line--without regard to radiation)
Fundamental theoretical investigations of the role of radiation in strong shock
waves were carried Aut by Ya. B. Zel'dovich and Yu. P. Rayzer. The results of in-
vestigations were published in 1957 in a cycle of articles [33-36] and were later
included in a monograph [37]. It ia shown that ltuninous heat transfer rearranges
the structure of the fronf at high amplitudes (Figure 3). The gas in front of a
strong shock wave is heated by powerful shortwave radiation from the front so much
that it begins to absorb longwave (specifically, visible) radiation from the front
and shields it. Therefore, the brightness temperature of the front, initially co-
inciding with the true gas temperature behind the front, lags behind it as the
shock wave amplitude increases, passes through a maximum and decreases to a rather
low value deternuned by the natural glow of the heated gas in front of tY:e f=or.t.
As an illustration, let us present the results of quantitative estimates of the
phenomenon for a shock wave in air of normal density, made by Yu. P. Rayzer [35].
The dependence of the brightness temperature of the shock wave front in red light
on the true temperature of the air behind the front is shown in Figure 4. The
shielding effect is still small at gas temperature behind the front of T1 =
= 65,000�K and the brightness temgerature Tya is equal to gas temperature T1. But
even at T1 = 90,000�K shielding of the front in red light is appreciable and Tya =
= 80,000�K. A�urther increase of amplitude intensifies the shielding of the
front so much that it leads to a decrease of brightness temperature. Thus, Tya =
= 67,000�K at T1 = 100,O00�K and the briqhtness temperature decreases to a maximum
value of Tya = 17,000�K at even higher amplitudes, which almost does not vary until
the wave amplitude increases stronqly.
TA
_B9000�M
///'0' t0000
"90000�fl T
Figure 4. Dependence of Brightness Temperature of Front on True Temperature
of Air Behind Front
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The sharp difference of the brighrness temperature of the front of a strong shock
wave from the calculated temperature of the gas behind the front was observed by
_ I. Sh. Model' [29]. Snock waves with velocity of 17 km/s were created by means of
explosives in gases with high atomic weight (xenon, crypton and argon). Very high
temperatures were achieved in this case--according to I. Sh. Model "s calculations,
who took into account the multiple ionization and radiant cooling of a shock-
heated gas, the temperature of xenon, crypton and argon were 'T' = 110,000, 90,000
and 60,O00�K, respectively. However, the brightness temperature of the front
measured behind a red light filter was several times lower for all three gases and
Tya = 35,000-30,000�K. This divergence was not contained in the temperature mea-
surement error 15 percent) and was explained by shielding of the radiation by
the heated gas in front of the front.
In the paper of I. Sh. Model' [29], the brightness L-emperature of the front was
measured with the same value of shock wave amplitude. The variation of the bright-
ness temperature of the front with an increase of shock wave amplitude could not
be followed experimentally for a long time due to the absence of si.mple methods of
producing rather strong shock waves. In 1964 A.Ye. Voytenko (38-40] proposed an
effective method of producing strong shock waves by means of explosives and two
yeaxs later A. Ye. Voytenko, I. Sh. Model' and I. S. Samodelov [41] observed the
lag of the brightness temperature of the front behind the calculated temperature
of the gas behind the front in experiments with xenon and air. The gas temperature
behind the front reached T= 110,000�K at wave velocity of D= 43 km/s, while the
brightness temperature of the front measured behind a red light filter comprised
only Tya = 72,O00�K. The brightness temperature of the front in xenon reached its
own maxir�um value of Tya = 50,000�K (T = 120,000�K) at D= 18 km/s and decreased to
a limiting value of Tya = 22,000�K with a further increase of amplitude.
The radiating properties of strong shock waves in argon, xenon and air was studied
by the authors jointly with Yu. A. Zatsepin [42]. The brightness temperatur.e was
measured immediately in several sections of the ,spectrtun from the visible and ultra-
violet regions. Not only the separation of the brightness temperature of the front
from the calculated temperature of the gas behind the front but the variations in
the intensity of radiation of the front at diffr�:rent angles indicated shielding of
radiation at high amplitudes. The effect of sh:ielding in the ultraviolet region
was manifestec3 more weakly than in the visible region. Experiments with argon to
which several percent air was added led to an u.nexpected result and in this case
the maximum brightness temperature did not exceed Tya = 30,000�K and was much lower
than in experiments with pure argon (T},a = 901000�K) or with air (rya = 75,000�K).
However, unsteady shielding of the radiation of strong shock waves which led to a
decrease of the brightness temperature of the front in time, discovered in exper-
iments with inert gases, was of great interest.
Fxperimental inves'-igations confirmed in only the r:uast general features the theo-
retical concepts about shielding of radiation in strong shock waves. Shielding was
observed in experiments at significantly lower shock wave amplitudQS than followed
from theoretical estimates. The possible reason for the differences--the absence
of thermodynamic equilibrium in the gas before the front of a strong shock wave--
was noted in [42]. To substantiate this hypathesis, one of the authors compared the
- times of relaxation processes in the heated layer in front of the front to the
E
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time the gas was in the layer [43]. It turned out that some of the processes can
= remain inconplete. Consideration of tlzis circumstance improved agreenent with
er.periment.
Absorption of radiation by the narrow layer on the front where ionization of a
shock-heated gas develops leads to additional decrease of the brightness tempera-
_ ture of the front. The authors of [13], stucying the glow spectra of shock waves
- formed upon discharge of detbnation from an explosive into inert gases, reached
the same conclusion. The absorption lines of ions in the emission spectrum of
shock waves kere recorded and a decrease of tne brightness temperature of the
front was observed. These aesults could not be explained by radiant heating of
the gas in front of the front, which was still too low in these experimentso
The unsteady nature of sl:ielding of the radiation of strong shock waves in inert
gases is not contained within the framework of existing theoretical concepts. The
characteristic features of the phenomenon found in experiments indicate the devel-
opment'of a much wider shielding layer in front of ihe shock wave front than was
ass-aned. It is appropriate to note in this regard that a significant electron
concentration fas in front of the shock wave front (the so-calZed "precursor") was
observed repeatedly in experiments in shock tubes. There are indications that
electron diffusion from a shock-heated gas to the region in front of the front
plays a specific role in formation of the "precursor." The argon temperature be-
fore the front (presumably due to energy transfer by these electrons) reached
8,000�K in (44]. Fiowever, most investigators link the formation of tl-ie "precurs-
or" to excitation of the atoms of gas before the front by radiation in the reson-
ance lines and their subsewent photoionization. L. M. Biberman and B. A. Veklenko
[45] showed that a layer of excited atoms forms in front of the shock wave front
due to absorption of resonance photons in the lens of the lines and subsequent
acts of re-radiation similar to diffusion. This process was considered in [461
- with regard to photoionization of excited atoms. There is no unified opinion on
the causes of "precursor" formation. Further investigations will show whether
the phenonena touched on above are related to unsteady shieldinq of the rsdiation
of strong shock waves.
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�2� Problems oP moving large cosmic bodies in the atmosphere
In the light of the progress made in the dynamics of a radiating gas, great
_ significance is being attached to the studies of the movement of large cosmic
bodies in the atmosphere during which powerful shock waves are formed, and the
- temperature of the gas behind the front reaches high values so that radiation
acquires an important role in this physical process. In particular, the broad
class oi meteor phenomena in the earth's atmosphere belongs here. Of the great
- variety of aspects of studying meteor phenomena, among which it is possible toname astronomical, cosmogonic, cheJnical and other studies j471, let us mention
the problems pertaining to meteor physics, the problems of the znovement of bodies
in the atnesphere, in rarefied and dense gases. On approaching the earth, cosmic
bodies ex.perience acceleration as a result of the earth's attraction; bodies with
zero velocity accelerate to 11 k=/sec this is the lower limit. The upper liLi.t
is defined from the addition of the orbital velocity of the earth (30 lm/sec)
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and the maximum possible heliacentric velocity of ineteor bodies which is equal
to 42 km/sec for nonhyperbolic orliits. Thus, the extra-atmospheric velocity
falls within the limits of 11-72 km/sec.
At such velocities, meteor bodies experience strong interaction with the
air in the atmosphere: in the upper layers, in the mol.ecular flux mode, and
in the lower layers, in the continuous flow mode with the formation of a powerful
shock wave. In the molecular flux mode at altitudes of 80-120 km where the free
path length of the molecules is much greater than the dimensions of the meteor
bodies, interaction with the air takes place just as with individtial molecules.
This interaction leads to loss of mass of the meteor by evaporation s,.-lder the
effect of the impact of the air molecules and to the excitation of the atoms of
the evaporated material which determines the radiation of ineteors.
In the continuous flu;c mode, behind the front of the shock wave formed
ahead of large cosmic bodies, the gas has a temperature from tens to hundreds or
thousands of degrees, and radiant energy fluxes developed to values on the order
- of 109 watts/cm3. These processes determine both the loss of mass (ablation) of
the meteor body and its radiation. The study of the radiative properties of such
shock waves, the radiant energy transport and the effect of powerful radiation
fluxes on matter is of great scientific interest.
At the present time there has been significant improvement of the physical
theory of ineteors small cosmic bodies entering the earth's atmosphere and com-
pletely burning up in its upper layers. Meteors are recorded by their glow;
the method of radar tracking of meteor trails was developed only recently [48].
The greater part of the available data on the cosmic bodies in thp atmosphere per-
tains to meteors, the movement of whicfi is not accampanied by the formation of
a shock wave. This sampling of observation data is explained by the comparatively
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(a)
Lw 40 1.;t...')
Figure 5. Distrib ution of ineteor bodies by mass
1, 2-- micrncraters on the moon, 3-- craters or. the moon, 4--
asteroids, 5-- Apollo group (Whipple), 6-- comets (Whipple),
7-- meteorites (Braun), 8-- meteorites (Hawkins), 9-- meteors
(Millman, Bohrland), 10 meteors (Hawkins, Apton), 11 meteors
(Lindblad), 12 meteors (Watson), 13 cosmic dust iWeinberg),
14 zodiacal light (Alsasser), 15 "Pegasus," 16 --"Explorer,"
17 "Mariner," 18 "Pioneer," 19 "Lunar Orbiter,"
20 OGO-III
Key:
a. m 2sec 1)
b. m(g)
high frequency of ineteors and the presence of regular meteor flow. The g.raph in
Figure S presents comparative data on the frequency of ineteor phenomena of differ-
ent scales from cosmic dust with a particle mass of 10'15 g to asteroids. The
logarithm of the mass is plotted an the x-axis in grams, and the logarithm of the
meteor body flow per square meter per second is plotted on the y-axis.
Let us present the basic principles of the physical theory of ineteors [49].
From the law of conservation o� momenttun we fiave
m ~ _ 1'.Spu', (1.8)
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where m and v are the mass and the velocity,of the meteor body, p is the air
density, S is the cross sectional area of the meteor body, I' is the drag.
Expressing tfie cross sectional area S in terms of the massm, the density
of the meteor body d and the shape factor A, we obtain the first equatian of the
_ physical theory of ineteors the braking equation
d~ = -rAa-~I.~.-4~,po.
One of the basic principles in the physical theory of ineteors is the prin-
ciple that energy transmitted to a meteor body by air molecules colliding with it
is predominantly spent on evaporation of it:
where Q is the energy of evaporation of one g of ineteoric matter, A is the heat
transfer coefficient (the fraction of the kinetic energy of the air molecules
colliding with the meteor body spent on evaporation). The heat transfer coefficient
A turns out to be a comparatively large value on the order of 0.5.
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Q dM = - L ASpv',
t 2
(1.9)
(1.10)
_ From (1.8) and (1.10) we obtain the second basic equation t'ie mass loss
equation
dn ~u
dt - (f.'tU ~i ~
(1.11)
where 6=11/2PQ depends weakly on the velocity so that when t.he mass of a meteor body
decreases significantly, the velocity loss is very small. The baJic equations also
include the glow equation
2,1 m )~7
(di i
and the ionization equation
dm
�u CdI '
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(1.12)
(1.13)
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where I is the xadiation of the meteor per unit time, T is the fraction of the
kinetic energy of the meteor atoms converted to light enexgy (ltuninosity),
a is the linear electron density of the meteor trail, S is the number of free
electrons generated by one evaporating atom of tfie meteor body (the ionization
factor), u is the average mass o� an atom of the meteor body.
Combining equations (1.11) and (1.12), it is possible to express the value
of cr in terms of ineasured values of the brightness of the meteor T and its veloc-
ity v:
r,
1 dt) u d~ . (1.14)
By processing actual data obtained by camera recordings, in reference [50],
reliable confirmation was found for the fact that the value of Q varies little with
variation of the velocity and mass of the meteor.
The primary recording technique and source of information about meteor
phenomena remains recording the glow of the meteor in the atmosphere. Therefore
the importance of the radiative properties of ineteor bodies is unquestioned.
The visually noted brightness of a meteor trail is related to the radiation
intensity of the meteor I [51] and it is denoted by the absolute stellar magnitude
A1 = 24,6-2,5 lg I,
(1.15)
and it is also related to the illumination E on the earth's surface created by the
meteor radiation and expressed by the visible stellar magnitude m[52]:
Is = 2,1�10-8�2,512-". lux.
(1.16)
The stellar magnitude is related to the initial mass and yelocity of the
meteor body. A meteor of zero stellar magnitude corresponds to a velocity of
40 km/sec and an initial mass of about 1 g.
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A great deal of actual data have been accumulated on the radiation of
meteors. The application of night photographic patrolling using special cameras
for automatic recording of ineteors equipped with obturators for measurins the
velocity and diffraction gratings for recording the glaw spectrum of the meteors
offers the possibility of simultaneously measuring the brightness of the meteors I,
their velocity v and the spectral characte r3stics.
The recorded spectra of ineteors (their number in 1971exceeded 1300 [53])
basically are of a linear nature with luminescence of the lines of the atoms making
_ up the meteor body. This indicates that basically the meteor radiation is
recorded in the molecular flux mode where the atoms of the meteor body excited by
impacts with the molecules of the air emit. Meteor physics is still experiencing
a number of difficulties with its improvement. A survey of the physical theory of
meteors indicates that many values entering into the equations are insufficiently
precisely knawn and subject to significant refinement; therefore it is necessary
to exercise caution with regard to the conclusions of the theory. For example,
= the estimation of the density of ineteor bodies from velocity data based on optical
measurements diverges strongly from the actual meas ured value as it turne3 out for
the Prshibram meteorite [54] (by the estimate based on trajectory measurements
0.4 g/cm3, actually according to the specimens found 3.6 g/cm3) and for the Lost
City meteorite [55]: according to the optical measurement data 0.1 g/cm3, and
_ actually for the bronzite chondrite which this meteorite turned out to be, the
density is 3.8 g/cm3. The exact determination of the constants T and S in the glow
and ionization equations (1.12) and (1.13) has great significance. This offers
the possibiiity of a quantitative comparison of the results of optical and radar
- measurements which recently have been accumulated very rapidly. Whereas the meteor
- problem has not been fu11y resolved theoretically, in any case there is a large
� amount of factual data for the solution of this problem.
:
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Another situation is observed for the phenomenon of the movement of quite
large cosmic bodies in the atmosphere. First of all, here we note the extra-
ordinary shortage of factual data frem recording the glow of large bolides although
this phenomenon is not so rare, as is clear fram the graph in Figure 5. Many
processes pertaining to this phenomenon have not even been isalated for detailed
szudy as a result of the complexity and absence of the data.
With the formation of a pawerful shock wave in front of the moving cosmic
body, many physical processes occur, among which it is possible to isolate the
following as independent: ionization of the gas behind the shock wave, the radia-
tion of the powerftil shock wave, radiant energy transported in the heated gas
behind the front (tomparable to or exceeding the hydrodynamic transport, the
effect of radiation on the matter of the cosmic body and destruction of it under
the effect of radiation (ablation). All of these processes also determine the
laws of movement of a large meteor body in the atmosphere, the variation of its
mass and velocity.
The progress recently made in plasma physics, in the dy'namics of the high-
_ temperature gas and in adjacent fields have determined the well-known progress in
_ the mentioned proble*_ns of the movement of cosmic bodies in the earth`s atmosphere.
A large number of papers have been written on the ionization of a gas
behind a shock wave and the optical properties of the ionized gas, including as
applied to meteor physics [17-19, 56-100]. This problem is the best developed.
Intensive studies of the problem of the effect of radiation on matter
have been started 19-11, 101-120J. Here it is especially necessary to note the
large ncunber of papers on the e�fect of laser radiation on inatter appearing in
connection with the rapid development of laser engineering 1101-120]. Neverthe-
less, the study of the effect of radiation with a continuous spectrum is of the
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greatest interest for the problem of the ab2ation of cosmic bodies in the
_ atmosphere.
In spite of the development of such research on the general physics level
the studies of the ab lation of bodies in the situation of flora of a continuous
gas around thera have been made at random. It is necessary to note that a detailed
_ investigation of the specific process of the ablation of a cosmic body under the
conditions of radiant energy transport in a dense gas f low behind the shock wave
front can give a result which will be difficult to reconcile with the re5ults for
small meteoroids by selecting the value of the coefficients in the basic equations.
In this respect, as was pointed out earlier 117, 19], the experiments have great
significance. It is possible to set up experiments on the modern level of the
development of engineering reproducing the actual meteor flight conditions and
processes occurring on interaction of them with the air. The flight of ineteors in
the upper layers of the atmosphere at a velocity of 16 km/sec has been reproduced
by shaped-charge firing of inetal balls from a rocket at high altitude [121]. The
glow spectrum of a meteor with a velocity to 56 km/sec has been reproduced by the
effect of an electron beam on a specimen [122]. Under laboratory conditions it is
possible to accelerate metal particles to a velocity of 40 km/sec [123, 124] using
an explosive charge. An interesting study of the ab lation of soli.d states simu-
lating meteor bodies was performed using a plasmotron producing a plasma f lux at a
temperature of 10000�K [125].
New possibilities for studyring the effect of powerful radiation fluxes on
meteor bodies are being opened up in connection with the use of explosive high-
temperature sources of light, the emitter in whicfi is a powerful shock wave in a
gas. By this method it is possible to obtain a light source with a temperature
- of more than 100,000�K, producing a radiation flux for the investigated specimen
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with a density on the order of 100 Mraatts/cm2. Under the effect of such a power-
ful radiation flux the material of the specimen evaporates, and further effect
of the radiation occurs in the presence of a Iayer of vapor over the surface of
the specimen, which reproduces the ablation conditions of a meteor body behind the
powerful shock wave. This method is being developed by the authors of 19, llJ
in connection with studying the radiative properties of powerful shock waves in
gases.
What has been stated with respect to the ablation of large cosmic bodies
can also be applied to their movement in the earth's atmosphere, to the law of
- variation of their mass and velocity. It is necessary to expect that variation of
the specific process of the interaction of a meteor body with the air flow from
small meteor bodies to large meteorite-forming bolides will have its impact ori the
basic equations, the values of the coefficieuts in them, and their dependence on
the velocity. This is noted when processing the results for a large bolide [126]
when the value of the coefficient Q in the equation (1.11) quickly decreases with
a decrease in the velocity from Q=9�10'13 at v=20 km/sec to a=2�10-13 for v=7 km/sPC.
Accordingly, it is necessary to note the result obtained in reference [127] from
estimating the intensity of the ablation of a meteor body in the radiant thermal
conductivity mode in the gas and in the vapor behind the shock wave front where
the mass ]_oss turns out to be proportional to the velocity of the meteor body
which, as was demonstrated [17], does not differ from the solution of equation
(1.10) with constant coefficient A. In referen ce 1127] an effort was made to
estimate the nature of the variatinn of A and its influence on the ablation.
