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Observation of cyclotron echoes from a highly ionized plasma
Volume 22, number 5
P H YS I C S L E T T E R S
16. G. Bret, Compt.Rend. 260 (1965) 6323. 17. E . J . Stansbury, M.F. Crawford and H. L. Welsh, Can. J. of Phys. 31 (1953) 954. 18. E.Ishiguro, T.Arai, M.Mizushima and M.Kotani, Proc. Phys. Soc.A65 (1952) 178. 19. R.W. Terhune and C.W. Peters, J. Mol. Spect. 3 (1959) 138. 20. L.Galatry, Phys.Rev. 122 (1961) 1218. 21. R, W. Minck, E. E. Hagenlocker and W. G. Rado, to be published. 22. C.H.Townes, 4th Quantum electronics meeting, Phoenix (April 1966). 23. G.Bret, Compt. Rend. 262 (1966) 881.
8. R.W.Terhune, private communication. 9. G.Hauchecorne et G. Mayer, Compt.Rend. 261 (1965) 4014. 10. N. Bloembergen and P. Lallemand, Phys.Rev. Lett. 15 (1965) 1010. 11. P . L . Kelley, Phys.Rev. Letters 15 (1965) 1005. 12. Y.R.Shen and Y.I.Shaham, Phys.Rev. Letters 15 (1965) 1008. 13. G.Bret and G.Mayer, Physics of quantum electronics, eds. P. Kelley et al. (McGraw Hill, 1966). 14. G.Bret, F . G i r e s et G.Mayer, 4th Quantum electronics meeting Phoenix (April 1966). 15. G. Bret and M. Denariez, Appl. Phys. Letters, March 1st 1966.
OBSERVATION
OF
CYCLOTRON
15 September 1966
ECHOES
FROM
A HIGHLY
IONIZED
PLASMA
*
D. E. K A P L A N and R. M. HILL Lockheed Palo Alto Research Laboratory, Palo Alto, California and A. Y. WONG Department of Physics, University of California, Los Angeles, California Received 1 August 1966
The observation of cyclotron echo phenomena from a highly ionized cesium plasma in a Q-device is r e ported. The implication of these measurements for a velocity dependent collision frequency mechanism of cyclotron echo formation is discussed. The i n i t i a l o b s e r v a t i o n of c y c l o t r o n e c h o e s [1] in r a r e g as a f t e r g l o w p l a s m a s has s t i m u l a t e d s e v e r a l t h e o r e t i c a l e f f o r t s [2-6] to e x p la in the o r i g i n of this new phenomenon. T h e s e t r e a t m e n t s a r e s i m i l a r in adding a n o n l i n e a r t e r m dependent upon e x c i t a t i o n am p l i t u d e to the usual l i n e a r m o del of f r e e e l e c t r o n c y c l o t r o n r e s o n a n c e , f r o m which an echo cannot r e s u l t . The n o n l i n e a r t e r m d i f f e r s f o r e a c h model. H e r r m a n n and W h i t m e r [2] d i s c u s s a n o n l i n e a r i n t e r a c t i o n b e t w e e n e l e c t r o n and d r i v i n g field. Gould and K e g e l [3] and H i r s c h f i e l d [4] d i s c u s s a shift in r e s o n a n t f r e quency due to r e l a t i v i s t i c m a s s e f f e c t s , and a v e l o c i t y dependent c o l l i s i o n f r e q u e n c y m e c h a n i s m [7] is c o n s i d e r e d by C r a w f o r d and H a r p [5], and Hill et al. [6]. While the r e s u l t s of the a f t e r g l o w e x p e r i m e n t s indicate that the f o r m a t i o n of c y c l o t r o n e c h o e s in the a f t e r g l o w p l a s m a r e g i m e is due p r i m a r i l y to this l a t t e r m e c h a n i s m , the c o n c l u s i o n s a r e clouded by the c o m p e t i t i o n between e l e c t r o n - n e u t r a l and Coulomb c o l l i s i o n p r o c e s s e s in t h e s e weakly i o n i ze d p l a s m a s . A c c o r d i n g l y we
have c a r r i e d out c y c l o t r o n echo e x p e r i m e n t s in a c o m p l e t e l y d i f f e r e n t p l a s m a r e g i m e , a highly i o n i zed c e s i u m p l a s m a in the UCLA Q d e v i c e [8], in which the c o l l i s i o n p r o c e s s e s a r e e x c l u s i v e l y Coulombic. The o b j e c t i v e s of this e x p e r i m e n t a r e twofold - to d e m o n s t r a t e the utility of the c y c l o t r o n echo technique as a d i a g n o s t i c p r o b e f o r a b r o ad c l a s s of p l a s m a s , and to study c y c l o t r o n echo p h e n o m e n a in a p l a s m a m e d i u m m o r e suitable f o r v e r i f y i n g a p a r t i c u l a r echo m e c h a n ism. A s c h e m a t i c d i a g r a m of the c o n f i g u r a t i o n f o r t h i s Q - d e v i c e e x p e r i m e n t is shown in fig. 1. The r a n g e of e l e c t r o n d e n s i t i e s , he, extends f r o m 101I to 2)< 1012 e l e c t r o n s / c m 3 . The l o w e s t dens i t i e s in t h i s e x p e r i m e n t a r e in fact at the u p p e r density l i m i t f o r the a f t e r g l o w p l a s m a e x p e r i m e n t s . T w o - p u l s e and t h r e e - p u l s e c y c l o t r o n * Supported jointly by the U. S. Office of Naval Research, the U.S.Air Force Office of Scientific Research and the Lockheed Independent Research Fund. 585
