Frequency multiplication in high energy electron beam

Getty, W. D.

Lomax, R. J.

Masnari, N. A.

Rowe, J. E.

English

NASA Technical Reports Server

THE UNIVERSITY OF MICHIGAN 
ANN ARBOR, MICHIGAN 
SEMIANNUKG PROGRESS REPORT NO. 1 
ON 
FREQUENCY MULTIPLICATION I N  HIGH-ENERGY ELECTRON BEAMS 
This report  covers t he  period October 1, 1966 t o  Apr i l  1, 1967 
By: W. D. Getty 
R. J. Lomax 
N .  A. Mo.snari 
J. E. Rowe 
Electron Physics Laboratory 
Department of E lec t r i ca l  Engineering 
o $  
P L L  
Approved by: 
G. I. Haddad, Acting Direct 
Electron Physics Laboratory 
Project 08400 
RESEARCH GRANT NO. NGR 23-005-18-5 
OFFICE OF SPACE SCIENCE AND APPLICATIOVS 
NATIONAL AERONAUTICS AND SPACE ADMIPIISEATIOU 
WASHII;GTON, D. C . 20546 
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https://ntrs.nasa.gov/search.jsp?R=19670018039 2020-03-12T11:39:53+00:00Z
TABLE OF CONTENTS 
1. GENERAL INTRODUCTION 
2. RELATIVISTIC ELECTRON-BEAM DEVICE 
3 - BEAM-PLASMA INTERACTIONS 
4. TIME-DEPENDENT NONLINEAR ANALYSIS OF ELECTRON- 
BEAM PLASMA INTERACTION 
5 .  INSTABILITIES AT CYCLOTRON HARMONICS I N  A NON- 
MAXWELLIAN PLASMA 
Page 
1 
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2 
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SEMIANNUAL PROGRESS REPORT NO.  1 
ON 
FREQUENCY MULTIPLICATION I N  HIGH-ENERGY ELECTRON BEAMS 
- 1. General Introduct ion (N. A .  Masnari) 
The bas ic  objec t ives  of t h i s  research program a r e  t o  i n v e s t i -  
g a t  e : 
a.  i n t e r a c t i o n  of high-energy e l ec t ron  beams with quasi-  
o p t i c a l  c i r c u i t s  and plasmas (Cerenkov r ad ia t ion ) ,  
b .  e lec t ron  beam-plasma in te rac t ions  using cold-cathode 
discharges,  
c . nonlinear e lec t ron  beam-plasma theory, and 
d.  i n s t a b i l i t i e s  i n  non-Maxwellian plasmas. 
This r epor t  covers t he  f i r s t  s i x  months of e f f o r t  on the  program 
which was i n i t i a t e d  on October 1, 1966. 
t h e  repor t  summarize the  s t a tus  of t he  var ious p ro jec t s  and include 
discussions o f  r e s u l t s  and plans f o r  futm-e i m e s t i g a t i o n s .  
The following sect ions of 
- -  2 .  R e l a t i v i s t i c  Electron-Beam Device 
Supervisor: J. E. Rowe 
Staf f :  G. T .  Konrad 
The object  of t h i s  phase of t h e  program i s  the  generat ion of 
mil l imeter  wavelength r ad ia t ion  by use of a t i g h t l y  bunched r e l a t i v -  
i s t i c  e l ec t ron  beam. The device t o  be used f o r  t h i s  purpose c o n s i s t s  
of (1) a 100 kv e l ec t ron  giln capable of producing a beam 2 mm i n  
diameter and carrying a current of 0 .1  ampere, ( 2 )  a coupled-cavity 
-2 - 
. 
bunching c i r c u i t  resonant a t  approximately 7.5 GHz, (3) a high- 
vol tage anode f o r  accelerat ing the  bunched beam t o  approximately 
600 kv, and (4)  a water-cooled bean co l l ec to r .  
The high-voltage anode, i n  addi t ion t o  being used f o r  accel-  
e r a t ing  the  beam, a l so  contains an e l l i p t i c  cavi ty  coupler.  The 
bunched r e l a t i v i s t i c  e lec t ron  beam passes through a quartz cone 
which i s  placed along one focus of t he  cavi ty .  In  so doing the  
beam rad ia t e s  power a t  t h e  harmonics of t he  bunching frequency by 
t h e  Cerenkov e f f e c t .  In par t icu lar ,  t h e  coupling and detect ing 
c i r c u i t r y  have been optimized for t h e  15th  harmonic, which corre- 
sponds t o  a wavelength of 2 mm. A t  t he  o ther  focus of t h e  e l l i p t i c  