In equation (1.12) whicli descrities the glow of ineteors, it is proposed
that the radiation energy is proportional to the kinetic energy of the lost mass
of the meteor body inasmuch as the emitter is the atoms of the meteor body
excited by the air molecule impacts. When a large meteor body is moving in the
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atmosphere, the emitter is the shock wave that is formed; in this case the
radiation process is accompanied by the formation of a shielding layer Rhead of
the wave front and other effects.
Thus, the problem of the radiation of a large meteorite-foYming bolide is
more complicated than the radiation of small meteroids. The results of .the exper-
' imental st udy of the radiative properties of shock waves in gases presented in the
- given book will promote the statement of this problem.
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3. Problems of Experimental Invest=gation
~ The deficiency of experinental data on the radiating properties of a gas in op-
tically dense layers and in strong shock waves in dense gases was noted in pre-
vious sections during survey of some problems of the dynamics of a radiating gas
related both specifically to the radiating properties of shock waves and to ap-
plied probiems.
Fsn optically dense shock wave rarely became the subject of investigation. This
situation is explained by the specifics of experiments with explosives except
ti:ese waves have not yet been produced in thesn. The glow of shock waves with
velocities of approxir.,ately 8 km/s, which can be produced comparatively simply
uaon discharge of a detonation to a boundary with a gas, was studied in more de-
_ tail. Hokever, the contradictory results obtained (7, 281 require further exper-
inents. The glow of shock waves with velocities above 10 }an/s was studied in only
two paoers [29, 41). The mai.n purpose of these invAstigations was achieved--to
detect the self-shielding of stronq shock waves predicted by theory under
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laboratory experi.ment conditions. However, if the spectral composition of visible
radiation was studied during discharge of detonation and if the first measurements
were made in quartz ultraviolet, then one would have to make a judgment about the
radiating properties of str.onger shock waves only from measuremenL-s in red light.
= The angular distribution of the radiation of the front was not investigated in a
single one of the papers known to us, although the idea of a shock wave as a radi-
ator remains incomplete without it. With regard to the theoretical aspect of the
problem, the influence of a number of effects on the radiating properties of shock
waves has still not been studied. Thus, the estimates of the optical thickness of
the layer on the front in which gas ionization develops, which we made, shows that
- the layer can appreciably affect the nature of radiation nf the shock wave. One
can also show the absence of thermodynamic equilibrivm in the heated layer before
the front, which should be taken into account when calculating the brightness tem-
~ perature of strong shocx waves.
Familiarity with papers whose main results were discussed above and estimates of
the influence of some effects on the radiating properties of waves determine the
~ need to set up systematic experi.ments. We posed the following specific tasks:
- --to estimate the influence of the shielding effect of strong shock waves on
their radiating capability on the basis of ineasuremeni:s of brightness temperature
in different regions of the spectrum and with different initial gas pressures;
--to compile a more complete concept of the spectral composition of the radi-
ation of shock waves by measurements in the ultraviolet, visible and infrared re-
gions of the spectrum and to obtain data on the angular distribution of radiation;
--to calculate the brightness temLrierature of shock waves in some gases and to
compare the results of experiment and calculation on the basis of existing theo-
retical concepts.
Based on the results of experimential investigation of the radiating properties of
waves, it was suggested that one turn to problems related to the use of a shock
wave as a light source. Almost all the papers published on this problem are de-
voted to generation of lamp flashes for high-speed photography. The authors re-
cently suggested that an amplitude-stable strong shock wave created by specially
shaped explosive charges'be used as a high-temperature brightness standard [12-14].
I. V. Nemchinov earlier pointed out the possibility of using explosive sources for
experimental investigation of the effect of powerful ultraviolet radiation on a
solid. The authors designed a source suitable for these purposes in which the
radiator was a strong shock wave in argon. A glowing region occurred above the
targets exposed to a radiation source and the piezasensor installed below the tax-
get recorded the mechanical pulse [9, llJ. Further investigations in this direc-
tion were concentrated on solving the problem of generation of an explosive source
with radiant flux density of 107 W/cm2 and above for experimental study of optical
and mechanical phenomena that accompany the effect of powerful radiation with con-
tinuous spectrum on a solid.
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MODUCING STFiONG SHOCK WAVES IN GASES
- Moscow IZLUCHATEL'NYYE SVOYSTVA UDARNYKH VOLN V GAZAKH in Russian 1977 pp 24-36
[Chapter 2 from the book "Radiating Properties of Shock waves in Gases", by M. A.
Tsikulin and Ye. G. Popov, Izdatel'stvo "Nauka", 173 pages]
[Text] Experimental investigations of surface-radiating shock waves are closely
related to the method of producing them in dense gases. Explosives are used to
produce these waves in the papers known to us. If one takes into account that the
pressure behind ;he front of strong shock waves in dense gases can reach 104-105
atmospheres, the use of explosives is the simplest and still the most practically
unique solution.
Production of strong shock waves by aneans of the focussed admission of pulsed
lasers may be promising to study these waves in gases. Experiments are described
in the literature [128-130] in which a process similar to a strorig explosion oc-
curred after gas absorption of thi.s emission and the velocity of the shock wave
was initially equal to approximately 100 lan/s. �
1. E::citing Shock ;�7aves when Detonation Exits into the Gas
This method of producing shock waves is the simplest and most thoroughly studied.
L. D. Landau and K. P. Stanyukovich [15) calculated the motion of disintegrating
detonation products [15); references to experimental papers can be found in the
survey of Ya. B. Zel'dovich and Yu. P. Rayzer [36] and in the survey of Lochte-
Holtgreven [131]. Yu. N. Ryabinin, I. I. Tamm and M. A. Tsikulin [19, 1321
studied the similarity of shock waves from explosive charges in the near zone.
A number of simplifications that raiae doubts of the accuracy of the results is
usually made when determining the parameters o� a shock wave by calculation.
Therefore, when the question of the parameters of a shock wave created by a spe-
- cific device arises, experimental methods of determining them are preferable.
A plane shock wave in a cuvette with the gas under investigation was created in
our experiments by the device shown i.n Figure 6. The velocity of the shock wave
was determined by photoscanning achieved by means of the SFR-2 device in the slit
photochronograph version.
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The highest velocity of a shock wave measured during the first moment after dis-
- charge of the detonation comprised the following in different gases (in km/s):
Ho Na Air Ar Kr Xe
11.4 10 64 9.8 9.4 $.,7 & 3
The density and effective index of the adiabatic curve of the gas are contained in
solution of the problem of scattering of detonation products to the gaa. Since the
adiabatic curve of the gas is approximately identical at high temperatures for dif-
ferent gases, the velocity of the shock wave should depend only on density. This
dependence is approximated by the straight line in the coordinate axes selected in
Figure 7.
.D, A'M/C6K ' (1)
Figure 6. Device for Producing Shock Waves: 1--supplementary charge (lens)
that produces a plane detonation frontj 2--charge 50 man in diam-
eter and 60 mm long cast from TG 40/60 (mixture of 40 percent
trotyl and 60 percent hexoqen)j 's--glass cuvette 200 mm long with
quartz window
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J
10 "He Ne (2), I
y � Ba4ay0
B Ar K" 7{e
O,~f Lg p
TCey :
Figure 7. Dependence of Shock Wave Velocity D During Discharge of Detonation
from TG 40/60 on Gas Density p Related to Air Density
1. km/s
2. Air
Along with the good recurrence of the results with this method of shock wave pro-
duction, we note the weak influence of charge size on the value of velocity near
its surface. Thus, a decrease of the diameter and length of the charge by one-half
_ in experiments with argon and air did not lead to an appreciable decrease of ve-
locity. The stronger attenuation of the shock wave along the length of the cuvette
observed in this case agrees with the concluaiona on the similarity of shock waves
from explosive charges [19, 1321. This influence of charge size, naturally from
the theoretical viewpoint, permits one to compare the results to the measurements
of other authors.
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Lochte-Holtgreven [1311 gives a velocity of 9.5 km/s of a shock wave in air upon
discharge of a detonation from TG 50/50. If the linear dependence of shock wave
velocity on the velocity of explosive detonation observed in [132] is used, the
given value is equal to 9.8 km/s upon recalculation for TG 40/60 and coincides with
our measured values.
Christian and Yarger [1331 achieved a lower velocity of 8.7 }nn/s than in our paper
upon discharge of a detonation from TG 40/60 into argon. The difference is easily
explained by the fact that a plate oF inert material was located betweeri the ex-
- plosive and the gas in [133]. Anderholm [30] presents a value of D= 9.3 km/s
close to our value. Roth [28) presents a velocity of 8.3 km/s upon discharge of
a detonation from TG 40/60 into argon= this value does not agree by the temperature
measured by him (a velocity of D= 9.5 }Qti/s corresponds to this temperature) and it
does not agree with our value of D= 9.4 IQn/s.
Unlike the otheL experimeiits described above, Roth [28) did not observe attenuation
of the shock waves in argon near the charge. Tt is appropriate to note in i-.his re-
gard that attenuation of a shock wave in argon near the charge was also not ob-
served in our first experiments with the devices shown in Figure 6. The reason for
the confusion was bending of the front near the cuvette walls toward the motion of
the shock wave.* Having separated the wall from the charge, this bending could be
prevented and attenuation of the shock wave could be observed by measuring thu ve-
- locity of the plane section of the front. Apparently the divergence of the mea-
sured value of shock compression pl/po = 7.9 with the calculated value of 9.3 and
to the measurements of other authors (pl/po = 9.4) [133] is also related in [29]
to bending of the front near the wall.
Unfortunately, measurements of shock wave velocity in xenon and other gases, which
would permit better judgment of the results obtained here and which would permit a
check of the functiion in Figure 7 that generalizes similar measurements, are not
described in the literature.
Although methods of producing stronger shock waves have been developed recently,
the possibility of achieving a temperature up to 30,000-40,000�K behind the front
. supports the interest in these types of experiments during discharge of detonation
from powerful explosives into heavy inert gases.
2. Producing Shock 'Javes by Detonating Charges With a Cumulatiue Channel
Shaped charges were and remain the subject of numerous investigat3.ons. Koski et
al, N. N. Novikov, Novak and others produced jets with velocities of 60-100 km/s
(134-1371 when metal shells were squeezed by explosion of these charges. However,
- such high velocities are achieved only in a strongly rarefied gas. Thus, if the,
jet moves in it at velocity of 60 km/s during initial argon pressure of 10'3 mm Hg,
an increase of pressure to 100 mm Hg reduces the velocity to 8 km/s [136]. Cylin-
- drical shaped charges described below are more effective to produce strong shock
waves in a dense gas. The jet in the channel of these charges is formed during
collapse of detonation products (gas cumulation) rather than by collapse of the
*
- This problem is considered in more detail in Chapter, Section 4.
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metal shell. Shock waves with velocitiea of approxima.tely 16 km/s can be produced
in gases with initial pressure of 760 mm Hg by usinq these charqes.
Figure B. Flow Pattern During Detonation of Shaped Charqe. PV--explosion
products
Let us consider the gas dynamic flow pattern and let us eetimate the velocities of
the jet and the shock wave. The flow pattern in the coordinate system where the
detonation front is quiescent (Figure 8) is steady. It is assumed that the ex-
ternal dimensions of the charge are rather high and can be disregardedo
_ For steady flow along the streamlines, the Bernoulli inteqral is retained
w 2 = const. (2.1)
On streamlines beginning with the detonation front,
s
"
wl -f- z= w+ 2~ (2.2)
where w2 and u2 are the enthalpy and velocity of products behind the detona.tion
front and wl and ul are the same values in the jet. Equality (2.2) is also ful-
filled on a special streamline passing alonq the axis of symmetry with unlimited
external dimensions. The equation of state of the explosion products p= Apn,
toqether with relations on the detonation burst, yields
ui =u. -}-Y=V1(n-}-1), (2.3)
n (2.4)
~s n -1 Ps~P9~
Ps = PeeV'/(n -F- i), (2.5)
Ps _ n n 4 Paa, (2.6)
where u2 is the velocity of the products behind the burst in a fixed coordinate
system, V is the rate of detonation of the explasive and pW is its density. Dur-
ing flow into a vacuum wl = 01 during flow into a gas
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n n py tln pl
wt n-! Pt~P1 = n-1 Pi P. ' I (2. 7)
and pressure pl is found from relations on the contact burst between the jet of
the explosion products and the gas shock-compressed by it. If U is the flow ve-
locity in a fixed coordinate system (it is the velocity of the piston creating the
strong shock wave), then
Yt
(2.8)
Pi = PYu.e ~ 2 ~US'
where Y is the effective index of the adiabatic curve of a shock-heated gas and
Pp is the initial gas density. After the derived expressions are substituted into
- equality (2.2), the following equation is found for dimensionless flow velocity
x = u/v:
n-i
_ nzna ~ _ (x - 1)2 na'~s n i Y -I-
( f lt~n n � (2.9)
~ /
One can note immediately that the flvw velocity is linearly related to the rate of
detonation V. During flow into a strongly rarefied gas pp 0 and
U=(1-f- Yn 1 f V; (2.10)
i
if one assumes that n= 3, then U= 2.06 V. Let us compare (2.10) to the known
expression for the velocity of products after the detonation wave has been dis-
charged into a vacutun:
U = 3n -1 i,.
p na_1 +
(2.11)
if n= 3, then UP = V. Higher scattering rates Up = 1.5 V have been observed ex-
perimentally. The divergence is caused by the fact that the explosion products
are easily described by a power equation of state with index n= 3 at denaities of
p ti pW, whereas the index decreases to n= 1.3-1.4 upon expansion into a yas at
PO � PW [138]. The process of product expansion can be fully described by intro-
ducing the effective value of n= 2. Thus, we find Up = 1.67 V for this value of
n, which is c].ose to the experimentally observed velocities. It is obvious that
the value n= 2 will better describe the expansion of products upon detonation of
a shaped charge. The flow velocity is U= 2.15 V for n= 2 and pp 0. Thus, the
uncertainty in selection of the value of n hardly affects the fl.ow rate in the
channel.
Let us present the results of calculating the flow rate U and the shock wave D
found after substitution of pW = 1.69 g/cm3 and V= 7.8 ]anjs (TG 40/60), normal
gas density pp and index y of an ionized gas into equation (2.9) (see Appendix).
AiY Ar Xe oS-�p
U, ]ctt/S n= 2
16.4
16.41
16.1 16.8
n- 3
15,9
15,9
15.7 16.1
1), km/g n- 2
18.3
18.4
18.5 -
n= 3
170
17.8
18.0

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Let us emphasize again that, as follows from these data, the problem of the value
of index n plays no siqnificant role. On the other hand, the flow velocity is
weak'Ly dependent on gas density and is almost equal to the flow velocity to a
vacuum.
The considered problem (Figure 9) has one typical dimension--the diameter* of
the shaped channel d. The solution obviously correctly describes detonation of
a charge of limited dimensions if the length of the charge channel 1>> d and outer
- diameter 0 d. It is also obvious that it is sufficient to require that 1� d
for the existence of steady flow. However, the Bernoulli integral on a special
streamline passing along the axis of symmetry is not expressed in this case by the
same relations on a detonation burst. It is qualitatively clear that the dis-
charge from the size reduces the flow velocity at 0 ti d and the flow velocity will
- asymptotically approach the values calculated above at 0/d
More than 100 experiments were conducted in which the effect of charge configura-
tion and of different explosives on the flow velocity and the shock wave in a qas
was studied.
After initiation the detonation wave emerges to the bottom of the charge channel
(see Figure 9) and excites the shock wave in the gas. An advancing detonation
front of the jet is formed as a result of subsequent collapse of products in the
chan:.el (Figures 10 and 11). The flow velocity increases and accordinqly the
shock wave velocity increases. Covering a path of approximately 8-10 diameters
of the channel d, the shock wave gains maximum velocity and maintains it during
subsequent motion in the channel. A photochranogram of a shock wave and jet in a
glass tube attached to the charge is shown in Fi.gure 11 (a truncated charge with
1= 5d was used in the experiment, which made it possible to observe the acceler-
ation of the jet and the shock wave to maxiunwn velocity in the tube). The value
- of the maximum velocity depends on the ratio of diameters 0/d. The shock wave
velocity increases with an increase of ratio. Figure 9. Shaped Charqe: 1--length of chargej d--depression for detonator
The adherence to geometric similarity in motion of the shock wave was checked in
experiments with charges whose channel diameter d varied from 3 to 18 mm. It
*
Axial symmetry is not used in solving the problem. It is easy to show that the
results are valid for the case of plane symmetry and generally for a channel with
arbitrary cylindrical surface.
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turned out that similarity is disturbed with thin channel walls (o - d!5 10 mm for
TG 40/60). The velocity of the shock waves decreased in these cases. Deviation
from similarity can be explained by the proxi.mity of the wall thickness to the
critical diameter of explosive detonation. Experiments with charges of cast
trotyl for which deviation from similarity was checked more intensively, indicate
this. Figure 12 reflects the noted characteristics where the dependence of steady
shock wave velocity in air on the ratio of diameters 0/d of a charge of TG 40/60
are plotted from experimental results.
-N, KM/GCK
1g
16
- !Z
!O
Figure 12. Dependence of Shock Wave Velocity on Ratio of Diameters 0/d:
dark circles--d = 8 mmj light circles--d = 15 mmt 1 and 2--
calculated values of velocity at 0/d -for n= 2 and n= 3,
respectively
_ The velocities of shock waves and the detonation rates of charges of different cast
explosives were also measured in the experiments. Both velocity and the rate of
detonation was meast:red in a separate experiment, for which the charge and glass
tube attached to it were placed in the visual field of the photochronograph. The
results of the measurements are presented in Figure 13.
II, ,vr lc�x (1)
16
!S
!V
1,9
Figure 13. Dependence of Shock Wave Velocity in Air on Rate of Charge
Detonation
_ Key:
1. km/s
The effect of initial gas pressure (o= rather of density) on the shock wave veloc-
ity in the channel can be judged from the following values measured in experiments
with argon (charge dimensions were d= 25 mm, 1= 180 mm and 0/d = 2.4):
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Po~ Atm Hg 760 300 200 100 50
D, xin/s 11.0 12.2 ' 12.8 13:3 ,l4.5
- Formation of the jet surpassing the detonation front was observed in several ex-
periments with charges having the plane of symanetry (two parallel explosive
glates).
Comparing the results outlined in this section, one can state that there is good
agreement of approximate theory with experiment. Analysis of flow and an estimate
of flow and shock wave velocity do not take friction into account. It is obvious
that lengtheninq of the jet and column of a shock-heatea gas leads in the final
analysis to intensive slowing of them in the channel as the charge detonates. Con-
tact with jet products and the shock-heated gas may cause breakdown or detonation
_ of the explosive. In some experiments the length of the channel reached 30 d
(40 d with attached tube), but a reduction of shock wave and flow velocity was not
observed. Friction and interaction with the explosive in the channel still appar-
ently play no significant role at 1/d 5 30 (according to [139], these effects are
manifested at 1/d 2 100).
Using a lens with delay of the detonation front near the axis to initiate a shaped
eharge, shock waves with velocities up to 20 km/s were produced in air and argon.
Velocity wzs increased from 15 to 19 km/s when conical constricting nozzles were
- installed at the channel output.
Shaped charges are used extensively i.n this paper during investigation of the rad-
iating properties of strong shock waves. The stability of shock wave amplitude
in experiments with these charges gave the authors the idea of using it as the
= radiator in a high-temperature explosive brightness standard.
3� Producing Strong Shock aaves b,Y Compressinbz Gas Under Conditions of
Acute-Angled Geometry
A. Ye. Voytenko (38-40] developed this method of producing shock waves. The capa-
bilities of the method characterize shock wave velocities oE 43 km/s in air and
37 km/s in xenon measured in [41] (the initial gas pressure was atmospheric).
Velocity comprised 90 km/s in (38] during flow of shock-compressed hydrogen into
air rarefied to 10-1 to 10-2 mm Hgf a plasma with temperature af approximately
200,O00�K can be produced during shock deceleration of a hydrogen jet.
This method is used in the present paper with several nonessential changes during
investigation of the raciiating properties of strong shock waves (D > 20 km/s).