Volume 22, number 5
STAINLESS
STEEL
PHYSICS LETTERS
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0 HOT PLATE
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15 September 1966
layer becomes vanishingly small as ¢o ~ wc and the external electric field can reach the central column. The apparent absorption maximum for an incident wave remains at Wc on the wing of the upper hybrid resonance with increasing electron density because of a propagation cutoff region for 09>0) c.
U
__.,o.
_j
Fig. 1. Schematic d i a g r a m of the e x p e r i m e n t a l a r r a n g e ment. The cesium plasma, approximately ;3 em in d i a m e t e r and 40 em long is generated by the hot plate and t e r m i n a t e d by the cold end plate. The radial gradient of the axial magnetic field is 2% a c r o s s the p l a s m a column. X band h o r n s were used to couple radiation in and out of the p l a s m a column. echoes were observed with the microwave propagation direction k very nearly perpendicular to t h e a x i a l m a g n e t i c f i e l d B o. T h e f r e q u e n c y of e x c i t a t i o n w a s 8.55 G c , c y c l o t r o n r e s o n a n c e f o r f r e e e l e c t r o n s i n t h e m a g n e t i c f i e l d of 3.05 kG. T h e f r e q u e n c y a t w h i c h the e c h o w a s o b t a i n e d r e m a i n e d c o n s t a n t , i n d e p e n d e n t of e l e c t r o n d e n s i t y , o v e r t h e d e n s i t y r a n g e of o b s e r v a t i o n . T h e e c h o a m p l i t u d e w a s e n h a n c e d by a 2% m a g n e t i c field inhomogeneity over the plasma column produced by soft iron segments, symmetrically pos i t i o n e d a b o u t t h e m i c r o w a v e p o r t . 10 n s e c d u r a t i o n m i c r o w a v e p u l s e s a t 10 w a t t p e a k p o w e r w e r e c o u p l e d to a s e g m e n t of t h e p l a s m a c o l u m n t h r o u g h t h i s p o r t . T h e t w o - p u l s e e c h o l i f e t i m e in this experiment typically varied from 50-200 nsec. The echo decay envelopes were usually nonexpon e n t i a l . T h e l i f e t i m e of t h e t h r e e - p u l s e c y c l o t r o n e c h o w a s a p p r o x i m a t e l y t w i c e t h a t of tile t w o pulse echo. T h e p l a s m a f r e q u e n c y Wp v a r i e s f r o m 0.3 ¢oc to 1.3 coc f o r t h e e l e c t r o n d e n s i t i e s a t w h i c h e c h o e s w e r e o b s e r v e d , xand t h e u p p e r h y b r i d r e s o n a n c e ~o, r, = (w 2 + w~)~ f o r t h e e x t r a o r d i n a r y m o d e r a n g e s f r o m n e a r l y ¢oc to 1.5 w c. T h a t t h e e c h o r e m a i n s u n s h i f t e d in f r e q u e n c y a t w c w h i l e Wuh a t t a i n s v a l u e s a s h i g h a s 1.5 w c i s a n i n t e r e s t i n g r e s u l t r e q u i r i n g f u r t h e r s t u d y . It a p p e a r s unlikely that this echo results from scatter into a l o n g i t u d i n a l m o d e of p r o p a g a t i o n f o r w h i c h e l e c t r o n s w o u l d e x h i b i t a r e s o n a n c e a t ¢Oc, a l t h o u g h the experimental configuration does not preclude t h i s . One p o s s i b l e e x p l a n a t i o n f o r t h e c o n s t a n c y of t h e e c h o f r e q u e n c y i s t h a t t h e r a d i a l d e n s i t y p r o f i l e g i v e s r i s e to a n e v a n e s c e n t r e g i o n f o r p e r p e n d i c u l a r p r o p a g a t i o n [9] a t w > coc. S u c h a 586
