CHERENKOV'S EFFECT AND THE COMPLEX DOPPLER EFFECT (USSR)

• Document Type: CREST
• Collection: General CIA Records
• Document Number (FOIA) /ESDN (CREST): CIA-RDP82-00039R000100100025-3
• Release Decision: RIPPUB
• Original Classification: C
• Document Page Count: 6
• Document Creation Date: January 4, 2017
• Sequence Number: 25
• Publication Date: January 6, 1951
• Content Type: REPORT

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e ~ p~0i1 ~ S ~"FECT AND THE CO~LE~ DOP
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a~ L. Iryu~b~'ekiy end Yap 8. p~e~Ynberg
by A. I ~ Ak~Y`ez~,
8888 Vol LxXI~I~ No 1~ Cpp ~~-~9~
8oaroes Doklad3~" Akader~ii Nauk
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A, t. Akhiyemer
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Q~ ~ I~r Lyub~arekiy ~
Ya ~ 8. Faynberg
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There are many oomplex wave~uides in whioh ooz~ditions are suoh that
the base velooity oP wave propagation is less than the velooity of light
P
in a vaouum these aonditions~ na~nely~ be~sg oreated by tk:e speoial
disposition o~ metallio partitions without tlae use of dieleatrios~ when
a ohar ed artiole moves unifor~1.~r along euoh a system,~e velooity e~
1 g p
r~~s~l, , � p?e;ales} exoeeds the phase velooity of wave propagation
dust as when a oharged partiole moves in a dieleotrio~ ther? eleatromag-
netio waves are radiated ~Cherenkov'Q effeot)~
Thin radiation oan be :simply determined in the ease of linear peri-
l
i
odio atruotutiea whioh are a series of identioal oorapartmenta interoon-
i
i,
~ neoted with esoh other by apertur�e through whioh a oharged partiole
~ r
mouse
We shall seek the transverse part of a veotor potont~al ~ in the
i
Following form:
y .s
A
~
~
where A (r) ~ exp (it~~ t) represents the various wave a whioh are able to i
be ro ated in the periodic atruoture in the abaenoe of a oharge (NOT~c
p p~
K s is the set of oontinuous (K } and disorete (e) parameters 9_ ,,~i
r, ~
oharaoterizing the wave q are oertain funotions of time ~ The spatial
Y ~
is
fvnotion A (r~ oan be r�prea�nted ~.n the following form: ~ r
` ~ _ ~ ~r
~ J rwM I~? ~f , , /1 ~ r~ C K ~ err
,
.t ~ k where ~ is a periodio funotion of th�x coordinate (along whioh the
1 ~ ~
r~
;~=i ' ~ . Oo artmenta are arranged) ~ the f~uaotion bei:ag norma;L~ red sooording to
~
the following oondition s
ti
~~1 ~ ~e- ~~4
k ' 1

~q i ~ ,
~,3` ; ~ ~
I
-s ~
c i , 4,
a x
f
~ ~ r i ~ ~ ~ ' ' t ~
i d ~ 1 i a ~t~ ~ ~ ~ '~i r p c ~ i
+
'p T ''r ,t ~ 5'
,y,~ ti a : ~ r a. ~
(,}J,~ ff
~ i ~~.~tl~Y ~.7f "'n~5 era ~~c1 k.~S f~ il~, .fi
1 '1+'+ t~
r y~~~ ~^7
z ~ {i _~rs r+~l.~~~~, hl st...A sal ~ ~ t - _ Y,
Y: C. q 6Y
i ~ ,
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r _
C.
~ ~
~ ~ r r
4
A ~
~ f
~ ~ ~ ~ r
~t ~ ~
`a
~ ~e
Q, ~ ~ 1/ 'C ~ ~ ~s
(U is the vole off" one aompartt and is the period o� the etrua-
I tore)
Tho !'uunotion q (t) eatiai'iea the equation oi' an oaoillator of ire-
~ ,
quenoy ~ ~ whioh (i.e., oaoillator) is under the action o� a roroing
' �oroe ~
� ~ ~z _
~ ~ ~ a (1)
where
~
C
r
is the ourrent density aonn�oted with the partiole f N is the numi�
I
ber o� a artments and V is their volume)
~p 3 n ~
The energy a� the aleotromag~netio field equalA t
z
~w ~
N C a
2 ~
If radiation ooaure, then K is proportional to t for t-~ oo ~ ~uoh
i
r
an asynaptotio ~havior holds true only for reeonanoe between (a) the
i
i
r
eigenosaillations (that is, the aharaoteristio or proper oscillations)
i
q ~ o� the asoillators and (b) the forcing (oroe f~ (t) (NOTB s see 2~
r and 3 in the Bibliography),
f
t
r t
When a charge a move� uni:~~rm1y with v�looity v along the x-?axis,
then equation (1) above assumes the Following Farm:
' O0 /~ryy 2 7T 17
v 1 I~ /~i ~ 2
r
~ a ~ n=~~
~,n
~ x ;
~r. a a. ~x,a, o~ e ~ X f .
(where ~ A and
~ ~
0
e is the unit vaotor o� polarization) j namely, along the x-a~ais the
value o� tha current d�nsity ~ is s ' .
~ ~
~X -
r ,
r
' ' ~ The �oroe ie oharaaterized by the speotrum of frequenaiess
~
,
~r
, d~,~� IG - 'ti
~ r F ~
~1 �~e ~