The shock wave velocity reached 80 km/s and the temperature behind the front was
T= 120,O00�K in experiments with helium of normal density. A plasma with temper-
ature of 300,O00�K and particle density of 1.7�1021 cm 3, higher than in [381, can
be produced in the reflected wave. Further improvement of the method that permits
production of as high-temperature dense plasma as desired under laboratory condi-
tions is of undoubted interest for the problem of thernionuclear fusion.
A device to produce strong shock waves ia shown in Figure 14. The lens 1 initi-
ates a plane detonation wave in charge 2 0� hexogen pressed to density of '
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1.74 g/cm3. Plate 3 accelerated by the explosion products squeezes the gas in
chamber 4. The mass velocity of the gas is close to the phase velocity of the
point where the plate joins the chamber and exceeds several times the flight
velocity of the plate. ThQ heated compressed gas is expelled into the tube :i and
generates a strong shock wave.
Figure 14. Device to Produce Strong Shock Waves in Gases: 1--lenst 2--
charge 84 mm in diameter and weighing 500 gramsl 3--duralium
plate 1 mm thick; 4--duralium chamber with radius of curvature
of R= 84 mm (d = 10 mm)f 5--glass tube 10 mm in diameter and
200 mm long.
According to [38-40], an increase of the radius of curvature R of chamber 4 in-
creases the shock wave velocity, but the shock wave velocity decreases at R > 0
(presumably due to friction and heat dissipation). In our experiments chamber 4
had optimum radius of R= 0 in this regard. Zb reduce friction and radian* heat
dissipation, chamber 4 and plate 3 were polished to a mirror finish. In [41],
chamber 4 was filled with hydrogen and was separated by a thin diaphragm from tube
5 containing the gas to be investigated. In our experiments with the chamber
filled with helium, no appreciable increase of shock wave amplitude in the gas un-
der investigation was cbserved= therefore, in most cases both the chamber and tube
were filled with the gas to be investigated (a diaphragm was not installed). Plate
3 was glued to the charge 2, by which the air inclusions between the plate and
charge were removed, which coul& lead to ruptures of the plate during explosion.
BQcause of this it was possible to use thianer plates than in [41], without the
danger of their breakdown. A linear dependence of shock wave velocity on plate
velocity was observed in [40]. The use of a more powerful explosive and thinner
plates in our experiments than in [38-41) and also the closer contact between the
charge and plate favored acceleration of the plate to high velocities. The plate
velocity was measured and was equal to 6 lan/s in one of the experiments.
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4. Other Methods of Producing Strong Shock Waves
The methods suggested below were tested in the search for more effective methods
- of producinq strong shock waves. Although these methods were not used in i.nvesti-
- yation of the radiating properties of shock waves, the results are of definite
interest.
if a detonating rod is placed in a channel (Figure 15), a piston moving at the
rate of detonation is formed under certain conditions of scattering proclucts by
closing the channel walls. Obviously, P2 > pl, where p2 is the pressure in the
expanding products and pl is the qas pressure in the shock wave, is required. Ex-
pressing pressure pl by piston velocity V and assiuning that n= 3 in the power
equation of state of products with one-half decrease of density behind the detona-
tion explosion and n= 1.3 with a further decrease of density [1381, the condition
p2 > pl can be reduced to the following:
0,05EB (Sols)l.s > Y 2 1 po,
(2.12)
where Sp and S are the cross-sectional areas of the rod and channel. We find
S/Sp < 18 for pp = 1.3�10'3 g/cm3, Y= 1.2 (air), V= 7.8 km/s and pW = 1.69 g/cm3
(TG 40/60).
p1 Pi po
. . BB .
f18
Figure 15. Production of Shock wave Upon Detonation of a Rod in a Channel
In the experiments a TG 40/60 rod 300 mm long was placed in a steel tube 50 mm in
diameter and with wall thickness of 5 mm. Filling the cross section of the tube
with shock-heated air and argon was observed at S/Sp 116, which is in good agree-
ment with the given esti.mate. This filling was not observed at S/Sp > 16--the
shock-heated gas sliQped between the tube walls and explosion products.
The problem of detonation of a rod in a channel has much in common with that of
- detonation of a shaped charge. Specifically, one can show that the explosion
- products will overtake the detonation front at P2 > pZ and their velocity will
approach the calculated values fn Section 2 at S/Sp 1. In experiments with
S/Sp = 4, the shock wave velocity in sir comprised 9.5 km/s. Mass qas velocity of
8.6 km/s in the wave, which exceeds the rate of detonation of TG 40/60, corre-
sponds to it. This excess may be an indirect confirmation of the formation of a
jet overtaking the detonation front. However, the possibility of an increase of
the rate of detonation of the exploaive cannot be axcluded. A similar explanation
- is sugqested in several papers on investigation of the "channel effect"--the ef-
- fect of a shock-heated gas on an explosive in similar experiments [140].
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Experiznents were conducted to intensify shock waves during motion in a constricted
conical channel (Figure 16). The channel, cut in a strong steel ingot, usually
did not break down under the effects of the explosion. A shock wave with concave,
approximately spherical front was created by a charge of cast TG 50/50 weighing
500 grams with delay of the detonation wave in the center. Z`he effect of" angle S
at the vertex of the cone on amplifica::ion was studied (see Fiqure 16, a). It is
clear that the wave will be attenuated at small value of a rather than amplified
(as occurs in a tube with parallel walls). Shock wave velocity in the attached
tube comprised D= 9 km/s in experiments with argon and air at $ = 22� and D=
= 12 km/s at $ = 26 and B= 30�. To evaluate the capabilities of the method, a
transparent plexiglass cone was attached to a steel truncated cone (see Figure
lE, b). In experiments with air, the shock wave was decelerated sharply (to D=
= 5 km/s) without travelling 0.4 cm to the vertex of the cone and having velocity
of D= 26 ]an/s. The wave was decelerated over a distance of approximately 5 cm
from the vertex in argon, having velocity of D= 12 3an/s.
From the gas-dynamics viewpoint, the motion in the cone is equivalent to a con-
verging spherical shock wave. The problem of aonvergence of the shock wave to the
center has an automodel solution R ti Iti a, where R is the radius of curvature of
the front, a= 0.715 for the index of the adiabatic curve Y= 1.4 and a-* 1 at
- Y- 1 C151. Analysis of photochronograms of a shock wave in a cone with air
showed that mation is close to automodel at R< 6 cm and up to deceleration (R =
= 0.4 cm) with automodel index a= 0.75 + 0.05.
An explanation for premature deceleration of the shock wave in experiments (not
at the vertex of the cone) should apparently be sought in the instability of the
converging spherical shock wave. This instability could be manifested due to the
asphericity of the shock wave created by an explosive charge or due to subsequent
_ distortion of the shape of the wave front when it interacts with tne channel wall.
The latter is the mcst probable since the shnck waves were created by identical
explosive charges both in argon and in air. At the samE time ci:rvature of the 40
front caused by heating of the channel walls and by radiation of the shock wave
adjacent to them cou13 be observed directly in experiments with argon. We shall
dwell on these experiments somewhat later (Chapter 4, Section 4). we note here
that addition of a slight air impuritp to the argon, which intensively absorbs
the ultraviolet radiation of the shock wave, led to the fact that the wave was de-
celerated later than in pure argon. 2-3 cm from the vertex of the cone at D= 14-15
lan/s.
a
(2)
;TP
Figure 16. Amplification of Shock Wave in Cone. SFR--high speed photo-
recorder 36
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88(1)
E- 0 ITOMM
7-
aa G (D P
b
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i4E,'I'HOD FOR :.SASURING THE INTENSITY TEMP'ERATiJRE AND OTHER VALUE.S
Moscow IZLUCHATEL'NYYE SVOYSTVA UDARNYKH VOIN V GAZAKH in Russian 1977 pp 37-61
[Chapter 3 from the book "Radiating Properties of Shock Waves in Gases", by M. A.
Tsikulin and Ye. G. Popov, Izdatel'stvo "Nauka", 173 paqes]
[Text] The parameters that characterize the radiating praperties of strong shock
waves in gases and namely the radiant flux density in various regions of the spec-
trum and accordingly the brightness temperature in these regions were measured
with time resolution using modern optical and electronic equipment to record high-
speed phenomena. The photographic method was used in the visible and near ultra-
violet regions and the photoelectric method, which also duplicated measurements in
the visible regions, was used in the infrared region.
l. Basic Concepts of the Radiation Theor,y
- The radiating properties of strong shock waves in gases, like other self-luminous
objects, are analyzed by comparison to the radiation of an absolutely black body.
" Since the radi.ation intensity of a black body is dependent only on temperature, it
is possible to characterize the brightness of radiators by the corresponding tem-
perature of an absolutely black body or brightness temperature.
Let us present in more detail, following [37], the main concepts of the physical
theory of radiation.
The following three main values are introduced by means of the photon distribution
function by frequencies v in space r and by the directions af prop-
agation of radiant energy near the solid angle vector P.
The spectral intensity of radiation IV 3.s the amount of radiant energy in the
spectral range dv passing within one second through an area of 1 cm2 placed at
point r perpendicular to the direction of propagation lying in the element of solid
angle dSt near vector SZ :
ly = hvcf (v, r, 0),
(3.1)
where hv is the photon energy and c is the speed of propagation. The dimensional-
ity of this value is erg/cm2�steradian. After integration by frequencies, we find
the radiant flux density per unit of solid anqle--erg/cm2�s�steradian.
37
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The spectral radiation density Uv is the amount of radiant energy in spectral
range dv in 1 cm3 of space:
U. = hv SIdS2 - ~ S I, d5d.
(4rt) (4R)
(3.2)
The dimensionality is erg�s/cm3. After inteqration with respect to frequencies,
we find the energy density--erg/cm3.
The spectral flux Sv is the amount of radiant energy in spectraZ range dv passing
within 1 second through an area of 1 cm2 in all directions:
S. = hvc S/ cos 6 dSd = S 1., cos 9 dia.
(4R) (4n)
(3.3)
The dimensionality is erg/cm2. After integration with respect to frequencies, we
find the energy flux density--erg/cm2�s.
With isotropic distribution of radiation when f and IV axe not dependent on direc-
tion Z, the radiation density is equal to .
p, - 4nhvf = ~
(3,4)
and there is no flux: Sv = 0 since an identical :iumber of photons is transported
in both directions.
For a medium in a state of thermodynamic equilibrium at constant temperature T, the
radiation field is also equilibrium, i.e., the number of photons emitted by matter
during 1 second in 1 cm3 in a given frequency range dv and in a given direction Q
is exactly equal to the number of absorbed photons. The field of equilibrium radi-
ation is isotropic, i.e., it is not deper;__nt on. the direction and on the specific
properties of the medium, being a universal function of temperature and frequency.
The function of the spectral equilibrium radiatian density U~p introduced by Planck,
has the fornt
8rthv' 1
U~~- ~Avl kT _i I
hence
2hv3 =
p c2 ehvM _ ~ �
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(3.5)
(3.6)
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These formulas k= 1.38�10'16 erg/deg is a Boltzman constant and c is the speed of
light.
We find the value of uni3irectional flux, i.e., the aznount of radiant energy pass-
ing in one direction through a unit area by integrating IVp with respect to a
hemisphere:
S�p = S I,P cos 6 dSa. (3.7)
(2n)
Substituting IVP here and bearing in mind that
we find
dil _ R$ s[ ~9 d9 dW _ gin 8 dA dff, (3.8)
n
SyP=2nSl,pcosAsiii 0d0 = nI�p, (3.9)
0
2nbvs i (3.10)
S~p = C2 ~hvi--- ,
The integral unidirectional flux with respect to the spectrum is
00
Sp = S S,pdv = aT�. (3.11)
n
2,6k i
where a-fSh,el - 5,67 � 10-b 3pz/c,u' � cex � xpa8' is a Stefan-Boltzman constant.
There is a very general confirmation for the ration of the absorbing and radiating
capability of bodies. Assume that a cavity filled with equilibrium radiation is
identified in an arbitrary body with ccnstant temperature T, sufficiently long so
that radiation does not penetrate it fully but was absorbed. A radiation flux SVP,
part af which is reflected and part of which is absorbed by the body, impinges on
the surface of the body from the cavity. Let the reflectivity of the body be Rv
and let the absorptivity be AV = 1- Rv. The amount of radiation absorbed in the
body is Svr�Av. Due to equilibrium, the same amount of energy is radiated by the
body into the cavity Jv = Svp�Av. The values of Av, R,v and Jv are the character-
istics of the body, but the ratio Jv/Av, i.e., the ratio of the radiating capacity
of the body to its absorptivity 3s not dependent on the property of the body and is
a universal function of frequency and temperature:
T�/A� = S~P. (3.12)
This statement is called Kirchhoff's law.
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A body which fully absorbs the radiation impinging on it, i.e., for which AV = l,
Rv = 0 and Jv = Svp, is called an absolutely black body.
Let us consider a sufficiently long body with constant temperature T and with re-
fractive index equal to unity in which radi.ation is in equilibrium with the matter
and let us mentally cut it into two parts iind let us take away one part. The uni-
directional radiatian flux through a plane from the direction of the body is then
SvP. Thus, a plane space filled with matter with constant temperature T radiates
_ from the surface like an absolutely black body with temperature T.
Let us calculate the luminous flux (D per ianit area dQ with radiating area d� lo-
cated at distance R(Figure 17):
d(I) - j cos 0~q~ s 9a dE,
(3.13)
where I is the equilibrium radiation intisnsity from the surface of the radia'ting
body. Expressing dE by R and angles 61 ,gnd 92, one can in each specific case cal-
culate 0 at a given point of space. For example, if area E is the circular layer
in a disk, one can easily calculate the radiation flux 0 on the axis through area
6 parallel to the disk. From Figure 18, el = e2 and 6 and
dE = 2rcl,i2 tg 8 dA,
Hence,
or
(3.14)
o.
~U = 2nIS sin0cos9d0 = rclsin2 0o (3.15)
0
(D = 5,,sjn' 60.
(3.16)
In similar fashion, we have for a radiat.ing sphere (Figure 19)
~j
dE - 21tR siti 02 Rde, ,
cos e, (3.17)
e.
_ (l) = 2n! S sin 99 cos 09 d8s = nl sinz Oo, (3.18)
0
(D = Syp sin' 80.
(3.19)
Measuring ~ and then determining the value of Svp from geometric concepts, we can
clearly determine the temperature of the radiating body.
These measurements are usually made with out making absolute measurements of radi-
ation flux, but by comparing it to the flux from a standard source. We shall re-
turn later to this problem.
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ds
dC
Figure 17. Calculation of Rad3ation Flux Density
Figure 18. Calculation of the Flux Density From a Disk-Radiator
Z'hus, the flux is determined at same distance for flat disk and spherical radiators
by the square of the sine of half of the angle at which this light source is visi-
ble since specific differences of shape of the light source axe unimportant. There-
fore, both the sphere and generally any source of circular radiation are visible as
a flat disk to us. This property is the consequence of Lambert's law or the law of
cosines which says that the radiation flux through a surface is proportional to the
cosine of the angle between the direction of propagation of the radiation and the
normal to the surface.
The condition of "blackness" of a given body is total absorption of the radiation
- impinging on it, for which the dimensions of ths body ehould exceed many-fold the
length of radiation travel, i.e., the optical thickness af the body should be
great.
Let us consider the equation of radiation transfer in a medium.
An amount of radiation IvdQdt flows in an elementary cylinder (Figure 20) with area
of the base da and height da whose axis coincides with the direction of the lumfn-
ous flux during time dt to the base located at a point with coordinate s while
(Iv + dIv)dQdt flows from the base located at a point with coordinate s+ ds. The
_ increment of beam intensity consista of the local increment during the passage of
path ds by the light and of the increment upon transition from coordinate s to co-
ordinate s+ ds at a qiven moment of time:
41.
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Figure 19. Calculation of Flux Density from a Spherical Radiator
Figure 20. Deriving the Equation of Radiation Transfer
a$ ar~
"
'
dl, = a a, ds.
(3.20)
Beam intensity varies due to emission and absorption of light in the given elemen-
- tary cylinder. The amount of radiation emitted in the cylinder during time dtv is
equal to
'
i` I + 2ItV3 I�) dQdt,.
(3.21)
~ where jv is the emissive capacity of matter. The second term in parentheses takes
_ into account the so-called stimulated or induced emissfon (the probability of stim-
ulated emission of a photon of given frequency and given direction is proportional
to the radiation intensity of the eame frequency and the sazne direction existing at
a given point of space). An amount of radiation cfvIvdQdtds, where Xv is the ab-
sorption coefficient, is absorbed in the cylinder during the same ti.me. Compiling
the balance and dividing the derived expression by the product of differentials
- dQdtds, we find the equation
i a1~ aIy ~a
c ar + aa + zhv. I~~ - x~1~� (3.22)
,
. 42..
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T'he ratio of the emissive and absorption capability of the body, according to
Kirchhoff's law, is a universal function of frequency and temperature in a state
of equilibrium
i" 1,P
X - Cg ~
v ' + 2hv- f -+p
(3.23)
where radiation intensity IV is substituted for the equilibrium value IVp (3.6),
hence
J. = MvIvp (1 - B'hv/kT).
(3.24)
Let us remove the parentheses in the riqht side of equation (3.22) and let us re-
place j'v in the second term for the derived expression into which we substitute the
expression for Ivp. The right side of equation (3.22) then assumes the form
)v - X. (i - C-hv/kT) I

(3.25)
Hence, it is obvious that stimulated emission can be interpreted as a decrease of
absorption,, part of the photons seems to be absorbed and emitted again at the same
point with the same frequency and in the same direction. These acts of "reradia-
tion" can formally be disregarded if ane asstiunes that the absorption coefficient
has a somewhat smaller value:
X;, = x�(i - e;nvlicT), (3.26)
In this interpretation Kirchhoff's law acquires the following form:
fv = x;,l�p, (3.27)
and then the transfer equation is written in the following form:
1 aI, at, . (3.28)
c 8t _(3a - )ti� (l�p - I�).
Noting that tP,e differential expression in the left side is a final product of in-
tensity along the path of propagation, we rewrite the ecsuation in the form
di, x;,1, - x�t,P.
d, + (3.29)
Equation (3.29) has the solution
i e
I~ = S I~p eap S u� ds"]x� ds' + const. (3.30)
r
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Let us consider examples. Let a body with constant temperature T occupy an infin-
ite half-spacQ s> 0 and is limited *4 plane surface. The intensity near the
surface is then equal to
00
-S I�pe Tl, dv" - I"p' (3.31)
0
i.e., it is equal to the radiation intensity of an absolutely black body with tem-
kvds perature T(in this formula t, - is optical thickness).
0
Let us consider the radiation of a plane layer of finite thickness A. For radiation
intensity we have
ela,s e
I ~~e) = S I~ 1~~ooee dT, ~e cos0 - I�P(i -e--_l/coei(3.32)
r
0
here Tv is the optical thickness in a direction perpendicular to the surface. For
an optically thin layer tV � 1 we find
I� = I.,PTv/cos 9 (3.33)
--the brightness of this radiating body increases with deviation of the observation
angle from the normal.
Thus, an optically thin layer radiat:es differently at different angles, i.e., not
according to Lambert's law. One of the methods of experimental checking of the
"blackness" of a body is based on this effect: if the radiating body is of dif-
ferent brightness at different angles tn the surface it does not radiate like a
black body.
Not only the radiation intensity at a given angle to the surface is of interest,
but the radiation flux from the surface of the body, i.e., the radiation flux
emerging in all directions--the so-called spectral surface brightness, is also of
interest.
For the radiation flux we have (see (3.7))
sv - S r, c09 0 dQ.
