Plasma waves between electron cyclotron frequency and upper hybrid frequency in collisionless hydrogen plasm

Malmberg, J. H.

Wharton, C. B.

English

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GENERAL ATOMIC DIVISION 
GENERAL DYNAMICS CORPORATION 
John Jay  Hopkins Laboratory f o r  Pure and Applied S%ience 
P.O. Box 608, San Diego 12, Cal i forn ia  
Work done by: 
W. E .  Drummond 
J. H. Malmberg 
C .  B. Wharton 
* 
GACD-6009 
Copy No. 39 
EXPERIMENTAL INVESTIGATION OF THE F"DAMENTAL 
MODES OF A COLLISIONLESS PLASMA 
QUARTERLY REPORT NO. 3 
September 11, 1964 through December 10, 1964 
Report wri t ten by: 
J. H. Malmberg 
C .  B. Wharton 
Contract No. NAS7-275 
National Aeronautics and Space Administration 
Western Operations Off ice  
150 Pic0 Boulevard 
Santa  Monica, Cal i forn ia  
General Atomic P ro jec t  No. 407 December 22, 1964 
https://ntrs.nasa.gov/search.jsp?R=19650010288 2020-03-17T00:39:50+00:00Z
INTRODUCTION 
During t h e  current period we have i d e n t i f i e d  t h e  previously observea 
waves as cyclotron waves on ariiting beans i n  the  plasma. Tnese Dems nave 
been e i m i n a t e a  and w i t h  improvea tecnniques we now observe the  plasma wave 
between the  electron cyclotron frequency and the  upper hybrid frequency. 
We have now accumulated enough data on these  waves t o  c o n s t i t u t e  a substan- 
t i a l  experiment. A paper e n t i t l e d  "Cyclotron Waves i n  a Col l i s ion less  
Plasma", by C .  B. Wharton and J. H. Malmberg, w a s  presented at the  APS 
Annual Meeting of the  Division of Plasma Physics, New York, November 4, 1964. 
Port ions of t h e  data given i n  t h a t  t a l k ,  plus  subsequent r e s u l t s ,  are included 
i n  t h i s  report .  
2 
Beam Waves 
The dispersion curves i n  t h e  las t  quar te r ly  repor t  showed waves near 
1 t h e  e lec t ron  cyclotron frequency , 
t h a t  these  waves were cyclotron resonance waves on d r i f t i n g  e lec t ron  streams, 
We have been ab le  t o  show t h a t  these beams were due t o  secondary e lec t rons  
generated by ions plowing i n t o  t h e  wave launching hel ix .  
t h e  group veloci ty  o f  these  waves can be accurately computed from t h e  d i f -  
ference i n  the  po ten t i a l  of t h e  he l ix  and t h e  p o t e n t i a l  of t he  plasma. 
That is, t h e  group veloci ty  i s  j u s t  equal t o  the ve loc i ty  of t he  secondary 
e lec t rons  i n  the  plasma. 
i s  an i n t e r e s t i n g  e f f e c t  bu t  not the one we set out  t o  look for ,  so  we have 
eliminated them by el iminat ing the  h e l i x  and using probes t o  lmnch  the  waves. 
This reduced the wave launching eff ic iency,  bu t  by using improved instrumen- 
t a t i o n ,  w e  have s t i l l  re ta ined  s u f f i c i e n t  reso lu t ion  t o  f i n d  cyclotron waves. 
Secondary e lec t rons  from t h e  ion t r ap  suppressor g r i d  are s t i l l  a minor prob- 
l e m  for wave propagation i n  the  upstream di rec t ion ,  leading t o  abnormal 
damping, and i n  some cases even wave growth. 
low t o  cause an i n s t a b i l i t y ,  and no e f f e c t  on downstream propagation i s  
evident.  
A t  the  t i m e  of t h a t  repor t  we suspected 
I n  pa r t i cu la r ,  
The existence of these beam-waves i n  the  plasma 
Their current  densi ty  i s  too 
Cyclotron Waves 
A t  least th ree  (and perhaps more) d i s t i n c t  waves having resonances 
(wavenumber becoming l a r g e )  a t  o r  near t he  e lec t ron  cyclotron frequency have 
been catalogued. 
v > c and i s  a forward wave. The other  i s  a "slow wave", having a phase 
t h a t  r e t a r d s  with frequency, i.e., a backward wttve. 
i s  an electromagnetic waveguide mode, perturbed by t h e  plasma. 
Two waves l i e  above t h e  cyclotron frequency. One has a 
pl 
The fas t  wave apparently 
The slow 
'Quwterly Report No. 2 ,  GACD-5716, Fig. 1 
3 
wave apparently is  the  C cyclotron having a propagation cutoff  