cavi ty  i s  located an antenna, which i s  terminated i n  a rad ia t ing  
horn f o r  t ransmi t t ing  t h e  2 mm wavelength r ad ia t ion  t o  a de tec tor .  
Attempts were made on a previous program t o  operate t h i s  
device, but  poor vacuum conditions precluded the  attainment of 
s u f f i c i e n t l y  high vol tages .  A t  t h e  present time a l l  components 
of t he  device a re  being carefu l ly  cleaned and a new vacuum pump 
has been placed on order and i s  scheduled f o r  de l ivery  i n  the  near 
fu ture .  Upon a r r i v a l  of the  pump, t h e  device w i l l  be prepared f o r  
operation and t e s t i n g  w i l l  commence shor t ly  t h e r e a f t e r .  
2. - Beam- Plasma I n t  e rac t i ons 
Supervisor: R .  J. Lomax 
S ta f f :  J. D. Gillanders 
A computer program has been wr i t t en  t o  p lo t  t h e  roots  of a 
dispers ion r e l a t ion .  
i n t eg ra t ion  of t h e  der iva t ives  of t h e  dispers ion re la t ion ,  a f t e r  
This program follows t h e  roots  by Runge-Kutta 
-3 - 
l oca t ing  the  roots  by i t e r a t e d  appl icat ion of a f i r s t - o r d e r  Taylor 
s e r i e s  cor rec t ion .  
The progrmi was checked out  by reproducing t h e  r e s u l t s  
obtained by Simpson' using a d i f f e ren t  method. The program w a s  
then  run with f i n i t e  values of  c o l l i s i o n  frequency and e lec t ron  
temperature included. Smal l  values of c o l l i s i o n  frequency (on t h e  
order  of 0.01 times t h e  plasma frequency) have not iceable  e f f e c t s  
on the  gain without not iceable  change of t he  r e a l  p a r t  of the  
propagation constant.  For l a rge r  values of c o l l i s i o n  frequency 
(up t o  ha l f  t h e  plasma frequency) both the  ga in  and propagation 
constants  a r e  considerably changed. More d e f i n i t e  da ta  i s  now 
being co l lec ted  and s tudied.  
A plasma e l ec t ron  gun of t h e  type described by Boring and 
Stauf fer2  has been b u i l t  and t e s t ed .  This gun has t h e  advantage 
of not requir ing d i f f e r e n t i a l  pumping which i s  normally required 
when a conventional gun i s  used for  beam-plasma s tud ie s  i n  the  
intermediate pressure range around 1 Torr.  A system t o  couple t o  
t h e  beam and plasma generated by t h i s  gun i s  now being b u i l t  and 
w i l l  be used t o  study the  in t e rac t ion  problem. 
1. Simpson, J. E., "An I n s t a b i l i t y  of a Beam-Generated Plasma i n  a 
Uniform Magnetic Field",  Tech. Report No. AF'AL-TR-66-3, Stanford 
University,  Stanford, Cal i fornia;  November, 1965. 
2 .  Boring, K. L.  and Stauffer ,  L .  H. ,  "A New Non-Thermionic Electron 
Gun", Proc. N a t l .  Electronics Conf ., pp. 535-544; 1963. 
- -  Time-Cependent Nonlinear Analysis of Electron-Beam Plasma 4 .  
In%eract ion 
Supervisor: 2.  E. Rowe 
S t a f f :  A. Lin 
Much of t h e  i n i t i a l  e f f o r t  on t h i s  program has been involved 
wi th  an evaluat ion of previous beam-plasma in t e rac t ion  s tud ie s .  I n  
p a r t i c u l a r ,  Dawson ' s  reports'' 2J have been thoroughly reviewed. 
The two-dimensional pl-asma phenomena w i l l  be inves t iga ted  i n  t h e  
near  f u t u r e  by using t h e  charge-filament. model i n  which motion i s  
permitted i n  two d i rec t ions .  An i n i t i a l  pos i t ion  and ve loc i ty  w i l l  
b e  assigned t o  each fi lament and t h e  t r a j e c t o r i e s  of a l l  f i laments  