(Zn) (3.34)
Substituting the expressions for IV and d;3, we find
n
Z 00 !lt
s, = zn S cos e si o ae S jyPC_T~ICOS (I c09~e (3.35)
0 0
ox
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m ~
S� = 21t S I,p dY� S e`'/��� e d(cos 9).
n n
Having substituted 1/cos6 = w, we have
1 ~ ~svdw
S e-t yi~ a d(cos 9) = S e" = Ea (t�),
ioa
0 1
(3.36)
(3.37)
m
where En(Z) - r e_Za dw is the inteqral exponents. Znstead of (3.36) we now find
~ wn
t
s, = 2 S svp~'2 ~Y~� (3.38)
0
m '
For a semi-infinite body S Es (z) dz -1/1 R s., = S,p� For a layer of finite thick-
ness TV we have
_I
s~ = 2SrP S E. (T,,) dY, = S�p ( 1- 2E3 (3.39)
0
The values of 1- 2 E3(TV) at given values of tv are given in Table 2.
Table 2.
t~ I 1-2 !is ITV I I i~ I t-2 Be (ty tV I 1-2 Ei (TV 1
U 0 0,6 0,616 2,0 _ 0,938
- 0,115 0,0416 0,8 0,712 2,5 0,968
0,2 0,300 1,0 ' 0,782 3,0 0,988
0,4 0,/i76 1,5 0,888
The following effective parameters can be determined for a radiator different from
an absolutely black body:
--the spectral brightness temperature for a given wavelength, setting the
given spectral flux Sv equal to the corresonding value for an absolutely black
body:
S, = S~p (TA); (3.40)
--the integral brightness temperature for a complete flux from a given radia-
tor S, setting this value equal to the complete flux from a"black" radiator:
- .45 ~
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S - a T". (3.41)
The integral brightness temperature averages all the specific characteristics of
the radiator. Therefore, it is more convenient in most cases to use the spectral
brightness temperature. We shall subsequently use only this concept and will omit
the word "spectral" and the subscript .
The.brightness temperature for an optically thick body is usually dependent on fre-
quency. This is related to the fact that the layer radiating from the outside near
this body is one with thickness 2-3 lengths of radiation travel. But the edge of
the body is not heated uniformly and the temperature decreases toward the surface
due to xadiation losses. Due to the dependence of the absorption coefficient on
frequency, the travel distances of different photons are different since different
photons emerge to the outside from different depth where the temperatures are
different.
For example, the total absorption coefficient for water-hyarogen-like atoms, which
includes free-bound anci inhibited absorption by electrons in the atom, is given by
the Unsold-Kramers formula for small photons less than ionization potential hv � I
16n2 ea72kTN - I-hv
xv _ h~~e e kT
3 ~ = 0,96 � 10-' NZa `cm-t ( 3. 42)
~ fa x~ ,
where Z is the nuclear charge, N is particle concentration and x= hv/kT and xl =
= I/kT.
We then find the radiation paths 13 > 12 > 11 and according to this T3 > T2 > T1
near the edge of a radiating body w}iere temperature decreases toward the surface
for frequencies v3 > v2 > vl, i.e., "blue" photons are hotter than "red" photons. If
one is given the flux distribution in the frequency function (Sv) for an absolutely
black body at a specific integral brightness temperature, the observed flux dis-
tribution by frequencies is shifted toward the blue direction.
We considered the condition of the "blackness" of the body and established that
the optical thickness of the body should be great for this. The absorption coef-
ficient of matter is equal to the absorption cross section per particle multiplied
by particle concentrati.on. The absorption coefficient corresponding to resonance
absorption in the spectral lines whose absorption crosa section is very high emer-
ges to the forefront with low particle concentration.
In classical theory the model of a radiating atom is an elastically bound electron
which oscillates near a position of equilibrium--a harmonic oscillator. Since the
- oscillating electron moves in accelerated fashion, it emits light.
If the energy losses during the period are low, the rate of radiation is calculated
by the formula
z
- C- 3 c w2' (3.43)
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where w is acceleration. Since for an oscillator w= 4w2v~r, then frum (3.43)
we find the equation of energy loss
d1V 32nde2 ~ E -8nte2vo
dt - - �S = - 3ca v0r - - 31nc3 w' (3.44)
where W= 47T 2mv2r2 is the oscillator energy. The value
8nZeZV2,
Y 3mc'
(3.45)
- is called the attenuation constant and is an inverse value of time during which the
oscillator energy decreases by a factor of e.
Considering the problem of stimulated oscillation of an oscillator with attenuation
in the light wave field and calculating the work of the field, i.e., its energy ab-
sorption, we find the effective absorption cross section of the osr.illator
enY ! (3.46)
a" - 4nmc (v - v,}s
hence, the maximum absorption cross section in the center of a line with wavelength
a is:
3
o'~ = Z Xa.
This is a very high value. For example, for 71 = 650 nm at N= 1018 cm-3, the ab-
sorption coefficient comprises
xy = a,N - 2�109 cx-1 (3.47)
and the radiation path is 1v = 5�10"10 cm, whereas the radiation path comprises a
value on the order of a meter for the brakinq mechanism or by the Unsold-Kramers
formula with the same particle concentration and with low temperature of approxi-
mately 104�K.
Thus, conditions of the "blackness" of r&diation are achieved primarily in the cen-
ters of spectral lines. And since the radiation of a body cannot be greater than
that of an absolutely black body, the intensity of the spectral line when the con-
dition of "blackness" is reached "pushes against" the curve for a black body at
given temperature (Figure 21). A characteristic feature of the spectral line that
reaches saturation is a flat aection at the apex of intensity. The temperature--
the same brightness temperature, but already determined by the spectral line, is
also determined by the intensity of these saturated sp4ctral lines.
If the intensity of the spectral line does not reach saturation, the matter becomes
considerably more complicated. In quantum theory the spectral line intensity of
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10
a '
= Figure 21. Radiation Spectrum of Body Opaque in Center af Some Lines
frequency mn of transition from state n to state m, i.e., the energy emitted in
the line of cm3 within 1 second is equal to the product of the number of emit-
ting atoms Nn by the value of the photon hvmn and by the probability of transition
Amn:
Imn = Nn�/tYmn�Amn� (3.48)
The probability of transition Amn is an internal property and is not dependent on
_ external conditions with respect to the atom-ron temperature, particle concentra-
- tion and so on.
According to Kirchhoff's law or the principle of detailed equilibrium, one can es-
- tablish the relationship between the probabilities of emission and absorption for
a given transition. Making the analogy with classical concepts about the atom as
a set of oscillators, the absorption or radiating capacity of the atom in a given
line is usually characterized by the number of classical oscillators with natural
frequency mn which would produce the same effect as the atom being considered.
This number f is called the oscillator force--this is an average value calculated
for one degree of freedom of the electron. The total force is three times higher
- according to the fact that the elecfixon in the atom has three degrees of freedom.
Everything is usually expressed through the abaorption force fpogl, bearing in
mind the relation
gm
- fnm tan = ~mn nornr
~ (3.49)
where g is the statistical weight of state. The following determination occurs for
the value fiz1= 3 fn,m.izl - Anm/Y--the rat.io of the probability of transition
n- m to t.he classical attenuation constant Y. For a classical oscillator Anm = 1'
and fnm = 1/3. We then have
- 3YB
Inm - B m /tvnm/
/nmNn�
" (3.50)
Bearing in mind that Nn = gn Nloxp(- EnkTEt) , where subscript 1 denotes the
Ri
ground state and substituting the value of Y into (3.50), we find
Inm - 8JL2mEc3gtl gm /nmN1 exP r k~, r, (3.51)
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Knowing the constants for the given levels of the atom and measuring the intensi-
ties of the corresponding lines, one can determine the temperature and particle
concentration of the radiating body. The values of oscillator forces which are
unknown for far from all atans cause the qreatest difficulties. This value is
difficult to calculate precisely dnd is usually determined experimentally.
in conclusion let us dwell on the units of ineasurement of light values. Clarity is
necessary in this problem when discussing the different aspects of the radiating
properties of shock waves in gases.
- Since radiation is essentially a phenomenon of radfant energy transfer, it is nat-
ural that these values are measured in energy units. We shall also proceed in
this manner when di.scussing the results.
Determination of the main values of radiation theory with the following dimensions
was also presented above: spectral intensity IV--erg/cm2�steradian, spectral
' density Uv--erg�s/cm3 and spectral flux Sv--erg/cm2.
The following determination of energy flux F in a beam of light with the spectral
distribution $a occurs in illumination engineerings
F = K f Pa Vad,,,
(3.52)
where Sa is essentially spectral flux Sv integrated by the aource area, K is a
coefficient and Va is the so-called visibility curve corresponding to the averaged
spectral sensitivity of the human eye. The unit of value of F is the lumen.
Further, tne ratio of the value of flux inside a small solid anqle near a given
direction of radiation has luminous intensity
I-du'
(3.53)
_ If the source radiates uniformly in all directions, then 471 = F. The unit of
luminous force is the candle--the luminous force of a source yielding a luminous
flux of one lumen inside a solid angle equal to one eteradian.
Z'tie illumination at a given point is the flux per unit area:
F, ~ dF/dS; (3.54)
and is calculated in units of lumens/m2 (lux) or lumens/cm2 (phots).
T'he luminosity of a light source is the ratio of the total luminous flux of the
light source to its area:
R = dF/dS
with units si.milar to the units of illumination: radlux and radphot.
49
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The brightness of a light source is the ratio of the luminous force in a direction
, perpendicular to its surface to the size of the surface:
B _ t d/
(708e~r,-s � (3.56)
The unit of brightness is the stilb or candle/cm2. The unit nit or candle/m2 equal
to 10'4 stilb is also used. It is obvious from determination of the brightness of
a source B, luminaus force I and luminous flux F that it is the brightness of the
source B that is the analog of radiatiorA intenaity Iv with the difference that
brightness B is averaged by the light sensitivity of the human eye--the visibility
curve. The visibility curve VX is given in Fiyure 22 in the form of the relative
sensitivity of the eye averaged for many individuals with normal vision. The hiqh-
est sensitivity, i.e., the highest color sensation, was detected for wavelength of
555 nm and is taken as the unit.
vA,
4e
O,u
92
l~00 J90 600 Iti, NM
Figure 22. Visibility CurvE
Intrcducing the visibility curve in relative form, one must absolutely determine
the value of coefficient K in formula (3.52). The experimentally determined value
of K, measured from comparison of luminous flux F and spectral distribution Sa, was
equal to 683 lumens/watt accordin,g to the latest measurements.
2� ;fcasi.tring the Intens-ty Teraperature by Photography
The main element in the photographic method of recording luminous radiation param-
eters is the light-sEnsitivity of the photoemulsion. After being developed, as a
result of the effect of radiatian(exposure), the photoemulsion reveals darkening
which can be analyzed by its capability to retard radiation. The measure of
opaqueness--the optical density or densitp of darkening A--is the common logarithm
of the ratio of incident flux Fp to the passing flux F1 during translucence of the
developed film:
F
p Ig ; .
The dependence of darkening density A on the logarithm of radiant energy density
_ (exposure) 1g0t, acting on the photoemulsion, is expressionby the characteristic
curve (see FigurP 23 in which the typical regions are noted). The normal work of
the phntoemulsion as a measuring element is accomplished on the condition that the
darkening density does not go beyond the bounds of the linear section. One resorts
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to different exposure times t to remain withfn the limits of this section upon com-
parison of objects differinq strongly in brightneae from each other (10-30-fold or
more). In this case one relies on the so-called law of intersubstitution. The
latter means that all things being equal, darkeninq density is dependent only on
_ the product H=(Dt rather than on each value separately. However, if there is a
large difference of exposure times, deviations from this law are observed. The
- dependence of the exposure logarithm 1gH, which yields the same darkening density
A = const (isoopacity), on absolute exposure time is given in the graph of Fiaure
24. It is typical that no deviations from the law of intersubstitution are noted
in the range of 10'5 to 10'8 second [141, 1421.
d
~
tg H
Z, 0
>,,f
1,0
~7S
-6 -u -z o z 1/ bgt
Figure 24. Isoopacity Qf Hfgh-Contrast Panchromatic Film (according to [141,
142])
The quality of photoemulsions has recently reached a, high level in many reapects.
For example, the spectral sensitivity of photoemulsions extends from 120 xun in the
far ultraviolet to 1,100-1,200 nm in the infrared region of the spectrum. Z'he ab-
solute sensitivity of some photoemulsions exceeds by tens and hundreds of times
the sensitivity, for example, of ordinary aerial photographic film, which permits
objects to be recorded with comparatively low brightness temperature (on the order
of 10,000�K with exposure time of 10-7 to 10-8 second). The resolution of the pho-
toemulsion reaches several hundred linea per millimeter, which still makes th3.s
measuring e].ement incomparable to any other lxght sensitive element. Taking this
into account, the photographic method must be noted as one of the uost effective
methods of investigating radiation processes.
51,
~ -1
bg �t
Figure 23. Characteristic Curve of Photoemulsion: 1--fog and zone of under-
exposures; 2--zone of linear exposures; 3--zone of overexposures
and solarization; tgo = y--contraet coefficient
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I. Sh. Model' [291 used photographic photometry methods to study the brightness
of shock wavest he had already described the details and advantages of tl-iis method.
The brightness of a shock wave was recorded during its work by means of a two-lens
slit photochronograph. The sun, whoae brightness temperature was measured by a
pyrumeter at the moment of filmi.ng, was used as the comparison standard. The
standard was photographed twice at different rotational, frequency of the photo-
chronograph mirror, which corresponded to different exposure times. The results
of these filmings were used to construct a linear section of the characteristic
curve of the photoemulsian. A shock wave, being a brighter object, was photo-
graphed at higher mirror rotational frequency than the standard. The law of inter-
substitution was applied when plotting the characteristic curve and when determin-
ing the brightness temperature. The accuracy of ineasuring a temperature of 30,000-
35,000�K is estimated at + 15 percent.
This method was improved in [32, 41, 42]. An SFR device more improved than the
photochronograph described by I. Sh. Model' was used to record brightness (the er-
ror related to the inaccuracy of determining the mirror rotational frequency ;aas
actually eliminaked by this). Although;an IFK-50 xenon lamp (brightness tempera-
- ture of 6,300 + 200�K in red light) is a more convenient camparison standard than
- the sun [41], The disadvantages related to the great difference of the brightness
of the standard and the shock wave were retained. These disadvantages were elim-
inated in [42, 321, where an EV-39 flash lamp with brightness temperature of
41,000�K was used as the comparison standard.
I. Sh. Model' [29] nated one of the advantaqes of the photographic method--the
possibility of simultaneous recording of the brightnese and velocity of a shock
wave. It is even possible to record simultaneously the brightness of the front at
two different angles by measuring its velocity and checking the optical thickness
of a shock-heated gas (321. The specifics of explosive experiments, specifically
_ the laboriousness of expeziments to produce strc+ng shock waves (D > 20 ]an/s) forces
oze to be limited to minimum statistics and to extract as much information as pos-
siY,le from each experiment. Therefore, the noted advantages of the photographic
method predetermined its widespreaci use in the experiments descrxbed here. We de-
veloped the method jointly with Yu. A. Zatsepin.
B.rightness temperature is determined from photometric comparison of darkening
densities produced on a phatoemulsion during slit scannino of a shnak wave and
brightness standard on the SFR-2 device. The ultraviolet (aef = 330 nm), violet
(Xef = 432 nm), blup (aeg = 442 nm) and yellow (aef = 560 nm) Sections of the
spectrum were separated by light filters. The transmission curves of the light
filters used in the experiments, measured on the SF-4 spectrophotometer, are pre-
sented in Figure 25. The effective length aef is determined with regard to the
spectral sensitivity of the photoemulsions.
- The lenses of the SFR-2 device are replaced with quartz lenses, which were special-
ly designed by N. M. Sitsinskaya for aef = 330 nm and were manufactured at the OKB
IFZ [Special Design Office of Institute of Physics of the Earth imeni 0. Yu.
Schmidt], during measurements in the ultraviolet region of the spectrum. The de-
vice was adjusted and focussed on the object by means of a fluorescent screen
placed on the focal arc of the photochronograph. A mercury lamp is used for
_ illumination.
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I/I
r------ -
0,6
O,y
0,2
Figure 25. Transmission Curves of Light Filters Used
The brightness standard is an EV-39 pulsed light source that radiates like a black
body with temperature of 41,000�K over a wide spectral range of 200-600 nm [143].
The proximity of the brightness temperature of the standard to the measured temper-
ature reduces the error of the method and permits one to avoid the procedures that
compensate for the large difference in brightnesa of the standard and shock wave.
The standard and shock wave are photographed at identical error rotational frequen-
_ cy. Because of the short (180 microseconds) luminous pulse of the EV-39 source,
one can do away ;aith shutters that cut off one rctation of the photochronograph
mirro (the same is true of filming the shock wave).
- The darkening marks are imprinted when filming the atandard to plot the character-
= istic curve of the photoemulsion in each experiment. A graduated attenuator is
placed on the focal arc of the SFR device for this purpose. Synchronization of the
position of the rotating mirror with the EV-39 flash lamp is setected such that the
photoemulsion is exposed behind the graduated attenuator during the entire period
of the flash when its brightness remains unchanged. The standard and darkening
marks photographed in this manner are presented in Figure 26. If the temperatures
to be measured are expected to be higher than the standard temperature, the darken-
- ing marks are imprinted first by the sazne method and at the same mirror rotational
frequency, but with completely open lens diaphragm of the SFR device (so that the
range of darkening densities of the marks always encompasses the darkening densi-
ties from the standard and shock wave). The identity of the conditions for film-
ing the marks, standard and shock wave permits one to avoid relying on tha law of
intersubstitution when detern3ninq the brightness temperature.
When filming the EV-39 source, the SFR device is adjusted so that its slit cuts
out a strip in the center 0.5 mm wide from the discharge opening of the source.
- Thus, the radiation of the central spot of a discharge 1 mm in diameter, for which
brxghtness temperature of 41,O00�K is guaranteed, is separated during time scan-
ning from the radiation of the peripheral regions of the discharqe with lower tem-
perature. To increase the imaqe size of the radiator of the EV-39 source on the
negative (and thus facilitate densitometry of it), the latter is photographed from
the closest possi.ble distance 11 equal to 2 meters for the SFR-2 device. It was
required that the visual field of the photochronograph encompass no less than 15 cm
for simultaneous recording of the brightness and velocity of the shock wave. A
distance of 12 = 5 meters satisfied this condition. The difference in distances
~ is taken into account by multiplyinq the ratio of radiation intensity of the shock
wave and the standard, measured by the darkenings, by the value , where
53�
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f= 21 cm is the focal distance of the inlet objective of the SFR-2 device. Thas
correcting factor is close to 1 at f 12 km/s
T�!O-~' ' N
6
105,
' S !0 ff 11, K,v/ce~r
_ Figure 35. Brightness Temperature of Shock Waves in Argon With Air Impurity:
dark circles--X = 330 nms light circles--X = 442 nm; ligr.t
_ squares--a = 560 nmt curve--calculated temperature behind front
for pure arqon The radiating properties of shock waves in air and in inert qases differ appreci-
ably. A number of features were discovered in experiments with inert gases that
forced one to re-evaluate the caFabilities of a shock wave as a radiator. The
transient nature of radiation by strong shock waves and the presence of absorp-
tion lines in the spectrum could not be explained on the basis of existing theo-
retical concepts. On the one hand, it was required to determine and to scrupu-
iously describe the experimental results, being limited in this case only to some
of the more obviaus conclusions. On the other hand, one had to reconsider some
what the theory of radiation of strong shock waves cahen interpreting the results
(see the next chapter).