vv ,
~ ~ 4~
1 k
i~~ ! s
i I ~a ~ ~
x a )r ffi t ~ n , ;~r ~ ,
:i~ t ~~~~S ~i s.. 31~l~~~ : '~saAV tlR�~-u ~ r~M
)~r 1 ;i �4 ~ r4~1 ,9..ri a 15~t~;~~t 11~, io. ~
x ~ ~ 4 M y} i 5 ~ t - -
~ 'r i~~~ I~ r' ~ C _ ,
t ' ` ~ ied in ~ r o elease 20
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~ ~
- ~
~
I Y'9
~+J d tf 1 t I
i
ty ~
R
r
I ~ ' ,
t:
i
The aanditiao~~o~ reoonanoe~ whioh (i.e~~ reoananoe~ io the oondi-
I
f Lion ~ovornin~ radiation ~ has thQ rollowin~ t'orm ~
1 war ~ ~ ~
In an unb~aunded dieleotria we have:
t
~ I w
W = kG/~~ (k is the wave veotor; E io the dioleotrio oonstant
~i
= k~~ ~D,S,B (B ie the angle betwoen the direotion o~ wave ro a-
kn p P
gation and the velooit~r o~ the partiol�~ ~
n 0~ and
equation 1�ads to the well-known aonditian that governs the poeei-
bi1,ity of the Cherenkov e~feot:
aos 9 C I ,
VV~ ~
In the ogee of periodical struotures the oondition (3 7 can be ef~.
feoted, generally sn@aking, for various oombinations of the quantities
i s ~ n, K ?
,
t
In nn ordinat~r wevegui,do fillod ~~ith a dfeleatrie, w� have
~ ~ ~ ~ ~ ~
~ Ct~~ Gl K
~?here GJD is the S~imiting frequenoy and u ~ o/ The oondition
governing the Ch�renkov effeot (3~ ~.eads to the r-e~.ation GJ .
= G~Z-~ ~~KZ
~ o
= v ~ ; henoe it follows that the frequanoy that oan be radiated
equa~,s t
W W ~ Z
o U j
J
This relation determ,~.nes the discrete spectrum of frequenoies, sinoe u
i
is a oertain funot~.on of the frequency u = u(W)?
The general formula for the intens~.ty I of radiat~,on has the fol-
,
i ~.ow~.ng form=
~ , dw _ y w ~ ,
w ~
. t, _ _ _