w i l l  be followed on a computer by solving t-he exact equations of 
mot ion. 
5. I n s t a b i l i t i e s  a t  Cyclotron Harmonics i n  a Non-Maxwellian Plasma - - - - -  
(W. D .  Get ty)  
A plasma colimn i n  a uniform a x i a l  magnetic f i e l d  can 
scppert e l e c t r o s t a t i c  waves t.hat. propagate i n  a d i r e c t i m  perpen- 
d i c u l a r  t o  the  magnetic f i e l d .  The d e t a i l s  of these waves have 
been s tudied f o r  t h e  Maxwellian plasma by Bernsteinl  and f o r  t h e  
1. Dawson, J. and Smith, C . ,  "Some Inves t iga t ions  of Plasma 
I n s t a b i l i t i e s  i n  One-Dimensional Plasmas", Plasma Physics 
Lab., Princeton University,  Princeton, N .  J., Report 
Matt -1.52; November, 1.962. 
2 -  Cawson, J. and Smith, C . ,  "Some Computer Experiments wi th  a 
One-Dimensional Plasma Model", i'lasma Physics Lab., Princeton 
Ucivers i ty ,  Princeton, N .  J., Report Matt-1.51; January, 1963. 
3. Dawson, J., Shanny, R .  A .  ar;d Greene, F.  M. ,  "Numerical 
Experiments i n  Plasma Physics", Plasma Physics L,ab ., Princeton 
University,  Princeton, N .  3., Report Matt-441; July, 1966. 
1. Berristein, I. B.,  "Waves i n  a Plasma i n  a Magnetic Field" ,  
Phys. Rev., vol. 109, No. 1, pp. 10-21; 1958. 
-4- 
-5- 
non-Maxwellian plasma by Crawford and Tataronis2, Gruber, Klein and 
Auer3, and Speck and Bers4. 
it i s  found t h a t  under ce r t a in  conditions these transverse e lec t ro-  
s t a t i c  waves become unstable a t  frequencies r e l a t ed  t o  the cyclotron 
frequency of the electrons and i t s  harmonics. The conditions under 
which i n s t a b i l i t i e s  a r e  obtained pe r t a in  t o  plasma density, t r ans -  
verse  propagation constant (i .e ., plasma c o l m  diameter), plasma 
e lec t ron  energy and magnetic f i e l d  s t rength .  The experiment t o  be 
described i n  t h i s  report  i s  an attempt t o  observe these i n s t a b i l i t i e s .  
The main problem i s  the  production of a s u f f i c i e n t l y  dense plasma 
with an appropriate non-Maxwellian ve loc i ty  d i s t r ibu t ion .  
In  the case of t h e  non-Maxweilian plasma 
The i n s t a b i l i t y  of t h e  e l e c t r o s t a t i c  wave i s  of grea t  
i n t e r e s t  from the point of view of plasma physics because it i s  
a ve loc i ty  space i n s t a b i l i t y  and may be exci ted and observed under 
r e l a t i v e l y  "clean" conditions.  
trig point of view beczuse i n  pr inc ip le  it makes possible t h e  
generation of high micrcwave freqcencies by excFting a high 
cyclotron harmonic by t h e  i n s t a b i l i t y .  I n  the  experiment i t  i s  
planned t o  obtain conditions under which the second harmonic 
becomes unstable as w e l l  as the  fundamental. 
It i s  in t e re s t ing  from the  engineer- 
2 .  Crawford, F. W. and Tataronis, J. A., "Absolute I n s t a b i l i t i e s  
of Perpendicularly Propagating Cyclotron Harmonic Plasma Waves", 
Jour. Appl. Phys., vo l .  36, pp. 2930-2934; September, 1965. 
3 .  Gruber, S. ,  Klein, M. W .  and Auer, P. L., "High-Frequency 
Velocity Space Ins t ab i l i t i e s " ,  Phys . Fluids, vol.  8, pp. 1504- 
1509; August, 1965. 
4. Speck, C .  E. and Bers, A., " I n s t a b i l i t i e s  i n  Quasi-Static Waves 
Across Bo'', Quarterly Progress Report No. 79, Research Laboratory 
of Electronics,  Massachusetts I n s t i t u t e  of Technology; October 15, 
1965. 
. 
-6- 
The experimental device i s  e s s e n t i a l l y  a g l a s s  tube contain- 