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T�/o' M
~
, Z
Figure 36. Brightness Temperature of Shock Waves in Argcn at Pressure of
pp = 300 mm Hg, X = 432 run
T�/0-~'N
j
.7
IZI
2 .s 117 n
Figure 37. Brightness Temperature of Shock Waves in Argon at Pressure of
po = 100 mm Hg, a= 432 nm
l. Intensit,y of Strong Shock ',7aves in Air
The values of brightness temperature and velocities of the shock wave front in air
measured in experiments are presented in Figures 30 and 39. In Figure 30, the re-
sults of our measurements are supplemented by values of brightness temperature of
the front in red light measured by A. Ye. Voytenko, I. Sh. Model' and I. S. Samo-
delov [41]. The theoretical dependence of the temperature of shock-heated ionized
air on wave velocity, calculated by N. M. Kuznetsov [147], is presented in the
same figure ror comparison.
If the shock wave velocity did not exceed 20 km/s, the brightness temperature of
the wave front was identical in different sections of the spectrum (Figure 39).
The values of brightness temperature corresponding to the intensity of radiation
normal to the front and to radiation intensity at an angle of 450 to the plane of
the front also coincided with each other. All the measured values of brightness
temperature at velocities of D= 820 km/s are applicable within error to the theo-
retical curve for the gas temperature behind the front.
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T!O-;`�K
~
I
0
�
0
2
S . /O A A'/I/Lb'R
Figure 38. Bxightness Temperature of Shock Waves in Arqon at Pressure of
po = 50 mm Hg, X = 432 nm
i �/O :~`�R .
2
1
~
' -/~6~rM/ceK
D=.9KMICCK
O,Z O9S1 96 O9B /,O . 1,2 A;,a
Figure 39. Distribution by Brightness Temperature Spectrum of Shock Waves
in Air: dark circles--from spectrophotochronograms;.light cir-
' cles--photcelectric measurements; straight lines--gas tempera-
ture behind front
c
oo0.oaoo
0000 00 oo Rr Ar

3 ~
0o O 0000000 D
_ Z �s ~ ~j ~s i�~u -
41 He
10 km/sec it was possible
to observe an increase in the brightness of the front in 1 mic rosecond with
approximation of it to the end window of the couvette. This result also indicates
that ahead of the shock wave front at a distance on the order oi 1 cm there was a
plug of semitransparent gas shielding the radiation fram the front. No buildup
of brightness of the front was obse rved in the narrow couvettes 8mn in diameter
before its arrival at the end window. Obviously, in narrow couvettes the condi-
tions for the fomation of such a plug ahead of the front were wor.se, which also
appears to be entirely natural. In order to avoid confusian, let us note that in
the experiments with other inert gases the end window either was not installed
(argon, helium) or the observations were disturbed (argon at reduced pressures) by
the instability of the plane front which will be discussed in 94.
Thus, in order to give a noncontradictory explanation to the above-
enumerated characteristics of the radiation of powerful shock waves in inert gases,
it r.emains to confirm the previous proposition that a shielding layer on the order
of 1 cm thick is observed ahead of the shock wave f ront in a time on bhe order of
1 microsecond. Again we empfiasize that the formation of such a wide layer cannot
1
Analyzing the spectral dependence of the absorption coefficient, we considered
the corrections far tfie nonhydrogen nature of the absorption calculated in
reference 192j.
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be explained on the basis of the existing ideas of shielding the radiation of
powerful shock waves by a layer arising as a result of photoionization of the
cold gas ahead of the front by short-wave em3.ssion. Without touching on the possi-
ble aature of this layer, let us consider the results of ineas uring the brightr..ess
teriperature of shock waves in the front with an admixture of air.
In the first experiments the couvette was filled with argon not by purging,
but by forcing aut the lighter air. It was assumed that the air admixture, unavoid-
able in this filling approach has no influence on the shock wave brightness. The
values of the brightness temperature measured in these experiments are presented
in Figure 35. A comparison with the results of Figure 31 for pure argon (filling
by purging) indicates the significant influence of the admixture the bright-
ness temperature of the front of the powerful shock waves in argon with air ad-
mixture turned out to be appreciably lower. In order to see that the air admixture
- is at fault in this divergence, three experiments were performed in which the
volumetric concentration of the air was checked and amounted to 5%. The data
from these experiments sell well within the results presented in Figure 35. A11
of the above-noted peculiarities of the radiation of powerful shock waves indi-
cating the formation of a b road shielding layer ahead of the front were manifested
in argon with air impurity. In particular, with approach of a powerful shock
wave to the end window of the couvette the brightness temperature of the front
increased in 1-0.5 microsecond, reaching the same values achieved in pure argon
by the time of arrival at the window (these values are not ?resented in Figure 35).
Arranging the couvette parallel to the slit of the moving image camera (the radia-
tion recording time is presented in Figure 27, c), it was possible directly to
observe the formation of tfie weakly glowing plug ahead of the front extending
a distance of more than 1 cm. For a long time this glow ahead of the front was
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connected with re.flection of the couvettc walls. Subsequently, it was noted
that the glow is not manifested immediately, but 1-2 microseconds after excita-
tion of the shock wave (in contrast to ref.lection which was also observed, but
arose immediateZy). Similar glow was also observed in experiments with pure inert
gases, but, being weaker, it w3s not so clearly isolated against the b ackground
of the reflection.
In the conclusion of this section let us note that the efforts to convert
- to strict quantitative studies of nonsteadq phenomena in powerful shock waves
have run into a number of difficulties. First of all these include the highly
_ unstable nature of the phenomena themselves when apparently in identical experi-
ments nonsteady changes in intensity have been quantitatively distinguished. It
is convenient to investigate these phenomena in experiments where the shock wave
velocity does not change noticeably for at least 10 microseconds, b ut s uch waves
cannot be obtained with a velocity of D>15 km/sec. Great difficulties h ave also
arisen from the instabili.ty of the plane front during movement of the powerful
~ shock waves in the couvettes. This ptienomenon is the subject of 54 of the given
chapter, and here we shall only note that as a result of the disappearance of the
plane front 5-10 microseconds after excitation of the shock wave frequently it has
not been possible to establish what values the brightness temperature will drop to
as it decreases with time.
3. Results of Spectral Investigation of Radiation
From the results of the studies presented in 91, 2 of this chapter, it is
possible to draw the conclusion that shock waves with velocities of I=8 to 20 km/sec
in the air, D=7 to 14 km/sec in argon, I-7 to 25 km/sec in neon, and D=20 to 35
km/sec in heliiun radiated just as an absolutely black bc,dy in the experiments.
' This is indicated by the comparison of the tarightness temperatures in the various
sect4.:)ns of the spectrum and at different angles to the plane of the f ront among
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each other and with the calculated gas temperature behind the front. For the
same reasons it is necessary to consider the radiation of shock waves with the
velocities of D=4 to 10 km/sec in xenon simi.lar to absolutely black; in tY:e given
case the brightness temperature of the front in visible light was somewhat belaw
the calculated temperature of the shock-heated xenon, which indicates the radia-
tion shielding. These conclusions were more precisely defined during sp2ctral
studies of the radiation of shock waves, the results of which are presented below.
Figure 41. Moving image camera photograph of shock wave radiation
in the air obtained using the SFR-2 camera with SP-77 attachment
(X=390-700 nm)
1-- detonatian exit to the bottom of the channel, 2-- stable
shock wave in the channel, 3-- drift of the shock-heated gas
out of the tube
Figure 42. Moving image camera photograph of the radiation of a
shock wave in the air with a velocity of D=14 km/se c obtained using
the SP-111 (A =220 to 400 nm)
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' Figure 43. Moving image camera photograph of the radiation of a
shock wave in the air at a velocity of D=14 km/sec obtained on the
STE-1 camera
The top line is blue light, the botton line is yellow light, in the
upper right hand and lower lefthand corners are the ultraviolet
0>340 nm) and red (a xl, the velocity of the front near the tube walls in-
creases intermittently and on the section xl < x< x2 com-
prises 11.1 km/s (10 km/s at x> x2). The plane front not
affected by wall disturbances propaqates at velocity of S km/s
1. Microseconds
2. km/s
The shock wave velocity did not exceed 9 km/s in Shreffler
iments and the problem of which shape a front of stronger
mained unclear. The investigations of Yu. A. Zatsepin et
93
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and Christian's exper-
shock wave acquires re-
al [42] provided the
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answer to this question. Moreover, we detected a significant effect of the insta-
bility af a plane front on the radiating properties of strong shock waves.
Development of a section of front near the cuvette walls, sharply differing in
brightness, was observed in the first experiment with argon and helium set up to
investigate the radiating properties of strong shock waves in these gases. The
brightness temperature of this fo�rmation hardly varied over the entire investigated
range of shock wave amplitudes and ;aas comparatively low: 15,000-25,000�K in ex-
periments with argon and 25,000-35,000�K in experiments with helium. Within 5-10
microseconds the bright central section of the front disappeared completely, being
absorbed by this formation (Figures 28 and 47). This decrease of radiation in-
tensity could not be the result of the small optical thickness ot a shock-heated
gas. In the given case a smooth decrease of radiation intensity at an angle of
45� was not observed as it approached the wall of the cuvette, as occurred at cqm-
parat vely low shock wave velocities. The intensity decreased .intermittently and
was identical for radiation at an angle of 45� and for normal radiation. Due to
recording of radiation emerging at an angle of 450 to the cuvette axis, it was
possible to measure separately the velocities of the bright and diffuse sections
of the front. It turned out that the brightness of the front near the walls is ap-
proximately 20 percent higher than that in the central part of the cuvette. It i.m-
mediately became obvious that this difference of velocities should lead to bending
of the front. Specially run experiments confirmed this hypothesis. We made use
of the circumstance that the glow was cut off at the moment the shock wave touches
the end window of the cuvette to investigate the shape of the front.* The moments
of arxival of different sections of the front to the end window of the cuvette
were recorded by cutoff of the glow in the experiments. ICrsowing the time differ-
ence of arrival of individual sections of the front and the velocity of the front,
it is easy to restore its shape. To follow the variation of shape of the front
during motion, the end window was placed at different distances from a diaphragm,
after rupture of which a plane shock wave was generated in the cuvette.
Figure 48. Bending of Front During Motion of Strong Shock Wave a.n a
Channel
The results of these experiments are qualitatively il.lustrated by Figure 48. The
front plane the first 1-2 microseconds after generation of the shock wave near the
walls began to be bent in the direction of motion. This process was especially
*
~ A slight surge and then a sharp surge within approximately 0.1 microsecond was
observed when a stronq shock wave was reflectpd from the window and there was a
_ decrease of radiation intensity. Cut-off of the glow was apparently caused by
breakdown of the transparent material of the window.
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intensive if the temperature behind the front exceeded 30,O00�K. The plane section
. of the front then disappeared completely within 5-1,0 microseconds. The front ac-
quired a funnel shape which was maintained durinq subsequent motion. The bright- ness temperature of this front was approximately constant, 15,000-17,000�K, over
the entire area in experiments with argon (it was somewhat higher, approxi.mately
25,O00�K) in the ultraviolet section) and was 25,000-30,000�K in experiments with
neon and helium. The experimental conditions were sometimes such that the shock
wave attenuated rapidly during propagation in a cuvette. If the shock wave velo-
- city decreased to 7-8 km/s in argon or to approximately 20 ]an/s in helium, then the
front again became plane and the front immediately became equalized over its entire
su.rface. A front when at least a small plane section remained in the central part
of the cuvette was equalized in a completely different manner. In this case the
entire process proceeded in opposite order--the plane bright section increased
while the diffuse bent section near the cuvette walls decreased until it disap-
peared completely. Yet another characteristic feature should also be noted--some
increase of brightness temperature of the plane section of the front near the
boundary with the bent section. Although the difference was slight, only approxi-
mately 3,O00�K, it was always distinquished on a background of random fluctuations
of brightness temperature along the surface of the �ront. The distribution of the
brightness temperature of the front through the diameter of the cuvette reflecting
this characteristic is given in Figure 49.
Unique deformation of the front was observed in those experiments in argon where
the shock wave was created upon detonation of an explosive rod placed in a steel
tube. A shock wave with brightly illuminated plane front was initially propagated
in the channel formed by the tube walls and the rod. But slightly illuminated
bends, which increased and soon encompassed in the entire frQnt, occurred both near
the tube walls and near the rod within approximately 5 microseconds.
Bending of the front of strong shock waves was also recorded in experiments with
other gases. In experiments with xenon this process proceeded more slowly at
identical temperatures behind the front than in argon or helium. This significant
difference of brightness of the plane and bent section of the front was not ob-
served. An increase of brightness temperature was frequently recorded near the
walls of the cuvette prior to the occurrence of bending.
T�ro ;`�n
4
3
Z
/
-6 - V -2 0 1 0 6.v,v
~ Figure 49. Distribution of Front Temperature Along Cuvette Diameter in
One of Experiments With Argon (D = 14 km/s)
The results of experiments in which the cuvettes were filled with argon with an air
impurity are of special interest. In this case a front with insignificant bending
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near the walls (as at moment t2 in Figure 48) was established during motion of the
shock wave. The fact that the presence of an air impurity in argon prevented benci- -
ing of the front quite specifically indicates che important role of radiation in th
, the occurrence of instability of a plane frorit. Estimates show that air absorbs
approximately 70 percent of the radiant flux going to the area of transparency of
pure argon near the front with shock-heated gas temperature of 30,000�K.
The instability of the plane front was generally nst observed in air over the en-
tire investigated range of shock wave amplitudes. Only veiy slight bending of the
front occurred near the walls without variation of brightness. The hypothesis was
made that the instability of the front in air could not be manifested within the
15-20 microseconds during which the shock waves in our experiments propagated
along the cuvette. One can conclude from the experi.ments with i.nert gases that an
increase of shock wave amplitude and of the cuvette cross Gection contributes to
instability. The time between excitation of a plane shock wave and the occurrence
of bending of the front was reduced in this case. A special experiment was set up
in regard to all this. A shock wave in air with velocity of 14 km/s, produced upon
detonation of a shaped charge, was propagated along a long steel tube 18 mm in
diameter within.50 microseconds. The brightness temperature of the front was mea-
sured in the region of the spectrum at Xef = 432 nm. During the first 30 micro-
secands the briqhtness of the front was identical over its entire surface. The
measured value of brightness temperature of 25,000�K coincided with the calculated
temperature of the gas behind the front. However, slightly illuminated sections
with brightness temperature of 15,000�K then occurred near the tube walls. Slight-
ly illuminated sections, upon increasing, encompassed the entire front within an-
~ other 15 microseconds. The front had a funnel shape (as at moment tq in Figure
48) at the moment the shock wave was reflected from a window installed on the end
of the tube. Thus, the instability of a plane front can also be manifested in
air under specific conditions.
In experiments with reduced argon pressure, the instability of the front was mani-
fested more strongly than in experiments with argon at atmospheric pressure. The
front in these experiments, being bent near the walls in the direction of motion,
frequently acquired an irregular shape. Photochronograms of two of these exper-
iments are presented in Figure 50. One can judge the shape of the front at the
moment the shock wave is reflected from the window of the cuvette by the cutoff
of the glow.
The effect of the wall material on the development of instabi.lity was observed in
' the experiments. A plane f'ront was usually deformed more slowly in steel tubes
than in glass tubes. This process proceeded even more slowly in glass tubes lined
insicle by polished aluminum foil.
The results of experiments in which instability of the plane front was observed
during rropagation of shock waves in channels was stressed repeatedly among a
number of specialists. The most contradictory opinions were advanced with respect
to the nature of this phenomenon. In most cases attempts were made to explain the
occurrence of bending by friction of the gas against the wall. However, it re-
mained unclear how friction could lead not to a decrease but rather to an increase
of the velocity of the front near the wall. Hypotheses were also advanced that
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the front bends due to refZection of the shock wave from the wall. As is known,
during inclined impingement of a shock wave on a rigid obstacle, so-called Mach
- reflection occurs in which the front bends near the surface in the direction of
progagation of the wave. The possibility of this flow was first linked to the
presence in the experiments of a unique conical channel formed by the broken-down
walls of the cuvette that flew in all directions. But this explanation had to be
rejected after the instability of the plane front was recorded in experiments with
thick-walled steel tubes which did not break down. Authors have recently tended to
assume that the flow con.verging with transient Mach reflection could occur due to
the presence of a layer of heated gas near the wall.
. Comparison of the results indicates that the instability of a plane front is
caused by heating of the walls and the qas adjacent to it by the shock wave radia-
tion. The phenomenon was observed only at sufficiently high temperatures behind
the front and consequently at high radiant fluxes from the front. The instabil-
ities developed more rapidly in helium, argon and xenon than in air. Actually,
inert gases with their high ionization potentia"1 are more transparent to ultra-
biolet radiation than air, which absorbed a considerable fraction of the radia-
tion of a shock-heated gas before the front. Thus, heZium absorbs only apprAxi-
mateiy 2 percent of the Planck enerqy flux at a temperature of 30,000�K behind the
Front, argon absorbs 13 percent, xenon absorbs 29 percent and air absorbs 71 per-
cent. Even more convincing of the relat�onship of the phenomenon to shock wave
radiation is the fact that a slight addition of air'to argon prevented the devel-
opment of the instability. The thermodynamic characteristics of the gas in a
shock wave, specifically the temperature behind the front, essentially did not
_ change in this case, but the optical characteristicg of the gas before the front
varied considerably. Air absorbed a considerable part of the radiant flux from
- the front and consequently heating of the wa17.s and the gas adjacent to them by
radiation decreased.-
We notp yet another characteristic of the phenomenon--bending of a plane front in-
creased earlier and proceeded more rapidly with an increase of cuvette diameter.
Actually, the radiant flux density on the walls decreased more slowly as the dis-
tance of the wave front increased with large cuvette diameter than in small-diam-
eter cuvettes. Therefore, the gas near the waJ.l$ in large-diameter cuvettes was
heated more strongly by the moment the shock wave arrived. The effect of the wall
mate::ial, observed in experimente, was apparently determined by heat dissipation,
more intensive in the case of inetal walls.
It is very difficult to estimate.at which temperature the cuvette walls were heated
by radiation. Experiments will be described tn Chapter 6 in which intensive evap-
oration of different materials, including metals, was observed due to the effect
of shock wave radiation. The effect of radiation was weaker in the experiments
- desc:ribed here due to the small cuvette dimensions. The temperature of the inner
� surface of cuvettes rather did not reacYi the boiling point bnt even so was rather
high.* The temperature of a narrow layer of gas coming into contact with the wall
may be even higher since energy transfer by the electrons formed during the photo-
effect from the surface occurred along with ordinary thermal conductivity.
*
It was noted in [151] that nails placed into the tube were heated to incandescence
due to tre effect of shock wave radiation.
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According to some data [148], these "hot" photoelectrons may carry off up to ap-
proximately 10 percent of the incident radiant energy.
Aasuming a decrease of gas density pp near the wall due to heating and constant
pressure pi in the plug of ashock-heated gas due to the subsonic nature of flow
behind the shock wave front, it is easy to explain the increase of front velocity
near the wall. The following relation is valid for a strong shock wave
'L
P1= V + 1 PoD

(4.6)
In order that pressure pl be identical at all points behind the front, a decrease
of gas density Pp near the wall should be compens3ted for by an increase of
velocity D.
Based on these concepts, the authors are tempted to artificially induce bending of
the front near the exis rather than near the walls of the cuvette. To do this,
the output end of the cuvette was smoothly joined to an expansion nozzle. The con-
figuration af the channel was such that the cuvette walls were partially shaded
against radiation of the shock wave initially propagating througIz the nozzle. Ab-
sorbing ultraviolet radiation by i.mpurities, the argon in the cuvette was heated
and it was heated more strongly near tl:e axis. A shascp discharge of the front
near the axis was obser,ved in these experiments.
_ Shreffler and Christian [151) gave a somewhat different interprei:ation of the ex-
perimental results that they obtained. They link the occurrence of bending to
- heating, radiation and rapid expansion of the gas adjacent to the wall. Acting
similar to a pistan, the expanded gas, they feel, forms a secondary shock front
adjacent to the shock wave front near the tube wall. Reference is made in this
case to the fact that a sharply defined luminous front occurred above a target
placed in the tube even before the arrival of the shock wave. But investigations
[9, 11] showed that the accurrence of this glow was caused by evaporatian and sub-
sequent ionization of the target material.