at t h e  upper hybrid frequency, fuh = (fi + f;)'l2. It is  heavi ly  damped 
a t  wavelengths shor te r  than a b o u t 1 0  cm and we  have not y e t  been successful  
i n  p l o t t i n g  out  t h e  e n t i r e  dispers ion curve. 
measurements are now i n  progress.  
Figs .  I, 2, and 3. 
01 
Quant i ta t ive  damping-length 
P a r t i a l  dispers ion curves are shown i n  
Below t h e  cyclotron frequency the re  appear t o  be severa l  waves. The 
fastest of these,  f a i r l y  cer ta inly,  i s  t h e  plasma-perturbed TE waveguide 
mode mentioned above. 
m 
I t s  dispers ion curve matches t h a t  f o r  a waveguide 
whose cross-section is  1/10 f i l l e d  with plasma. W e  have a plasma column 
of about 2 cm diameter i n s ide  a 12 cm diameter tube, which, accounting for 
radial densi ty  gradients ,  i s  a reasonable f i t .  
4 wave is  very similar t o  t h a t  f o r  a wh i s t l e r  . 
The dispers ion f o r  t h i s  
The other  "cyclotron waves" may be higher modes, t h a t  is, those having 
circumferent ia l  f i e l d  var ia t ions .  One of them, shown i n  Fig.  1, between 
250-340 Me, seems t o  have a cutoff frequency cornpatable with the  Cll 
cyclotron wave. If so, it should exh ib i t  Faraday ro ta t ion ,  and we are 
cu r ren t ly  looking f o r  t h i s  e f f ec t .  Unfortunately, t h e  wave is  heavily 
damped and can be followed for  only a wavelength or two, making measurements 
very d i f f i c u l t .  The "whistler" mentioned above would a l s o  have Faraday 
ro ta t ion ,  except t h a t  t h e  ordinary wave component is  cu t  o f f  by the  
'Trivelpiece, A .  W. and R .  W. Gould, J. Appl. Phys. - 30, 1784 (1954). 
'Bevc, V. and T. E. Everhart, J. Electronics  and Control 13, 185 (1962). 
4 Heald, M. A .  and C .  B. Wharton, Plasma Diagnostics with Microwaves, 
John Wiley and Sons (1965). 
4 
waveguide cutoff,  leaving only the e l l i p t i c a l l y  polar ized extraordinary 
component. No evidence f o r  polar izat ion r o t a t i o n  of t h i s  wave has been 
found. 
The "lower branch" waves, the conventional spacecharge waves of a 
warm, f i n i t e  plasma column, have been extensively invest igated a t  General 
Atomic and elsewhere, and reported on i n  t he  l i t e r a t u r e 2 j 5 .  We have p l o t t e d  
t h e  dispersion curves here, s ince we use these waves i n  a diagnostic manner, 
t o  aid us  i n  understanding t h e  cyclotron wave  charac te r i s t ics .  
The three  f igures  show e f f e c t s  of various plasma dens i t ies  and 
cyclotron frequencies on the cyclotron family of waves. Ideal ly ,  we should 
a l s o  study the e f f e c t s  of various e lec t ron  temperatures, bu t  t h i s  i s  d i f f i -  
c u l t  t o  achieve. Recently we have t r i ed  adding an impurity of argon t o  t h e  
hydrogen, i n  an attempt t o  decrease Te from i t s  usual 10 t o  1 5  eV.  
t h a t  the  decrease occurs is meager, but  looks encouraging. 
l e s s )  damping of the lower branch can be decreased dras t ica l ly ;  we w i l l  
now look a t  the e f f e c t s  on t h e  upper branch (cyclotron family) t o  see i f  
t h e r e  i s  a l so  c o l l i s i o n l e s s  damping of these  waves. 
Evidence 
The (co l l i s ion-  
F inanc i a l  
Approximately $62,000 has been expended or committed on t h i s  pro jec t  
t o  date. 
'Malmberg, J. H. and C.  B. Wharton, Phys. Rev. L e t t .  - 13, 184 (1964). 
5 
0 .l .02 
i i  
, I  
.I /  .I2 .13 . I 4  . I S  ./b , 
Fig. l--cu-[i diagrams f o r  waves i n  the c ~ ~ l l i s i c n l e s s  H, plasm, over the 
frequency r q e  0 - 300 Mc. 
e 
L 
Cyclotron freclum-y f was 35C Mc and plaszna 
I; 
densiry n was approximately L.2 X i.\, ,8 /cm 3 . 
. 
6 
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7 
8 -  
Fig.  3--0-P diagrams as i n  Fig. 1, but fb = 450 Mc, ne ~ ~ 7 . 1  X 10 /ern-'. 


Experimental investigation of the fundamental modes of a collisionless plasma quarterly report no. 3, sep. 11 - dec. 10, 1964

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