ing  a t r i o d e  e lec t ron  gun and a c o l l e c t o r .  The g l a s s  walls of the  
tfibe - r e  e l e c t r o s t a t i c a l l y  shielded f o r  s t r a y  charge by a cyl inder  
and screen. The e n t i r e  tube i s  immersed i n  a uniform f i e l d  of 70 
t o  100 gauss.  An e lec t ron  beam of 10-m diameter i s  emitted from 
t h e  cathode and accelerated by the grid-anode s t ruc tu re  t o  1.50 v o l t s  
energy. The beam current  i s  control led by the  g r i d  independently 
of t he  f i n a l  acce le ra tor  voltage, and can be var ied  from zero t o  
60 m a .  The beam passes through the  shielded d r i f t  region and i s  
co l l ec t ed .  In  order t o  cont ro l  t h e  ion densi ty  i n  t h e  d r i f t  tube, 
t h ree  e lec t rodes  have been provided f o r  cont ro l l ing  the  space 
p o t e n t i a l  along t h e  tube.  The center  e lec t rode  w i l l  be biased 
s l i g h t l y  negative t o  provide a po ten t i a l  wel l  for ions .  Provision 
i s  made f o r  con t ro l  of t h e  background gas pressure up t o  lom3 Torr.  
The gas used i s  hydrogen. 
The t ransverse  energy of the  e lec t rons  i s  provided by a 
llccrkscrew'l winding which t r ans fe r s  a predetermined f r a c t i o n  of 
tohe e lec t ron  ax ia l  d r i f t  energy i n t o  t ransverse  motion. The 
r e su l t i ng  beam w i l l  be monoenergetic i n  both t h e  a x i a l  and t rans-  
verse  d i r ec t ions .  It w i l l  have approximately 120 eV a x i a l  energy 
and 30 eV t ransverse  energy. The guiding centers  of t he  e lec t rons  
w i l l  be uniformly and randomly spaced across  the  beam cross  sec t ion .  
With the  corkscrew turned on, the beam diameter w i l l  be approxi- 
mately 15  mm. 
The parameters of t h i s  experiment have been chosen i n  an 
attempt t o  reach conditions predicted by Gruber, Klein and Auer3 
t o  be unstable .  This p a r t i c u l a r l y  appl ies  t o  t h e  beam current ,  
-7- 
beam voltage, magnetic f i e l d  strength,  and beam diameter. The back- 
ground gas pressure cont ro l  and t h e  provis ion for ion t rapping has 
been included t o  keep the  electron beam approximately neut ra l ized .  
It i s  therefore  intended t o  have a two-component system consis t ing 
only of t h e  e lec t ron  beam and neut ra l iz ing  ions .  
i s  t o  operate  under "overneutralized" condi t ions when a background 
beam-generated plasma w i l l  be  present .  
The eventual plan 
Two tubes have been b u i l t  f o r  t h i s  experiment. The f i rs t  
tube, which contains  only t h e  electron gun and co l l ec to r ,  was 
intended t o  be a tes t  of t he  e lec t ron  gun construct ion.  The gun 
worked s a t i s f a c t o r i l y ,  producing up t o  60 ma cathode cur ren t  with 
an acce lera t ing  vol tage of 150 v o l t s  and a g r i d  vol tage approxi- 
mately 50 v o l t s  pos i t i ve  with respect t o  t h e  cathode. The second 
tube contains  the  ion-trapping e lec t rodes  i n  addi t ion  t o  t h e  
e l ec t ron  gun. Improvements have been made i n  the  gun construct ion 
and i n  the  cathode (which had in su f f i c i en t  l i f e  i n  the  f i rs t  tube)  
a ~ c ?  t h e  device w i l l  be ready f o r  f u r t h e r  study i n  the  immediate 
f u t u r e .  


Frequency multiplication in high-energy electron beams Semiannual progress report, Oct. 1, 1966 - Apr. 1, 1967

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