W e f i n d t h a t a t w o - p u l s e e c h o i s o b s e r v e d only w h e n t h e e l e c t r o n - i o n e o l l i s i o n t i m e Tel i s e q u a l to o r s h o r t e r t h a n t h e t i m e t D r e q u i r e d f o r a n e l e c t r o n to d r i f t o u t of t h e i n t e r a c t i o n r e g i o n , t D is an upper limit to the echo lifetime. This drift t i m e i s a p p r o x i m a t e l y 150 n s e c f o r e l e c t r o n s w i t h t e m p e r a t u r e 2300OK. If we a s s u m e t h e e l e c t r o n v e l o c i t y i m p a r t e d by t h e m i c r o w a v e p u l s e s i s t w i c e t h e t h e r m a l v e l o c i t y we r e q u i r e a n e l e c tron density n e ~ 1011/era 3 in order to have r e i < t D. T h i s c o r r e s p o n d s c l o s e l y t o t h e m i n i mum density for which echoes are observed. S i n c e Zei ~ v3/n e w h e r e v i s t h e t o t a l e l e c t r o n velocity, the electron-ion collisions are ineffective in producing an echo before the electrons d r i f t out of t h e i n t e r a c t i o n r e g i o n if n e < 1 0 1 1 / c m 3 In t h e a f t e r g l o w e x p e r i m e n t s t h e e l e c t r o n - n e u t r a l c o l l i s i o n t i m e Ten i s l e s s t h a n t D a n d i n d e p e n d e n t of n e. It i s i m p o r t a n t to n o t e t h a t e c h o e s of s u b s t a n t i a l a m p l i t u d e [10] a r e o b s e r v e d i n t h e a f t e r g l o w p l a s m a s a t e l e c t r o n d e n s i t i e s a s low a s 107/cm 3 although the macroscopic electric dipole moment diminishes directly as the electron density. This circumstance coupled with the disapp e a r a n c e of c y c l o t r o n e c h o e s i n t h e Q - d e v i c e plasma for electron densities below 1011/era 3 strongly suggests that the velocity dependent collision frequency mechanism dominates the format i o n of c y c l o t r o n e c h o e s i n b o t h t y p e s of p l a s m a s . There are several additional results which t e n d to m a k e q u a n t i t a t i v e d e t e r m i n a t i o n of t h e Coulomb interaction processes difficult. As the electron density is increased one expects the electron-ion collision time to decrease with a resulting decrease in the two-pulse echo lifetime. T h i s i s not o b s e r v e d a l t h o u g h t h e n o n e x p o n e n t i a l c h a r a c t e r of t h e t w o - p u l s e e c h o d e c a y m a y t e n d to m a r k t h e o b s e r v a t i o n . In a d d i t i o n , t h e t h r e e p u l s e e c h o d e c a y s h o u l d b e a m e a s u r e of t h e e l e c t r o n e n e r g y r e l a x a t i o n [1]. F o r t h e p u r e l y C o u lomb collision this relaxation should proceed via the electron-electron interaction which has a " c o l l i s i o n " t i m e [11] Tee ~ 1.4 Tel. W e do, i n general, observe three-pulse echo lifetimes which are twice the two-pulse echo lifetime, but at the highest density n e ~ 2x 1012/cm 3 there was a weak three-pulse echo that persisted for 40 /z s e c . T h i s e x p e r i m e n t h a s p r o v i d e d o t h e r u n a n s w e r e d p r o b l e m s i n c l u d i n g t h e e x i s t e n c e of
Volume 22, number 5
PHYSICS LETTERS
a v e r y weak echo at a f r e q u e n c y of a p p r o x i m a t e l y 1.1 coc. The f r e q u e n c y f o r this echo was a l s o i n dependent of e l e c t r o n density. T h e s e o b s e r v a t i o n s a r e c u r r e n t l y u n d e r f u r t h e r study. This e x p e r i m e n t s u p p o r t s the v e l o c i t y d e p e n dent c o l l i s i o n m o d el of c y c l o t r o n echo g e n e r a t i o n and d e m o n s t r a t e s that e n e r g y and m o m e n t u m r e l a x a t i o n p r o c e s s e s and diffusion can be studied in a p u r e l y Coulomb p l a s m a u s i n g this technique. We wish to acknowledge v a l u a b l e d i s c u s s i o n s with Dr. G. F. H e r r m a n n . One of us (A. Y. W.) w i s h e s to acknowledge d i s c u s s i o n with Dr. B. D. F r i e d , Dr. R. W. Gould and D r . W. Kegel. We wish to thank the UCLA p l a s m a group, p a r t i c u l a r l y Mr. F. Hal and Mr . Z. Lucky f o r t h e i r able a s s i s tanc e.