The target in these types of ex.periments was located normally to the incident flow
' an3�therefore was subjected to a more powerful effect than the walls. But never-
theless the velocity of the luninous vapor boundary was always somewhat lower than
_ the propagation velocity of disturbances from the tube wali to its axis. Bending
*
Interesting data that confirm these ideas of the mechanism of disturbances near
the wall were kindly presented by V. V. Adushkin to the authors. Experiments were
_ conducted in which the shock wave of an explosion propagated along steel plates.
The shape of the wave front was recorded by a system of pressure piezosensors.
Radiation of the wave could not be taken into account since its amplitude was com-
' paratively small. The plate was first brought to red heat by a burner and bending
of the front near the surface in the direction of motion of the shock wave was
then observed. G. I. Taganov fir.st explained the "thermal layer" effect (see
[172)).
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of the front in a tube lined on the inside with aluminum foil could be observed in
the same experiment, whereas a luminous region did not occurr above a target of the
same foil placed in the tube. All this indicates the difference of phenomena com-
inq into play during interaction of a strong shock wave with the wall of a channel,
on the one hand, and upon irradiation of solids by a powerful luminous flux, on
the other hand.
Some features make the phenomenon of instability of a plane front similar to that
of transient shieYding of the radiation of the front descxibed in Section 2, Chap-
ter 4. They were both obserwed in experiments with inert gases and almost always
simultaneously. The typical ti.mes of development of the processes coincide by an
order of magnitude. The dimensiofzs of the cuvette affected the course of the pro-
cesses in both cases and this effect was identical--the course of the processes
s]Awed down with an increase of cuvette diameter. Both one and the other phenomenon
led to a significant decrease of the brightness of the shock wave front. The dif-
ference here is perhaps only quantitative--bendinq of the front was accompanied by
a more significant decrease of brightness. There is also similarity of the phe-
nomena in the fact that transient shielding was manifested most frequently in the
form of dark spots which, spreading, encompassed the entire front. .A unique fea-
ture existeci which made it possible to confidently separate these two phenomena
if the shape of the front was not monitored during ':he experiment. Bending was
always distinguished by a sharp drop of brightness on the boundary with the plane
section of the front while clear boundaries had no spots.
Based on the internal similarity of ths two phenomena, it is interesting to sug-
gest that they are essentially the same phenomenon. An important confirmation of
this would be achieved if the occurrence of dark spots could be related to defor-
mation of the front. The section of the front on photochronograms not affected by
wall bending seemed to be only approximately plane. However, we were unable to
- establish any correspondence between the spots and the uneven surfaces of the
front.
it is difficult t4 judge the extent to which one or ancther details are significant
when the nature af the phenomena has not yet been finally determined. The question
_ remains open whether the disturbances caused by heating the gas near the wall are
capable of leading to total disappearance of the plane front, as was observed in
experiments.* Although further investigations are required to determine the mech-
anism of interaction of a strong shock wave with the channel wall, already avail-
able experimenta.l material permits one to make two important conclusions. First,
- the.flow mode with a plane shock front is not stable and is replaced by a flow mode
with convex, funnel-shaped front during propagation of strong shock waves in chan-
nels. A number of problems (attenuation of shock waves in channels, their effect
on oustacles placed in the channels and so on) has not yet been resolved in practic
. tice, for which the result is of considerable interest. Second, conversion to a
*
At one time S. P. D'yakov [152] noted that a flow with a plane shock front is in
itself not always sufficiently stable. The criteria of stability which he derived
to sma11 disturbances can be violated under certain conditions (specifically, upon
dissociation and ionization of the gas behind the front).
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flow mode with convex front is accompanied by a significant decrease of the radi-
� ating capability of the shock wave. This circumstance should be taken into account
when the question arises of the luminous effect of a strong shock wave, especially
when designing explosive sources of radiation.
~
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EVALUATION OF THE INFLUENCE OF THE FRONT STRUCTURE ON SHOCK WAVE RADIATION
Moscow IZLUCHATEL'NYYE SVOYSTVA UDARNYKH VOLN V GAZAKH in Russian 1977
' [Chapter 5 from the book "Radiating Properties of Shock Waves in Gases," by
M.A. Tsikulkin and Ye. G. Popov, Izdatel'stvo "Nauka," 173 pages]
LText] During the propagation of a shock wave, a sharp, discontinuous variation
of the parameters of the medium pressure, density and temFerature takes
place. The shock wave, the amplitude of which at distances of several radiation
path lengths varies insignificantly; it almost repeats the classical example of
an absolutely bZack radiator: the optically dense region of uniformly heated
material is bounded by a surfaca with a sharp temperature discontinuity. Al1 of
the differences from the radiation of a black body are determined in the given case
~
by the nature of variation of the parameters of the medium in the wave front, that
_ is, the structure of the front.
Shock compression and heating of the gas take place in a very narrosa layer,
the so-called viscous shock compression> The width of the layer is comparable to
the free path length of the gas molecules. Inasmuch as the rad.iation path length
is several orders higher under the same conditions, the layer is transparent and
has no influence on the shock wave emission.
In high-amplitude waves, dissociation, ionization and other processes
leading to the establishment of thermodynamic equilibrium in a heated gas take
place after the short-term shock compression. These processes also determine the
structure of the transition laye.r. In the conclusions with respect to the influ-
ence of the layer on the shock wave emission caution must be exercised, for the
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_ width of the layer approaches the path length of the radiation in the heated
_ gas.
In addition, with an increase in weight amplitude the radiant flux from
the shock-heated gas increases rapidly, and beginning with some amplitudes it
makes up a noticeable proportion of the hydrodynamic energy flux in the wave.
- The radiant heat exchange changes the structure of the front significantly. The
gas cools after viscous shock compression, radiating. Partially absorbing this
radiation, the cold gas is heated before the shock compression. ThE width of the
transition layer now is determined by the radiation path length the largest
scale of length. The structure of snrh a layer has the most direct influence on
the radiative properties of the shock wave.
However, before analyzing the effect of the frant structure, it must be
_ emphasized that even in the simple approximatitm of a temperature discontinuity the
sliock wave is not identical to an absolutely black radiator. Light is reflected
from the front of the wave, just as from the interface of two media that are
diffF.rent in optical respects a shock compressed heated gas and the cold gas
- before the front. The estimates proposed below indicate that this fact sometimes
must be taken into account.
Let us use the simple expression for the reflection coefficient with a
normal decrease in light
n, - no 3
r - ( n 1te ,
(5.1)
- where nl and no are the indexes o.f refraction of the gas on both sides of the
wave front (for example, in air of normal density n0=1.0003 for visible light).
The relation of the index n to the gas density p is described by the expression
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where K is the Gladstone-Daly constant, or the spec3fic refraction. Even with
tenfold shock compression of the air n1=1.003 and the reflection coefficient
turns out to be negligibly small r-2� 10-6.
In reality, the reflection coe�ficient is still smaller, for a real shock
wave is not an ideal discontinuity. Such an approximation is valid only in, the
case where the thickness of the frant is mucfi less than the light wave length. In
gases of normal density the thickness of the viscous sho ck compression is on the
order of 10-5 cm, that is, comparable to the wave length of visible radiation.
In this case the reflection coefficient depends strongly on the structure of the
transition layer. The latter fact was used by Horning, et al. [153, 1541 when he
investigated the structure of the front of weak (Mach ninnber 2-4) shock waves.
They compared the values of the reflection coefficients caYculated for different
angles of incidence and under different assumptions with respect to the structure
- of the front with the values measured experimentally. The primary difficulty
consisted in measuring the reflection coefficient which, as was expected, turned
- out to be very small within the limits of 10-5 to 10-7 for different gases.
~ Thus, it is possible to neglect the reflection of the light in shock waves
of small amplitude. Usually weak shock waves do not emit as an absolutely black
body for another reason as a result of transparency of the volume of the shock-
heated gas. Powerful shock waves in which ionization of the gas takes place after
c:ompression (causing their intense glaw) are of the greatest interest to us. The
presence of free electrons greatly decreases the index of refraction of the gas.
The propagation of elnctramagnetic waves in a plasma is determined by the value of
the dielectric constant which in the absence of a magnetic field has the form
4rc~2N ~ ^ (5.2)
e 1 - n~roa Y ~
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where W is the angular frequency of the electromagnetic wave, N is the ntunber
of charged particles per cm3 0f plasma, Y is the frequency of the electron
collisions in tfie plasma. It is possible to find the collision frequency from the
_ formula -
2 � f fl-AN i7,
Y- �
- For plasma the magnetic permeability u=1 so that the index of refraction
n=,r,-. Inasmuch as the imaginary part of tt-ie dielectric constant corresponds to
the absorption of the radiation, when calcula,ting the index of refraction only
the real part is taken into account.
Let us consider an example which is characteristic of our experiments.
A shock wave with a velocity D=14 km/sec is propagated through air of iiormal density.
The gas behind the front is tenfold compressed, heated to a temperature of
25000�K, completely dissociated and singly ionized (Z=1, N=1021 cm 3). From (5.2)
and (5.1) for the reflection coefficient of red light with a=6.5�10-5 cm we obtain
r=0.2%; for infrared radiation with a=1.3�10-1' cm r-0.5%. If the air in the wave
- is heated to 50000�K (D=23 km/sec), second ionization occurs (Z=2). Under these
conditions we obtain r-1% for red light and r-6% for infrared radiation.
Thus, with an increase in the shock wave amplitude the reduction
coefficient increases. Inasmuch as formula (5.1) does not take into account the
thickness of the front, it is possible to expect only significant reflection oi
the infrared radiation, the wave length of which is greater than the f ront wi3th.
Noticeable reflection from the front of the electromagnetic waves fram the ad.jacent
superhigh frPquency region is known to researchers studying plasma in shock tubes.
In our experiments the plasma approached metals with respect to the free electron
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concentration. Therefore the effects connected with distortion of the radiation
during reflection must be manifested more strongly.1
�1. Effect oP the Relaxation Layer
In powerful shock waves, the relaxation layer in which ionization, dissocia-
tion, electron excitation and other processes develop leading to the establishment
of therrnodynamic equilibrium in the shock-heated gas, is adjacent to the viscous
shock compression. Usually the width of the layer is determined by the ioniza-
tion relaxation of the gas as the slowest process. The poss3:bility of shielding
the radiation of the equilibrium-heated gas behind the front by this layer was
noted by the authors of 113, 32]. Let us consider this problem in ffiore detail here.
For estimation of the layer width let us use the paper by M. B. Zheleznyak
and A. Kh. Mnatsakanyan [73] in which the data were gathered on the structure of
the relaxation layer of shock waves in the air. With a wave velocity Io--14 km/sec
recalculated for the initial air pressure po=760 mm Hg, the width of the layer is
Q= 7 � 10-5 cm,
Now let us note the radiation path lengtfi uYnder these conditions. The
coefficient of photoionization absorption will be found by the Biberman-Norman
formula [91]
(5.3)
where N0 is the niunber of 3toms per cm3 0f ionized gas; E=E0(v, T) is the factor
taking into account the nonhydrogen-Iikeness of the absorption cross section by
the excited atoms (Figure 51); y is the ratio of the numlier of halflevels of the
atom corresponding to the given quantum ninnbers n and R to the analogous value
1
- It is known that the incandescent metals do not emit as an absolutely black body
as a result of the ref lection of light fram the inte rface.
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for the hydrogen atom; Eo is the statistical sum of the states of the atom.
The braking absorption coefficient will be found by the Kramers fornula
Z'N N
xW, = 3,69 � 10" 7,,/~� c'~ i. (5.4)
Ar
Xe
- Kr
1,S
' He
Key:
l.
LL
O,S - G
n
~ o
o (i
qs io y�io~rfi- ~
Figure 51. Calculation of the coefficient of photoionization
absorption by heated gases. Values of the factor E by the
data of [92, 100]
sec 1
In order to consider the effective decrease in the absorption as a resuit
of forced emission (see �1, Chapter III), the total absorption coefficient is
multiplied by 1-ehv/kT. Then for the radiation path length we have
f/l, (x', + x':)(1--c-Ar). (5> 5)
For example, 1et us calculate *_he path length of a quantum of red light
a=6.5'10-5 cm (v=0.46�1015 sec 1). Here, according to [91] in formul.a (5.3) the
factor ~=0.5. The splitting of the levels on nitrogen and oxygen is Y=15 judging
by [155]. The concentrations of the atoms, ions and electrons will be taken from
tables in [147]. After substitution of the numerical data in (5.3)-(5.5), we
ohtain R -6� 10-4 cm.
v
As is obvious from the presented estimates, the path length of a quantum
of red ligfit is an order larger tnan the thickness of the relaxation layer. For
radiation with a shorter wave length the path length is still longer so that the
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layer shields the visible and near ultraviolet radiation weakly. On the contrary,
in the infrared region of the spectrwn the shiel,3ing is significant. Thus,
for a=1. 3� 10-4 cm the estimates give the path length of lCV=10-4 cm comparable to
the layer thickness. Even if we consider that in the relaxation layer the concen-
trations Ni, Ne and the electran temperature T are lawer than behind the front and
we take the values that are hal.f the' equilibriumm values as the average for the
layer, we obtain kv=2�10 4 cm. In the last example the optical thickness of the
layer is
i ~
- s= S x, dr: = xv epeuii S dz = 0,3. ~ (5.6)
o (1) �
Key: 1. average
The intensity of the radiation normal to the front must decrease notice-
ably after passing through the layer
I = /oe-t = 0,710. (5.7)
The oblique beams will be attenuated still more strongly.
Now let us see haw the shielding capacity of the layer varies on varia-
- tion of the shock wave amplitude. With a decrease in amplitude, the temperature
of the shock heated gas decreases, and the radiation path length increases very
rapidly. As for the width of the layer, in the velocity range of D=5 to 14 km/sec
it varies nonmonotonically. The largest value of 1C=5�10-4 cm is reached for
D=10 km/sec. However, the radiation path length turns out to be much greater
(estimates by the gas parameters behind the front give Q,,=10-2 cm for a=6.5�10'5 cm
and k,,=2�10-3 cm for a=1.3�10-4 cm). Consequently, with a decrease in the shock
wave amplitude the relaxation la}*er. becomes more transparent.
For the velocities D>14 km/sec the information aUout the ionization
structure of the front is extrei;ely meager. D. A. Bronshten and A. N. Chigorin
[18] performed the calculations for three values of the velocity D=16, 47 and
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75 km/sec. For the initial concentration of the atoms after dissociation
NO=1020 cm-3 and a velocity D=16 km/sec the relaxation time will be t=3�10'9 sec.
If the shock wave is propagated- through air of normal. density, then after compres-
sion and aissociation in the wave front the initial atom concentration
Np=3�1020 cm 3 and, correspondingly, t=10-9 sec. Let us estimate the width of
- the relaxation layer as follows:
1 = tD/A,
where 8 is the average compression of the gas fcr the layer. After dissociation
of the air 6=6, and the equilib rium value of 6=11. As the average let us take
5=8. Then the width of the layer lC=2�10-4 cm. Now let us estimate the radiation
path length. As the averages for the layer let us take the values of the charged
particle concentrations and temperature half the equilibrium valu2s. Then the
calculations by (5.3)-(5.5) give QV=6�]_0-4 cm for a=6.5�1.0-5 cm and k.V=10-4 cm for
a=1. 3� 10-4 cm.
Thus, with an increase in the wave amplitude the radiation path length
approacnes the width of the relaxation layer. In order to be convinced of this
noteworthy trend, let us also consider the results of estimates for a shock wave
with a velocity D=47 km/sec. In this case the ionization relaxation time (for
Np=1020 cm 3) will be t=6.4�10-10 sec. In the recalculation for normal air density
ahead of the front t=3�10-10 sec, and the layer width k=2�10'4 cm (it is of
interest to note that although the relaxation time has decreased, the layer width
does not change). According to the data o� j181, setting the averages for the
layer Ne=1021 csn 3, Ni=5�1020 cin 3, Z2=4 and Te=6�104 �K, we obtain kv=10'4 cm
for a=6,5�10-5 cm and 2v=6�10-5 cm for A=1.3�10-4 cm. The radiation path lPngth
now is less than tfie layer thickness. .
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Let us collect the results of the estimates together; the degree of
transparancy of the relaxation layer wil 1 be characterized by its optical thick-
ness 1 zR/!C .
v
- D, km/sec 10 14 16 47
T(a=6.5�10-5 cm) 0.02 0.06 0.3 2
T(a=1.3�10-4 cm) 0.1 0.3 2 1
_ From the presented data it is obvious that as the wave amplitude in-
~ creases the relaxation layer hecomes less transparent for radiation. of the
equilibrium heated gas behind the front. Tne shielding first begins in the infra-
red region of the spectrum, and at sufficiently hign amplitudes it extends to
the visible region.
In experiments at high velocities the brightness temperature of the froiit
was noticeab ly belaw the air temperature behind the front (see Figure~30). In
red light this difference occurred at velocities of D=10 to 35 km/sec. In yellaw,
blue and violet sections of the spectrim: the lagging of the brightness temperature
occurred at somewhat higher velocities D=25 to 35 km/sec. The lagging of the
brightness temperature and also the difference in brightness of the front at.
different angles recorded experimentally indicate the shielding of the radiation
in powerful shock waves. Up to now this phenomenon was explained by the shielding
effect of the heated layer which is formed on absorption by cold gas ahead of the
short-wave radiation front of the shock wave. However, 1ay the estimates of
_ Yu. P. Rayzer and Xa. B. Zel'dovich 134-37]. This shieldi;xg becames noticeable
only at the air temperature behind the front T1.9�104�K (D=36 km/sec). At this
temperature the intensity of the red light emerging normally to the front must be
attenuated by 12%. In the e-kperiment tfie intensity is attenuated by 27% already
at T1=6�104�K when the radiant flux heating the gas ahead of the front is -5 times
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less than for T1=9�104�K. It is hardly possible to explain the results of the
measurements behind yellow, blue and violet light filters only oy tne effect of
the heated layer. Obviously, for T124000�K. In such shock waves in a heated gas
an electron avalanche develops immediately, and the relaxation time is determined
by the energy exchange tiine between the ions and electrons, which is proportional
to the atomic weight of the gas. These arglnnents can be confirmed, camparing the
relaxation times in argon and air by the available experimental data and the
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calculations. The atomic weight of argon is 3 times greater than the average
atomic weight of air. The initial concentration of the argon atoms is approx-
imately 2 times less, for the air dissociates. Therefore in argon the relaxation
time must be 6 times greater, which agrees with the data of [66, 73].
It is possible to e-xpect that in xenon, the atomic weight of which is
9 times greater than the average atomic weight of air, the relaxation layer is
much wider, and its shielding effect is stronger. Beginning with the above-
presenred arguments, we estimate the wI.dth of the relaxation layer in heavy inert
gas at T1=3�104�K. The results of the estimates in the comparison of them with
the average path length of red light for the layer appears as follows:
� Air Argon Krypton Renon
k, cm 2�10-4 1.1�10-3 1.7�10-3 2.2�10-3
SC~, ~m 6�10-4 1.4�10 2 9�10-3 5�10-3
It is obvious that in such gases as xenon and krypton the relaxation layer must
_ shield the radiation of the shock wave noticeably. Tn the experiments the bright-
ness temperature of the shock waves in xenon is appreciably less than the gas
- temperature after the front. The difference is especially high for the red section
of the spectrim (see Figure 32). The decrease in the b rightness temperature
toward the red end of the spectrum was observed also on emergence of the detonation
in krypton and xenon (see Figure 40). A reduction in brightness ~f the front was
_ recorded at a compaiatively low gas temperature behind the front when the shielding
of the radiation by the heated layer was absent. Unconditionally, at high tempera-
tures T1Z105�K and higher; a pawerful heated layer is foxmed ahead of the shock
compression whicfi has a decisive influence on the radiative properties of the shock
wave. However, as �or the reduction in brightness of the front detected experi-
mentally at temperatures of T1=2�104 to 6�1040K, it must be attributed to the
shielding by the relaxation layer.