,1, ~
~ t r
~d ~Y J i .t ri J, Ali ,X ~
r1", i
{ ! r
, z }
~ ~
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.
~ ~i
t~ ' ~ ~ ~ ff
'
l ii.
i 7+,
I
whom ~ ~ is rho oet off' f~t~tiea ~ ~~e~ �at~o.og rho a~uation
I ~
~ ~ 0~ and ~ ~ is the oet of quantiti�o aatia~ring the
a k~ ~
w ~ = o.
~~dtion ~
~n rho ease of a e~inoal Wavoguide this ~'�rn~a ~oado to the
�ollowin~ roo~~.t:
R ~ c ~ c
a
where ~ io the radiuA off' th� Yave~:ide, J1 ie ~eoool ~ o i~unotion~ mu
ie the rnato o� the ~OOae~ f~anotion ~ f the emanation is carried ~
o
i
out over t'~ioae values o� a for whioh w� hav� u( wk,s) < v. here
the radiated froq~~enoiea w are determin�d �rom the relation
KS
~ 2
w ~ u ~ j R ~ y (With increase in a tha frequency
kS ~5
increases, but the phano velocity u( W ~y) tends toward o f th�refore,
i
' starting �rom a certain e, th� condition u < o ceases to b� �ul�ill�d)
br ~ovee alon the x-axic~ with a velocity v, ~ ~'t,,~
If the osoilla~b g
~ and moment o~-!~"" ~'~1 G~ ~ and
aigen�re~~~ enoiee , a
d' respectively, then we haver
'r--WC~~CoSW'~'~C~-Yt~ ~ = ~0~
~ ~
~x ~
~ --r--- .
E wh�r�d d ~ ~ vZ/~~ and G~ wo � ~ v~/~~
The condition ~o~'e~ing radiations that is the condition of resoA
j Hance, has now the �orm:
r,
ZTt Yt
s w ~ K ) ~ Goo (6)
~ ~ Lion determines the Do ler ef�eot in p�riodio struatti~re~';
This rely ~P
For liven v,Wo,a we obtain from (6) a series of discr�te values of
Y
kappa K to whioh correspond de�~.nit� discrete �rec~uenoies of the radi-
at~.on
.r. ,
W~len the osoi~.lator moves ~.n an unbounded die~.ectric ~ condition
(6} assumes the ~ol~,owin~; Forms
. c~ ~ V ~ Cos ~ ~ ~J ,
7. ~ ~
f, .
,~~f,,
ZIy ~
. .4 1

t ~
' `
r:
. 'fir ,
7`l ~`}7' ~ a i~
t t ` t f4 t,~`, ~ . _ . _
Y
I q~~f ,~f i q F ~ "s': ,uY Cz
~ i, e iii if n � ' fj ~i.4 -
y b
7 J F r i#1 1
a `�y;s 1 x' ryfHr Yn, ~ ~
Y ~sy(~~ ~ti ~ i ti YN ' ~
{ -
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E ~ J ,
!
,1' ~
~ r. ~ ~ y . ~ a 1 ~
't ! ~ j
t .
9
..F ..`yhF~:9.,
i '
j "Y.. 11.�Sj
1
hor~oe tha well-k~ow~ Form~,lao (aoo tho ~bi~ogr~ ~ For th
A Y) o oo~.
i ~laac Oapplar o~'t'oot im~odiately follows
G
~r~' t7a
~ w , _ v y
W o ~ !off ~ / ~ ~p,~ / ~ t, ; )
(N~~ i ~n 7 e
pailon � iu a ~unotion oP W E ~ ~w)
Tho inters�it I of radi
anon fie determined by the Fo3to~,n~ gory.
oral. Formula s

i ~ ~ ~n~ ~ ~ r~ 2 j
wd ~b ,
~ ~
I b I
~
~C~C r ~~_1r , w ~ i
a 7~ K ~ y ~
~ ~ ~ ~
where ~ iQ the yet of titie� K
~ ( ~ a) determinod from t~~e e~ua-
JI
time GJ~= v(K 2~Tr~/,~) ~ ~ and fie tie aet of ur~ntit "
o ~ q iee
~ 2~r ~ ~
; e) d~f fined by tho o ~uat ion W- - - K
~ ) ~a
Submitted lg Nfearoh 1950
Submitted 2 May 1~50i
by Act S, I. Vavilov
~ ,
i
~I~IOf~RAP~IY
i
~ w, Naitler
q~e?ntu~n Thoory of Radiations Moscow 19~0~ ~
2 ~ V ~ Oirizburg, DAN S~~SN, Vol 56 6
~ , p 94 (~91~7) ~
i
e A. SOhr, K~1, Daneke Vidensk Se~,ekab Ma
t f
ye Medd i9 (~g~~)
~r~ Frank, SAN SSSR, ser fizj ~fol 6,a C19/~)~ !
i
~ ~ a~~
I j
i
i
-~ND-
,
5 W ~
,r ~ r~ ~
i. ~.f 1 ~ ' ~ti`:~~.
~ 'N i ~ ~
i
~ ~
~ i
t
~ ` 'gat F i~a~ t ~ ~ - _ _ _ ~
y~~~~~~"~~i.yyt'"itrt ~ ~
~ ~ ` it i ~i ~ , ~
i 1~'.~ ~ t ~ tR~
'i t..
~~if ~ ~ _ ~
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