BEAM-PLASMA
INSTABILITY
IN
15 September 1966
1. R.M,Hill and D.E.Kaplan, Phys.Rev. Letters 14 (1965) 1062. 2. G.F. Herrman and R.F .Whitmer, Phys. Rev. 143 (1966) 122. 3. R.W.Gould, Phys. Letters 19 (1965) 477; W.H .Kegel andR .W.Gould, Phys. Letters 19 (1965) 531. 4. J . L . Hirschfield and J.M.Wachtel, Bull.Am. Phys. S o c . l l (1966) 538. 5. F.W.CrawfordandR.S.Sharp, Phys.Lett. 21 (1966)292. 6. R.M.Hill, D.E.Kaplan and G.F.Herrmann, to b~ published. 7. The suggestion that a velocity dependent collision frequency would be a mechanism important for the formation of cyclotron echoes is due to J. P.Gordon (private communication). 8. N. Rynn and N. D'Angelo, Rev. Sci. Inst.31 (1960) 1326. 9. A.F.Kuckes and A.Y.Wong, Phys.Fluids 8 (1965) 1161; A.Y.Wongand A.F.Kuckes, Phys.Rev.Lett.13 (1964) 536. 10. R.M.Hill, D.E.Kaplan, Bull.Am.Phys.Soc.ll (1966) 496. 11. L.Spitzer, Physics of fully ionized gases, (2nd edition, Interscienee, New York) p. 132.
THE
HOLLOW
CATHODE
DISCHARGE
C. POPOVICI, M. SOME~AN and V. NISTOR Institute of Physics of the Academy of the Romanian Socialist Republic, Bucharest Received 6 August 1966
A new point of view is suggested that considers the hollow cathode effect as an expression of the plasma instabilities that arise when two antiparallel electronic beams are interacting in the plasma ("doublebeam instability").