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The experiment provided another proof of shielding of the radiation
by the relaxatian layer. On emergence of the detonation in heavy inert gases,
the absorption lines of multicharge ions were recorded. The number of lines
belonging to different ions is in accordance with the ionization composition of
the shock-heated gas (see Table 4 and the tables in the Appendix). Let us note
that the gas temperature in the heate4 layer was below 104�K in these experiments.
The presence in the spectrum of the lines �,aith excitation potential of -20 ev
cannot be explained by shielding by the heated layer.
�2� :3adiation Heat Elchange at the Shock Wave Front
With an increase in the shock wave amplitude, the radiant flux from the
front S=6Ti increases rapidly. The short-wave radiation is absorbed by the cold
gas ahead of the front, and this heats this gas to a temperature of T_.1 The
shock wave is now propagated through the advance-heated gas, and the temperature
after the discontinuity T+ is hi-gher than in the absence of heating. The shock-
heated gas cools, radiating, and its temperature drops from T+ to T,,.. Thus, on
propagation of a powerfixl shock wave the gas first is heated by the emission, and
experiencing shock heating, is cooled, releasing part of the energy which also goes
to the creation of the radiation flux S(Figure 52).
In gases of normal density the effect of the radiation on the structure
of the transition layer will become noticeable for temperatures of about T1=105OK
where the radiant flux S becomes camparable to the energy flux of the material in

the wave. The layer width is determined by the path length of the quanta with
energy of several tens of electron volts near the maximum of the Planck
lIn the next section it is demonstrated that the thermodqnamic equilibrium cannot
occur in the gas ahead of the front, and it is necessary to talk about its
temperature provisionally. Hawever, we have retained this notation in accordance
with references [33-37].
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distribution. In contrast to the less energetic quanta of visible and infrared
radiation these quanta are not so intensely absorbed by the.heated gas. Their
path length turns out to be at least an nrder'higher than the width of the lgyer
in which the ionization of the sfiock-heated gas develops. Therefore when 3.nvesti-
gating the structure of the transition layer in the large plan, the details
connected with ionization relaxatian of the gas disappear.
r_
- T
To
T~ Tf
T_
T
"o,,
Figure 52. Temperature profiles of shock waves of different amplitude
_ Table 6. Ratio of the Radiant Flux S=6Ti to the Energy Flux
of the Material poD3/2, %
T1�10-40K 3 4 5 6 7 8 9 10
_ Helium 3.9 4.1 5.3 7.7 11.2 14.4 17.7 20.2
Neon 4.7 6.9 9.4 12.3 14.7 18.0 22.0 25.9
Argon 4.3 5.6 8,4 11.8 14.0 16.7 19.9 28.5
Krypton 5.9 8.6 12.6 18.1 25.3 31.9 37.8 43.0
Xenon 6.7 8.7 12.1 16.5 21.2 27.5 35.6 44.0
Air 1.8 3.1 4.9 6.9 9.4 10.6 13.0 15.5
In Table 6 data are presented from which it is obvious that with an
increase in amplitude the radiant flwx increases faster than the energy flux of
the material in the wave. At the same time the energy losses to radiation in the
- shock waves are limited and usually small. The fact is that ahead of the front
the gas is not transparent for quanta, the energy of which exceeds the ionization
potential of the atoms and molecules. In addition to photoionization, other
absorption mechanisms o.ccur in molecular gases. Let us present the boundary
],13
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gases of the shock waves a beginning with which continuous absorption is observed
ir_ the gases (the values are taken from the book by A. N. Zaydel' and
Ye. Ya. Shreyder [148]).
Gas
Helium
Neon
Argon
Krypton
Xenon
Air
a, nm
50.4
57.5
78.7
88.6
102.2
190
At high temperature the flux Sco for the region of transparenc:y of the
n
gas is a small fraction of the total flux S. With an increase in temperature T1, olc
this fraction decreases still more. At the limit of very high temperatures the
flux S,, belongs to the Rayleigh-Jeans part of the spectrum so that the losses are
proportional not to the fourth, but the first power of the temperature.
The effect of the radiation on the gas parameters in a shock wave will
be taken into account if the radiation energy flux is included in the relation at
the discontinuity along with the energy flux of the material. The r elation
between the final and the initial parameters of the gas will be determined from
the expression (e is the internal energy)
1)0�11, ()0D,
p�� I- poD=, (5.8)
Vul) (e. NK~(~ u;0/2) ~ poD3l2 - 5~,.
It is important to note (and this is obvious from equations (5.8)) that
the final state of the gas depends not on the total flux S, but on the part S.
of it which belongs to the region of transparency of the gas ahead of the front
and goes to "in�inity" without inhibition.
Table 7 gives the ratio of the radiant flux S. to the energy flux of the
material in the wave characterizing the radiation losses and their influence on
the final state of the gas.
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From this table it is obvious that the radiation.losses in the shock
waves are limited. At low temperatures almost all of the radiation goes to the
region of transparency of the gas afiead of the front, and the fliix Sco=QTi
increases with an increase in the temperature more rapidlp than the energy flux
of the material. However, as the maximum of the radiated energy in the spectrum
shifts to the region of nontransparency of the gas ahead of the front, the situa-
_ tion changes the flux S. lags behind the energy flux material poD3/2. For
each of the gases there is a completely defined value of the amplitude (it
corresponds to the maximum of the ratio in Tab 1e 7), for which the radiation
losses and their influence on the final state of the gas reach the highest value.
The negligible radiation lasses in the air no more than 0.5% of the hydrodynamic
energy flux attract attention. Therefore for calculations of the air parameters
behind the front the flux S. is usually neglected in expressions (5.8).
Table 7. Ratio of the Radiant Flux S� to the Energy Flux of
- the Material pOD3/2, %

T,.10_40K 2 3. 4....5 ...6 7 8. .9. 10 12
Helium 2.8 3.2 3.9 4.5 5.6 6.9 7.4 7.6 7.4 7.2
Neon 4.4 4.7 5.2 7.1 7.5 7.6 7.6 7.8 7.5 6.5
Argon 3.5 3.7 4.6 4.6 4.9 4.8 4.7 4.5 4.3 3.7
Krypton 3.7 4.8 5.2 5.-6 6.0 6.2 5.7 5:3 4.9 -
Xenon 3.4 4.8 4.4 4.3 4.3 3.8 3.8 3.7 3.5 -
kir 0.4 0.5 0.5 0.4 0.4 0.4 0.4 0.3 0.2 -
In contrast to the air, the region of transparency of the inart gases
extends far in the direction of the vacuum ultraviolet. Hence, we have significant
_ radiation losses approaching 10%. When calculating tfie shock adiabats of inert
gases these losses must bE taken into account. The corrections to the gas
parameters behind the .front are easily found bp representing them in the form
pW=p1+Ap., u,o=u.+au.0, and so on. Separating the terms of different order of
1_15 ,
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smallness in the system of equations (5.8) and using the equation of state
e=(1/'(Y-1)) (p/p), it is easy to obtain the following expressions:
ofi.
Pt b - 1 p�[la ,
A P,0 8 2S.
Pi (Ta -1)z pap. ,
Aea, d (b -'l) 2So,
ei (b -1)2 paD2 '
nr._ 0167 e`~ A 0,08� nPW
_ 7't el Pi '
Here 6=p1/p0 =(y+l)/(y-1) is the shock compression of the gas. We found the
correction to the temperature using the interpolation formula e=aT1.5p-0.12
(5.9)
which describes the results of the exact calculations well (see the Appendix).
The expressions (5.9) are also applicable for calculating the corrections
to the gas parameters at the shock compression. For this purpose it is necessaYy
only that the flux S,, be replaced by the flux -(S-S.). Actually, in contrast to
(5.8) the relations at the discontinuity ha.ve the form
~~tu+ = PoD,
P} -I- P+u'+ = PoD', ,
(oD (e+ P+/()+ u+12) - S = poD3/2 ~5.10)
A specific representation of the influence of the radiation on the
parameters of the shock-heated gas can be presented by the following example.
A shock wave with a velocity Ik 36.5 km/sec is propagated through neon. Without
considering the radiation the gas parameters in the wave are ds follows:
T1=100 000�K, p1=10600 atm, pl/po=9.15. Considering the radiation we have
T=96000�K, p.=10700 atm, p,,,/p0=9.9; T+ 110 000�K, p+=10300 atm, p+ /po =7.3.
If we limit ourselves to the investigation of shock waves in gases of
normal density, the presented example illustrates, perhaps, the case of a strong-
est influence of the radiatian on the final state of the gas after the front.
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The radiation can be felt much more strongly on the state of the gas at the
_ front. This is caused by the fact that the radiant flux S-S,a increases with an
increase in the wave amplitude faster than the energy flux,of the material. For
small amplitudes the flux S-S.,, pertains to the Wien part of the spectrimm and
increases very rapidly with temperature T1. At high amplitudes when in practice
- all af the emission is absorbed in the heated layer, the flux is proportional
- to the fourth power of the temperature T1. From Tables 6 and 7 it is obvious that
the ratio 2(S-S.)403 increases monotonically with an increase in the amplitude.
The relations at the discontinuity (5.8), (5.10) supplemented by the
equation of state e=(1/(y-1))(p/p) can be solved directly without assinning small-
ness of the corrections. The increase in precision of the parameters of the
shock-heated gas obtained in this way does not exceed 1% for 2vTi/p0D320% these increases in precision will be approximate, for it is
necessary to consider the difference of the radiant flux S from QTi. In essence,
when the temperature profile of the shock wave begins to differ noticeably from
the ideal discontinuity, the relations at the discontinuity must be resolved
jointly with the radiation transport equations (3.29), (3.7). Iu addition, it is
necessary to be given the relation between the internal energy of the gas, its
density and temperature. .7oint solution of all these equations is a highly diffi-
cult mathematical problem. The situation is simpler with the gas parameters
behind the front. For any amplitudes the fYux S. is a small fraction of the
hydrodynamic energy flux in the wave. Therefore ezpressions (5.9) are applicable
for calcnlation of the corrections. 'There will also be no large error in consider-
ing the flux S..as part o# the Planck flux at a temperature TZ for the region
of transparency of the cold gas ahead of the front. Moreover, for quite large
- amplitudes when the radiation is almost campletely absorbed in the heated layer,
117 -
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it is possible to neglect the flux S� altogether, setting Tc,=T1, e,o~el, and so on.
Here the gas parameters in the wave front are more simply found, for the radiation
transport equations permit averaging over the spectrwn.
- In powerful shock waves the radiation has, althaugh significant, limited
effect on the state of the gas in the front. The heating temperature T_ is propor-
tianal to the radiation flux S-S,� and therefore it increases rapidly with an
increase in the wave amplitude. The amount that the temperature T+ exceeds the
final temperature T. increases correspondingly. At same temperature behind the
front T.=Tcr the Y;zating temperature T_ reaches T.. This temperature Tcr (equal
to approximately 300,000�K for air) can be called critical, for it separates the
_ two significantly different cases of the structure of the shock wave front. For
the temperatures behind the front T.>Tcr the quantum energy flux will suffice to
heat the layer on the arder of the path length in which the quanta are absorbed to
a temperature of T_>T,,.. However, such high heating cannot be realized, for the
heated layer would begin to emit intensely and would quickly cool to a temperature
of T.. The occurrence of the state with T_>T. would indicate that in the closed
system the heat is spontaneously pumped from the less heated layers of the gas to
the more heated ones a contradiction wi+:h the second principle of thermo-
dynamics.l Indeed, the energy picked up by the radiation from the gas heated at
the shock compression is reemitted and heats the thicker layers before the discon-
tinuity.
Thus, in waves of large, superc.ritical 3mplitude the shock compression
is propagated through the gas first fieated to a temperature of T_ T. Taking this
co
_ into account, for tfie gas temperature after the discontinuity T1 it is possible to
~
- lStrict proof of the impossibility of the state with T_>T00 is presented by
Ya. B. Zel'dovich [33].
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obtain the following expression [37]: T+ (3-Y)TCO. For Y=1.25 we have
T+-1.75 T.� If we use the intetpolation formula e=aT 1.5p-0' '12 considering incon-
stancy of the heat capacity of tfie ionized gas, we obtain T+=1.6 T..
The existence of a temperature peak at the front of a powerful shock
wave can be characteristically felt in its radiative properties. The width of
the peak is determined by the path length of the quanta with energy hv-(3 to 5) kT
which plays a primary role in the radiant cooling of the shock-heated gas. The
low-energy quanta (hv �kT), in particular, the quanta of the visible light, are
absorbed by the ionized gas more strangly. The region of the temperature peak for
these quanta is nontransparent. The brightness temperature of the front must coin-
cide with the temperature T+, that is, be higher th an the gas temperature after
the front.
In the experiments no noticeable excess of the brightness temperature
of the front over the gas temperature behind the front was observed. Moreover,
at high shock wave velocities the inverse picture was observed. The divergence
should be considered the result of radiation shielding. Measuring the b rightness
of the front at different angles, it was possible to estimate the optical thickness
of the shielding layer and reproduce the true temperature of the gas radiating to
the olitside. This temperature always turned out to be above the temperature of the
gas atter the front (see Figures 30-33).
On emergence of the detonation in xenon and krypton, the maximum in the
brightness temperature distribution over the spectriun was recorded (see Figure 40).
As we have already noted, the drop in brightness temperature toward the red end
of the spectrum obviously was caused by shielding of the radiation by the relaxa-
tion layer in which ionization of the shock-heated gas developed. The transparency
of the region of the temperature peak for ultraviolet radiation could be the
cause of a decrease in the b rightness temperature taward the other end of the spec-
119 .
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In the conclusion of this section let us discuss the papers by Griem,
- L. M. Biberman, K. N. U1'yanov and N. M. Kuznetsov j156-1581 indicating that the
radiation losses sometimes lead to disturbance of the thermodynamic equilibrium
in an optically thick medium, which, in turn, is felt in its radiative properties.
Although we are investigating optically dense shockwaves, this has direct bearing on the layer
of gas several. radiation path lengths wirie radiating to the outside. According to
reference [157], the equilibrium population of levels with the main quantum
_ number n is insured if
_ Ne > 7� 10'e (7h~;I. P (kTallz)',,
wherE IZ is the ionization potential of an ion with the charge Z-1. The estimates
show that for normal gas density ahead of the front in the temperature range of
T1=104 to 105�K, the condition of equilibrium population of the excited levels is
satisfied. According to reference [158], the temperature difference of the
electrons Te and the ion temperature Ti in a stationary optically thin plasma is
'
Ti?,T` �3,5�10-' A~� (~~2 k7Z + 2
e .
where A is the atomic weight of the ion, A is the Coulomb logarithm. The estimates
give (Ti Te)/Te 4 is established in the charge channel at 1> 8d. If an increase of charge
weight plays no role, then selection of the highest possible ratio of 0/d is
- justified. The shock wave temperature also increases in this case. Thus, for
charges with 0 = 60 mm (0/d = 7.5), a velocity of 16.7 km/s and temperature of
32,O00�K werE measured. However, the weight of these charges is fourfold greater.
Z'he type of radiation pulse upon detonation of a shaped charge can be judged by
Figures 10 and 41. With the selected dimensions, the glow time of a stable shock
wave in the charge channel is 5 microseconds. If a tube of cardboard or other
dense material not more than 160 mm long is attached to the charge, the shock wave
propagates through it without appreciable attenuation and the qlow time is extended
to 17 microseconds (Figure 59).
Sometimes, for example, during photographic recording of the time-integral radia-
tion by spectrograph or in measurements of radiation with a calorimeter, it is con-
venient to have a calibrated square-wave pulse. The time of stable shock wave
formation is reduced from 5 to 2 microseconds if one uses an elongated charge (L =
= 180 mm), the bottom of which is not flat, as in Figure 9, but is in the form of
a conical recess. One can reduce th2 leading edge of the pulse even more--to 0.1
microsecond. To do tnis, the initial part of the channel where a stable shock
wave is established must be separated by a thin opaque screen (for example, carbon
paper). The screen is destroyed by the shock wave without introducing appreciable
disturbances. The trailing edge of the pulse is cut off within approximately 1
microsecond when the shock wave encounters a quartz or glass window attached to the
end of the accessory tube (Figure 60).
ThP results of ineasuring the brightness temperature of a stable shock wave in air
with velocity of 13.6 km/s are presented in Figure 39. The temperature fluctua-
tions in tirtie and to the channel cross section did not exceed + 1,000�K. A tem-
perature variance was included in this same range from experiment to experiment.
= 142
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The brightness temperature was approximately 1,O00�K lower for charges manufactured
from TG 50/50. Avoiding inhomogeneities in casting the charge and initiating the
charge strictly along the axis, it was possible in some experiments to reduce the
temperature fluctuations to + 400�K.
It is obvious from Figure 39 that a shock wave in a channel radiated like an ab-
~ solutely black body with temperature of 24,000�K over a wide spectral range of a=
= 220-1,300 nm. The radiation spectrum was conoinuous. The lines were not record-
ed even on spectrograms with resolution of 0.1 A. In this regard ttie proposed
soures is similar to incandescent lamps a1tYough it differs from them by tenfold
higher brightness temperature.
Having.replaced the air by another gas, one can increase the radiation temperature
and can penetrate the vaccum ultraviolet region. In several experiments the charge
channel was filled with neon; in this case the temperature increased to 32,000�K.
The temperature was raised to 40,O00�K when the channel was filled with argon.
However, transient shielding and instability of the plane front complicated pro-
duction of stable radiation pulses in argon and heavier inert gases.
r�io~�oK
J
100 #00 6OO 11f, NM
Figure 61. Dependence of Brightness Temperature of EV-39 Souscce on Radia-
tion Wavelength Measured by Means of Explosive Brightness
Standard
Thus, shock waves in air formed upon detonation of a shaped charge were a suffi-
- ciently stable radiator. The source described here was used by the authors as a
brightness standard in laboratories and under field conditions. Its capaba.lities
are illustrated i.n this regard by Figure 61, in which the dependence of brightness
temperature of the EV-39 source on wavelength X is shown [13]. The low weight and
"pocket" size, the independence from an electrical system and other power sources
and the absence of noise typical for pulsed sources with an electric charge make
this radiator a convenient means of investigating explosive processes.
2� Installation of an Ultraviolet 3hock
The effect of powerful ultraviolet radiation pulses on solids is accompanied by a
number of interesting physical and gas-dynamic phenamena. These phenomena can be
studied experimentally by means of special explosive installations in which a
strong shock wave is radiated in an inert gas [9-11). These installations are
similar to existing pulsed lasers by the radiant flux density and are far superior
to them in the value of the radiated energy.
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We achieved the maximum radiant flux density from the front of a shock wave in ex-
periments with helium. At shock wave velocity of D= 78 km/s the density of the
ultraviolet radiation (shielding of which can be disregarded) was estimated at
S. = 3�108 W/cm2.
However, development of devices designed to investigate the effect of radiation on
matter consist not only in producing maximim fluxes from the wave front but in
providing those geometric ratios which would permit fuller use of the radiated en-
- ergy to affect the target being investigated. In this regard devices used to
- achieve high shock wave velocity were ineffective. It follows from formula (3.16)
for a disk radiator that the flux density on the target depends on the square of
the sine of the angle at which the radiator is visible. Therefore, the flux densi-
ty on the target (D = 3�10 8 W/s2 could be produced only for a very short time, on
the order of 10-7 second, when the wave would be in the immediate vicinity of the
irradiated surface. The integral energy density in ti.me E_ r~ d` distinguished
on the target would also be low, approximately 10 J/cm2. ~
The weight of the charge, which was limited to 1 kg in our experiments, is also no
less important when designing the installation. To compare explosive radiation
sources to each other, it is convenient to introduce the efficiency of the source
Is S
,q = Gq (6.1)
where E is the radiant energy density released on the target during operation of
the installation, S is the output cross-sectional area where the taiget is placed,
G is the weight of the explosive charge and q is the heat value of the explosive.