The s t u d i e s c o n c e r n i n g the m e c h a n i s m of the glow d i s c h a r g e in a hollow cathode g e o m e t r y a g r e e about the e x i s t e n c e of two c l a s s e s of e l e c t r o n s in the glow: the group of f a s t p r i m a r y e l e c t r o n s a c c e l e r a t e d in the cathode fall r e g i o n and the group of t h e i r f i l i a t i o n in the p l a s m a . Consequently we m ay c o n s i d e r the n e g a t i v e glow of a hollow cathode d i s c h a r g e as a t h e r m a l p l a s m a through which a r e t r a v e l l i n g two b e a m s of r e l a t i v e l y f ew but e n e r g e t i c e l e c t r o n s o r i g i n a t i n g in the two cathodic d a r k s p a c e s . Such a b e a m p l a s m a m o d e l of the hollow cathode d i s c h a r g e a g r e e s with the point of v i e w a c c o r d i n g to which in a hollow cathode d i s c h a r g e , m o s t of the e x c i tation and ionization p r o c e s s e s a r e o c c u r r i n g in the n e g a t i v e glow p l a s m a [1, 2] . A b e a m of e l e c t r o n s may e x c i t e in c e r t a i n c o n ditions in the p l a s m a through which it is t r a v e l ling, longitudinal w a v e s with a p h a s e v e l o c i t y rougly equal to the m e a n v e l o c i t y of the e l e c t r o n s
of the b e a m . If two a n t i p a r a l l e l e l e c t r o n b e a m s a r e t r a v e l l i n g through the p l a s m a the o s c i l l a t i o n p a t t e r n that r e s u l t s is a standing wave [3,4]. We a s s u m e that o s c i l l a t i o n s a r e g e n e r a t e d in the s a m e m a n n e r in the negative p l a s m a of a hollow cathode d i s c h a r g e , by the two s t r e a m s of f a s t e l e c t r o n s e m e r g i n g f r o m the cathodic dark spaces. The "diffusion" of the d i s t r i b u t i o n function of the e l e c t r o n v e l o c i t i e s [5], as an e f f e c t of the w a v e - e l e c t r o n i n t e r a c t i o n , explains the p r e f e r e n t i a l e x c i t a t i o n of the m e t a l a t o m s s p u t t e r e d by the cathode as c o m p a r e d to the e x c i t a t i o n of gas a t o m s [6, 7]. The fact that p l a s m a - b e a m i n s t a b i l i t i e s r e s u l t in a s t r o n g i n c r e a s e of the ionization and e x c i t a tion p r o b a b i l i t i e s of gas a t o m s in a p l a s m a in m a g n e t i c f i el d was e m p h a s i z e d a l s o by K a r c h e n k o [8]. Such an abrupt i n c r e a s e of the ionization p r o b a b i l i t i e s e x p l a i n s the hollow cathode effect 587
P H YS I C S L E T T E R S
16. G. Bret, Compt.Rend. 260 (1965) 6323. 17. E . J . Stansbury, M.F. Crawford and H. L. Welsh, Can. J. of Phys. 31 (1953) 954. 18. E.Ishiguro, T.Arai, M.Mizushima and M.Kotani, Proc. Phys. Soc.A65 (1952) 178. 19. R.W. Terhune and C.W. Peters, J. Mol. Spect. 3 (1959) 138. 20. L.Galatry, Phys.Rev. 122 (1961) 1218. 21. R, W. Minck, E. E. Hagenlocker and W. G. Rado, to be published. 22. C.H.Townes, 4th Quantum electronics meeting, Phoenix (April 1966). 23. G.Bret, Compt. Rend. 262 (1966) 881.
8. R.W.Terhune, private communication. 9. G.Hauchecorne et G. Mayer, Compt.Rend. 261 (1965) 4014. 10. N. Bloembergen and P. Lallemand, Phys.Rev. Lett. 15 (1965) 1010. 11. P . L . Kelley, Phys.Rev. Letters 15 (1965) 1005. 12. Y.R.Shen and Y.I.Shaham, Phys.Rev. Letters 15 (1965) 1008. 13. G.Bret and G.Mayer, Physics of quantum electronics, eds. P. Kelley et al. (McGraw Hill, 1966). 14. G.Bret, F . G i r e s et G.Mayer, 4th Quantum electronics meeting Phoenix (April 1966). 15. G. Bret and M. Denariez, Appl. Phys. Letters, March 1st 1966.