Devices to achieve record velocities and temperature had an efficiency of only
r1 ti 0.001 percent.
An explosive radiation source, under the effecti of which intensive evaporation and
flight of different solids was detected, is described in [9]. The sources was a
shaped charge filled with argon (Figure 62). The inner walls of the channel were
lined with polished aluminum foil that reflected part of the radiation to the tar-
_ get. The mean velocity of the shock wave in the channel was D= 9 km/s and the
brightness temperature in blue light was Tya = 26,000�K.* The plane front lost
stabil.ity and began to bend near the walls approximately 10 microseconds after
_ generation of the shock wave. Its temperature dropped in this case to Tya =
= 17,000�K.
The radiant flux density ID and the surface energy density E near the target axis
were calculated from the results of ineasuring the brightness temperature of the
front in blue light and its position in time. The inhomogeneity of the brightness
of the front through the channel cross section was taken into account in the cal-
culation. It was assumed that the shock wave radiated like an absolutely black
body up to the transparency threshold of argon. Circular regions of the mirror
*
The value of brightness temperature refined compared to [9) is presented here.
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Ar I
~
I
I
s
Figure 62. Explosive Radiation Sources 1--lens providing plane detonation
front; 2--charge of cast TG 40/60 weighing 400 grams (outer di-
_ ameter of 60 mm, innar diameter of 45 mm and length of charge
of 165 mm); 3--polished aluminum foil; 4--target
Mdm/cM t (1
2
1 Z
~
J
.(2)
0 10 20 30 t, vNcsK
Figure 63. Flux Density 4) with Different Positions of Target: 1--x = 21
_ cm, E= 15 J/cm2j 2--x = 27 cm, E= J/cm2; 3--x = 33 cm, E_
15 J/cm2
Key:
1. MW/cm2
2. Microseconds
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r
Figure 64. Explosive Radiation Source: 1--lens providing plane detonation
front; 2--charqe of cast TG 40/60 weighing 400 grams, diameters
of 84 mm and length of 70 mmj 3--polished aluminum foil; 4--
target
~ MBm/c~ ~ El ~
S
~
J
1 / 1
!
0 (2)
/O TOQMRaK
Figure 65. Flux Density 0 with Target in Different Positions: 1--x = 15
cm, E= 20 J/cm2J 2--x = 25 cm, E= 31 J/cm2j 3--x = 27 cm,
E = 32 J/cmz
Key:
1. MW/cm2
2. Microseconds
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image of the shock wave front bounded by beams at angles of 8p (without reflec-
tion), 61 - A0 (single reflection), 62 - 61 (double reflection) and so on, are
formed on the reflecting walls of the channel. In this case formula (3.16) for a
disk radiator acquires the form
cU = noT* Isin' @o -I- k(sin' 91 - sin= 80) -I- k' (sins 9t -
sin' 91) -I- . . . -I- k" (sin' 9� - s6n2 0�-i) -i- . . . l~ (6.2)
where K is the reflection coefficient of foil and a is a multiplier that takes
into account the opaqueness of argon for photons hv > 15.7 eV. According to
[148], the reflection coefficient of aluminum is weakly dependent on the angle of
incidence and hardly varies in the spectral region of interest to us. The mean
reflection coefficient for the spectrtan was assumed equal to k= 0.5.
The results of calculating the radiant flux density 0 and energy density E on the
target are presented in Figure 63. There is an optimum distance for installation
of the target x= 27 cm for which the flux density 0 and energy density E are max-
imum. The shock wave reached the highest amplitude at this distance. The contri-
bution of reflection from the foil to energy E comprised approximately 30 percent.
The efficiency of the source was estimated at r1 = 0.01 percent.
The source described above was used to investigate the effect of powerful radiation
- with continuous spectrum on a salid. A number of interesting results was obtained.
However, some deficiencies of the source were also determined during the experi-
ments. More than half the explosive products of the charge flew off to the sides
and did not participate in formation of the shock wave in the channel. Z'he wave
due to detonation of the channel walls was intensified only toward the end of ac-
tion of the source when the temperature near the walls decreased due to bendi.nq of
the front. The aluminum foil with which the channel walls were lined reduced the
shock wave amplitude somewhat.
Experi.ments were conducted from the results of which a more improved design of the
source was developed (Figure 64). The latter is a charge cast from TG 40/60 in
the form of a cylinder with seven conical recesses, placed in a tube of polished
aluminum foil. The tube diameter is two times greater than the channel diameter
of the source of the old design. The mean velocity of the shock wave when the
source is filled with argon is D= 11 km/s and brightness temperature in blue
light is 30,000�K. The results of calculating the radiant flux density (D and the
energy density E at the center of the target are presented in Figure 65. The max-
imum flux density 4) = 6 MW/cm2 is reached near the charge at x= 15 cm. The amp-
litude of the shock wave is highest at this location. The integral energy density
in time E is maximum when the taxget is installed at a farther distance, x= 27 cm�
Although the flux densa.ty on the target 0 decreases in this case, the time of oper-
ation of the source and the energy E increase. The efficiency of the source at
this distance is n= 0.07 percent.
It is significant that the source of new design permits irradiation of a target
84 mm in diameter (the maximcun target diameter was 40 mm in the previous design).
Becaiise of this, evaporation and scattering of the target material proceeded un-
der conditions similar to one-dimensional, which facilitated analysis and inter-
pretation of the results. The f.lux density distribution (D through the target
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radius is presented in Figure 66. The nonuniformity of illumination initialZy in-
creased (it was maximum at a distance of y= 4 cm from the wave to the garget) and
then decreased as the shock wave approached the target. Reflection from the tube
_ walls was not taken into account in calculations of distribution but it is quali-
tatively clear that it reduces the nonunifomtity of irradiation.
Experiments were conducted on evaporation of sulphur targets to compare the source
of the old and new design. The rate of rise of the luminous threshold of the va-
pors comprised 0.8 km/s for the old design and 1.1 km/s for the new design. More
intensive glow of the vapors was also observed in the latter case.
91/0o
Q9
47
o,s
Figure 66. Flux Density Distribution 4> Through Target Radius, Related to
Density (Dp at Center (y is the distance from the shock wave
to the target)
By using inert gases heavier than argon, one can reach higher temperatures at low-
er velocities D. Although the region of gas transparency decreases in this case,
an increase of temperature leads in the final analysis to an increase of flux
density (D on the target. The energy density E released on the target increases
even more strongly since the operating time of the source is extended.
Experiments were conducted in which the source was filled with xenon. To avoid
losses of the scarce gas, the source was filled by preliminary evacuation rather
than by purging. Changes were introduced in the design of the source for this
purpose compared to Figure 64. A charge with foil and the target were inserted
in a glass tube hermetically sealed on both ends by plates. The charge was ini-
tiated by a lens through the plate. The velocity and temperature of the front in
blue light at the beginning of operation of the source comprised D= 12 km/s and
Tya= 55,000�K, but dropped to values of D= 5.3 ]rn~/s and Tya = 30,O00�K within
27 microseconds. Despite the fact that xenon is transparent only to photons of
hv < 12.1 eV (argon is transparent for hv < 15.70 V), the flux density 0 and energy
density E increased appreciably (Figure 67). When the target was installed at dis-
tance of x= 14 cm, the flux dersity was maximum, lo = 15 MW/cm2. The integral
energy density in time was maximum at x= 21 cm and was equal to E= 130 J/cm2;
the efficiency of the source for this distance was estimated at n= 0.3 percent.
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12
s

;a
# - IO ~dm/tNr (l)
E- dOJar/cr � (2 )
C-.lJI~NCN~
~
I I E-IOSAac/avt
/ /
S
~P76M
I
/
S~I~LM ~
j I J
SJdar/cwt
i
. s ~61
Af zip ls f ARpf ~
3)
_ Figure 67. Flux Density 4~ and Energy Density E at Center of Target With
Source Filled With Xenon: the solid curves correspond to foil
reflection coefficient of 0.5; dashed line--without regard to
reflection
Key:
1. W/cm2
2. J/cm2
Key:
Z
I
3. Microseconds
4
l
Y
" !0 20 t,.v,rciK (2 ~
Figure 68. Flux Density 0 at Center of Target Ins+:alled at Distance of
x= 27 cm with Different Initial Pressures of Argon: 1--
pO = 50 mm Hg (E = 14 J/em2); 2--pp = 100 mm Hg (E m 18 J/cm2);
3--po = 300 mm Hg (E = 27 J/cm2)j 4--po = 760 mm Hg (E = 34
J/cmz)
1. MW/cm2 2. Microseconds
The source was filled with xenon to produce harder radiation with photon energy
up to hv = 21.5 eV. The mean wave velocity on the sQCtion of x= 27 cm was D= 13
km/s and temperature was Tya = 30,000�K. Tha radiant flux density reached (D = 4
MW/cm2 and energy density E= 30 J/cm2.
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Table 10
Pe. IItIR HCJ I 7150 I 300 - I 100 1 50
y, CM 20 8 1 20 8 i 20 8 i 20 8 i
D, xm/S 9.8 f0.4 10.2 W.0 W.6 10.8 l0�,6 11.2 11.4 1L 0 11.3 11.8
7' � l 0'9 K 26 29 28 24.5 27 28 23.5 26 27 23 25 26.5
The use of different inert gases in the source permits one to study the effect of
the spectral composition of radiation and the density of the surrounding medium on
the target. The parameters of the source when it was filled with argon of reduced
density were also measured in this regard. The values of temperature and velocity
of a shnck wave for three distances y to the target (x = 27 cm) at different
initial argon pressure are presented in Table 10.
Although the temperature does not vary very strongly with variation of the initial
pressure, the difference in the fluxes is significant (Figure 68). The difference
is even greater for energy E since the wave velocity increases with a decrease of
pressure and the operating time of the source is reduced. The energy E decreases
by a factor of 2.4 upon transition from initial pressure pp = 760 mm Hg to po = 50
mm Hg. But if one takes into account the energy released during the same time,
for example, during the first 22 microseconds, this difference decrases to a fac-
tor of 1.6.
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�3. Efficiency of Explosion Sources
Under laboratoxy conditions when the weight of the used explosive charge
is limited, it is possible to achieve an increase in radiant energy only by
increasing the efficiency of the source. Its highest value n=0.3% was obtained in
a blast source with xenon. This is approximately 100 times more than in ordinary
devices designed to obtain powerful shock waves. The preliminary results of
- several experiments indicate that as a result of further improvement of the struc-
tural designs of the source it is possibZe to achieve an efficiency of n=1%. For
this purpose it is necessary to use a sufficiently strong tube which will not be
= destroyed on passage of the shock wave and which at the same time will insure
slower damping of the wave. Between the charge and the walls of the tube it is
necessary to leave a wedge-shaped gap, as a result of which the flight of the blast
products to the sides will also be used for the creation of a shock wave in the
tube. It is necessary to use a higher quality mirror coating which is obtained by
depositing aluminum in a vacuum. Significant reflection in the ultraviolet region
can be achieved if we avoid ccmtact of the coating with air, for example, immed-
~ iately after deposition, fill the tube with an inert gas 1148].
For further significant increase in radiant energy yield, tlieoretically
new solutions are needed. The source efficiency introduced in the form af (6.1)
is in essence the product of three cofactors:
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~l = ~lt~la~ic~
(6.3)
where q, is the energy transfer coefficient from the e$plosive charge to the shock
- wave, n2 equals the efficiency of the shock wave as a radiator, n3 is the radiant
energy transfer coefficient from the shock wave to the target. Let us discuss
each of these coefficients in more detaii.
The energy transferred to the wave is made up of the internal energy of
_ the heated gas and its kinetic energy. In a powerful shock wave they are equal to
_ each other, and for a unit mass of gas it is possible to write
c - u2/2.
(6.4)
Expressing the gas velocity in terms of the front velocity u=(2/(y+l))D,
we obtain the following expression for the energy transfer coefficient to the wave:
p8~2v ~ (6.5)
- where V is the initial volume occupied by the gas (the volume of the working
chamber of the source), D is the average shock wave velocity, G is the weight of
the charge, q is the calorific value of the explosive.
- Shaped charges give higher shock wave velocity in the required direction.
The coefficient nl is higher for them. For example, the charge which we used
which had seven shaped depressions created a shock wave with an average velocity
of D=11 km/sec in argon. The charge cast without the shaping and having 1.3 times
more weight created a shock wave with an average velocity of D=8 km/sec in the
- working chamber of the source. Thu.g, as a result of shaping the coefficient
nj was increased by 2,5 times.
A significant effect can be achieved on going over to high-density gases.
Although the average shock wave velocity is somewhat lower in this case, the
combination pOD2 increases. Thus, on going from argon to xenon, the average
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velocity in the section x=27 cm decreased altogether from 11 to 10 km/sec, and
the density po increased by 3.3 times. As a result the energy transfer
- coefficient increased by 3.3 times, reaching a value of n1=18%. The dependence
of the coefficient on the density is such (Figure 69) that on filling the source
with xenon with pressure of p0=3 to 4 atm it is possible to approach a va7.ue of
n1=50%. There is a limit somewhere here, for the blast products expand in all
directions, and part of the charge energy is constmmed on creation of the shock
wave in the surrounding air. If the charge is separated from the air by a massive
rigid shell, then this limit can be shifted away.
P,
111 .
s
� / I  f pl, a/x (1)
w Figure 69. The coefficient nl as a function of gas density
p0 constructed accor.ding to experimental data
- Key:
1. g/liter
The greatest reserves for increasing the efficiency of b last sources con-
sist in increasing the effectiveness of the shock wave as a radiator. The work
done by a piston creating a powerful shock wave in a gas if it is reduced to a
unit time and a unit surface of the front is
A = nl� = P�u'D = (v :f4 - ? ' PoD'� (6.6)
f The energy emitted .from the unit surface of the front per imit time is
s = QQTI1
(6.7)
where a is the factor considering the opaqueness of the gas affiead of the front
for the quanta hv>I. Then for the sfiock wave-emitter efficiency we have
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(Y + 1)2 ao7'4
.
~1~ _ -P4l
From Table 11 it is obvious that with an increase in the temperature
(6.a
_ the coefficient n2 first increases and then decreases (this smooth dependency is
distorted somewhat by the peculiarities of ionization in each specific gas). For
_ each gas there is a defined temperature range in which the radiation yield is
maximal.
Table 11. Coefficient n2 for Different Temperatures, %
r�fo-4�x
14 1 in
llo
2,7
2,5
2,8
3,6
4,5
5,0
/,A
4,7
4,1
4,6
5,2
Ne
2,47
3,2
4,5
4,8
4,8
4,8
4,9
4,8
4,0
3,8
3,4
Ar
2,4
2,9
2,8
3;1
2,7
2,6
2,3
2,7
2,4
1,9
1,6
K r
2,9
3,2
3,5
3,8
3,9
3,7
3,5
3,1
-
-
-
Xe
3,1
2,8
2,8
2,7
2,5
2,5
2,5
2,3
-
-
-
Helium and neon are distinguished by high value of the energy deexcitation
coefficient n2=5%. The application of these gases is expedient at temperatures
above 60000�K when, along with high efficiency, large radiation flux densities
with respect to absolute magnitude are achieved. Accordingly, experiments were set
up [165] in which couvettes 25 mm in diameter and the devices described in �3 of
_ Chapter II were used. For several microseconds the shock waves glowed with a
temperature of -100,000�K. The radiant flux density was estimated at 108 watts/cm2.
The deficiency of the devices was the low energy transfer coefficient to the wave
nlZl%. For gases with high atomic weigh the deexcitation coefficient n2 is
smaller, b ut it is higher than the energy transfer coefficient to the wave nl so
that on the whole the efficiency of the source gains. Obviously the shaped
charges used in combination with xenon or krypton insure the highest radiant energy
yield.
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It is possible to determine the effect of the initial gas pressure on
the efficiency of a shock wave emitter according to the data in Table 12.
Table 12. Coefficient n2 for Different Argon Pressures, %
_ T- 10-40K
2
3--
4-
pO=760 mm Hg
2.3
2...4
2.9
p0=300 mm Hg
4.2
5.3
5.6
p0=100 mm Hg
9.2
12
14
pO =50 mm Hg
15
22
23
The radiation yield 3ncreases quite rapidly as the gas pressure drops.
The growth is such that it almost compensates for the decrease in the energy trans-
fer coefficient to the wave (the product nln2 at p0=760 mn Hg is a total of 1.2 times
greater than for p0=50 mm Hg). On the other hand, if the pressure increases above
atmospheric, the variation of the coefficient r11 slows (see Figure 69) whereas the
value of the coefficient p2 persistently decreases. Therefore the optimal initial
_ pressure insuring the highest source efficiency must be realized. According to
the data presented in Figure 68 for argon this pressure is approximately equal to
atmospheric pressure.
Intentionally selecting various gases, we have complained aany times that
in nature there is no gas with such a high atomic weight as xenon and with such high
ionization potential as helium. As a result of the high atomic weight this gas
would be heated to high temperatures with effectiveness energy transfer to the
wave. As a result of the high ionization potential, the cold gas ahead of the
front would remain transparent in the far ultraviolet region so that a significant
pronortion of the radiation from the heated gas would be emitted to the outside.
Considerations ahout this question have led us to the conviction that a medium with
the required properties can be ofitained axtificially.
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T �/O'~'M
~ ' Ce 5 Et Ne Ar
S - M 11
Nt
~
.I -
2 -
~ S /O IJ D MM/CCAf ~ 1~
Figure 70. Shock adiabats of alkali metal vapox and inert gases
Key:
1. km/sec
_ All of the alkali metals have low primary, but quite high secondary ionization
potentials. The estimates which follow below indicate that the radiation of a
powerful shock wave propagated in alkali dietal vapor is capable of singly ionizing
the vapor far ahead of the front. However, the singly ionized vapor absorbs quanta
weakly with energy less than the second ionization potential. Therefore as a
result of the fast ionization of the body of the vapor powerful radiation begins
to reach the target iminhibited.
Let us try to substantiate this picture quantitatively. In Figure 70 we
- see the temperature of shock-heated vapor as a function of the wave front velocity
(the initial vapor temperature was assumed equal to the boiling point at atmospheric
pressure; see the Appendix). A comparison with the analogous relations for inert
gases which are also presented in Figure 70 is of interest. The ener,gy expenditure
on the primary ionization af alkali metals is much less. Therefore in practice
for equal atomic weight (ANe=20.18 and A,Na 22.99, AK=39.10 and AAr 39.94, AKr 83.80
and ARb=85.48, AXe=131.3 and AcS=132.9) higher temperatures are reached in the
alkali metal vapor. The noted characteristic feature itself leads to noticeable
increase in tfie energy deexcitation coef.ficient of the shock wave.
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Figure 71. Calculation.of the fliix density in the center of the target
_ Let us demonstrate that the radiation is capable of quite fast ionization
of the body of the vapor separating the front and the target. Alkali metal vapor
at a temperature of -1 ev in pxactice is entirely ionized. The expenditures on
eating the cesiinn vapor to this temperature, for example, are 6.9 ev/atom. In
1 cm3 of vapor under atmospheric pressure at the boiling point (963�K), there are
7.6� 1018 atoms so that the expenditures on heating 1 cm3 of cesitmn vapor amount to
8.4 joules. For heating a column of vapar 1 cm2 in cross section and 30 cm long
_ it takes 250 joules. At the temperature behind the front T1=105�K this energy is
emitted from 1 cm2 of front surface in -0.5 microseconds. Thus, fractions of
microseconds are needed for the ionizatian of the body of the vapor separating the
- front and the target. As a result, inasmuch as the ionized vapor absorbs very
weaklyl, the powerful radiation reaches the target.
Beginning with the fact that the quanta less than the second potential of
cesium(hv