OBSERVATION
OF
CYCLOTRON
15 September 1966
ECHOES
FROM
A HIGHLY
IONIZED
PLASMA
*
D. E. K A P L A N and R. M. HILL Lockheed Palo Alto Research Laboratory, Palo Alto, California and A. Y. WONG Department of Physics, University of California, Los Angeles, California Received 1 August 1966
The observation of cyclotron echo phenomena from a highly ionized cesium plasma in a Q-device is r e ported. The implication of these measurements for a velocity dependent collision frequency mechanism of cyclotron echo formation is discussed. The i n i t i a l o b s e r v a t i o n of c y c l o t r o n e c h o e s [1] in r a r e g as a f t e r g l o w p l a s m a s has s t i m u l a t e d s e v e r a l t h e o r e t i c a l e f f o r t s [2-6] to e x p la in the o r i g i n of this new phenomenon. T h e s e t r e a t m e n t s a r e s i m i l a r in adding a n o n l i n e a r t e r m dependent upon e x c i t a t i o n am p l i t u d e to the usual l i n e a r m o del of f r e e e l e c t r o n c y c l o t r o n r e s o n a n c e , f r o m which an echo cannot r e s u l t . The n o n l i n e a r t e r m d i f f e r s f o r e a c h model. H e r r m a n n and W h i t m e r [2] d i s c u s s a n o n l i n e a r i n t e r a c t i o n b e t w e e n e l e c t r o n and d r i v i n g field. Gould and K e g e l [3] and H i r s c h f i e l d [4] d i s c u s s a shift in r e s o n a n t f r e quency due to r e l a t i v i s t i c m a s s e f f e c t s , and a v e l o c i t y dependent c o l l i s i o n f r e q u e n c y m e c h a n i s m [7] is c o n s i d e r e d by C r a w f o r d and H a r p [5], and Hill et al. [6]. While the r e s u l t s of the a f t e r g l o w e x p e r i m e n t s indicate that the f o r m a t i o n of c y c l o t r o n e c h o e s in the a f t e r g l o w p l a s m a r e g i m e is due p r i m a r i l y to this l a t t e r m e c h a n i s m , the c o n c l u s i o n s a r e clouded by the c o m p e t i t i o n between e l e c t r o n - n e u t r a l and Coulomb c o l l i s i o n p r o c e s s e s in t h e s e weakly i o n i ze d p l a s m a s . A c c o r d i n g l y we
have c a r r i e d out c y c l o t r o n echo e x p e r i m e n t s in a c o m p l e t e l y d i f f e r e n t p l a s m a r e g i m e , a highly i o n i zed c e s i u m p l a s m a in the UCLA Q d e v i c e [8], in which the c o l l i s i o n p r o c e s s e s a r e e x c l u s i v e l y Coulombic. The o b j e c t i v e s of this e x p e r i m e n t a r e twofold - to d e m o n s t r a t e the utility of the c y c l o t r o n echo technique as a d i a g n o s t i c p r o b e f o r a b r o ad c l a s s of p l a s m a s , and to study c y c l o t r o n echo p h e n o m e n a in a p l a s m a m e d i u m m o r e suitable f o r v e r i f y i n g a p a r t i c u l a r echo m e c h a n ism. A s c h e m a t i c d i a g r a m of the c o n f i g u r a t i o n f o r t h i s Q - d e v i c e e x p e r i m e n t is shown in fig. 1. The r a n g e of e l e c t r o n d e n s i t i e s , he, extends f r o m 101I to 2)< 1012 e l e c t r o n s / c m 3 . The l o w e s t dens i t i e s in t h i s e x p e r i m e n t a r e in fact at the u p p e r density l i m i t f o r the a f t e r g l o w p l a s m a e x p e r i m e n t s . T w o - p u l s e and t h r e e - p u l s e c y c l o t r o n * Supported jointly by the U. S. Office of Naval Research, the U.S.Air Force Office of Scientific Research and the Lockheed Independent Research Fund. 585
Volume 22, number 5
STAINLESS
STEEL
PHYSICS LETTERS
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15 September 1966
layer becomes vanishingly small as ¢o ~ wc and the external electric field can reach the central column. The apparent absorption maximum for an incident wave remains at Wc on the wing of the upper hybrid resonance with increasing electron density because of a propagation cutoff region for 09>0) c.
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Fig. 1. Schematic d i a g r a m of the e x p e r i m e n t a l a r r a n g e ment. The cesium plasma, approximately ;3 em in d i a m e t e r and 40 em long is generated by the hot plate and t e r m i n a t e d by the cold end plate. The radial gradient of the axial magnetic field is 2% a c r o s s the p l a s m a column. X band h o r n s were used to couple radiation in and out of the p l a s m a column. echoes were observed with the microwave propagation direction k very nearly perpendicular to t h e a x i a l m a g n e t i c f i e l d B o. T h e f r e q u e n c y of e x c i t a t i o n w a s 8.55 G c , c y c l o t r o n r e s o n a n c e f o r f r e e e l e c t r o n s i n t h e m a g n e t i c f i e l d of 3.05 kG. T h e f r e q u e n c y a t w h i c h the e c h o w a s o b t a i n e d r e m a i n e d c o n s t a n t , i n d e p e n d e n t of e l e c t r o n d e n s i t y , o v e r t h e d e n s i t y r a n g e of o b s e r v a t i o n . T h e e c h o a m p l i t u d e w a s e n h a n c e d by a 2% m a g n e t i c field inhomogeneity over the plasma column produced by soft iron segments, symmetrically pos i t i o n e d a b o u t t h e m i c r o w a v e p o r t . 10 n s e c d u r a t i o n m i c r o w a v e p u l s e s a t 10 w a t t p e a k p o w e r w e r e c o u p l e d to a s e g m e n t of t h e p l a s m a c o l u m n t h r o u g h t h i s p o r t . T h e t w o - p u l s e e c h o l i f e t i m e in this experiment typically varied from 50-200 nsec. The echo decay envelopes were usually nonexpon e n t i a l . T h e l i f e t i m e of t h e t h r e e - p u l s e c y c l o t r o n e c h o w a s a p p r o x i m a t e l y t w i c e t h a t of tile t w o pulse echo. T h e p l a s m a f r e q u e n c y Wp v a r i e s f r o m 0.3 ¢oc to 1.3 coc f o r t h e e l e c t r o n d e n s i t i e s a t w h i c h e c h o e s w e r e o b s e r v e d , xand t h e u p p e r h y b r i d r e s o n a n c e ~o, r, = (w 2 + w~)~ f o r t h e e x t r a o r d i n a r y m o d e r a n g e s f r o m n e a r l y ¢oc to 1.5 w c. T h a t t h e e c h o r e m a i n s u n s h i f t e d in f r e q u e n c y a t w c w h i l e Wuh a t t a i n s v a l u e s a s h i g h a s 1.5 w c i s a n i n t e r e s t i n g r e s u l t r e q u i r i n g f u r t h e r s t u d y . It a p p e a r s unlikely that this echo results from scatter into a l o n g i t u d i n a l m o d e of p r o p a g a t i o n f o r w h i c h e l e c t r o n s w o u l d e x h i b i t a r e s o n a n c e a t ¢Oc, a l t h o u g h the experimental configuration does not preclude t h i s . One p o s s i b l e e x p l a n a t i o n f o r t h e c o n s t a n c y of t h e e c h o f r e q u e n c y i s t h a t t h e r a d i a l d e n s i t y p r o f i l e g i v e s r i s e to a n e v a n e s c e n t r e g i o n f o r p e r p e n d i c u l a r p r o p a g a t i o n [9] a t w > coc. S u c h a 586
W e f i n d t h a t a t w o - p u l s e e c h o i s o b s e r v e d only w h e n t h e e l e c t r o n - i o n e o l l i s i o n t i m e Tel i s e q u a l to o r s h o r t e r t h a n t h e t i m e t D r e q u i r e d f o r a n e l e c t r o n to d r i f t o u t of t h e i n t e r a c t i o n r e g i o n , t D is an upper limit to the echo lifetime. This drift t i m e i s a p p r o x i m a t e l y 150 n s e c f o r e l e c t r o n s w i t h t e m p e r a t u r e 2300OK. If we a s s u m e t h e e l e c t r o n v e l o c i t y i m p a r t e d by t h e m i c r o w a v e p u l s e s i s t w i c e t h e t h e r m a l v e l o c i t y we r e q u i r e a n e l e c tron density n e ~ 1011/era 3 in order to have r e i < t D. T h i s c o r r e s p o n d s c l o s e l y t o t h e m i n i mum density for which echoes are observed. S i n c e Zei ~ v3/n e w h e r e v i s t h e t o t a l e l e c t r o n velocity, the electron-ion collisions are ineffective in producing an echo before the electrons d r i f t out of t h e i n t e r a c t i o n r e g i o n if n e < 1 0 1 1 / c m 3 In t h e a f t e r g l o w e x p e r i m e n t s t h e e l e c t r o n - n e u t r a l c o l l i s i o n t i m e Ten i s l e s s t h a n t D a n d i n d e p e n d e n t of n e. It i s i m p o r t a n t to n o t e t h a t e c h o e s of s u b s t a n t i a l a m p l i t u d e [10] a r e o b s e r v e d i n t h e a f t e r g l o w p l a s m a s a t e l e c t r o n d e n s i t i e s a s low a s 107/cm 3 although the macroscopic electric dipole moment diminishes directly as the electron density. This circumstance coupled with the disapp e a r a n c e of c y c l o t r o n e c h o e s i n t h e Q - d e v i c e plasma for electron densities below 1011/era 3 strongly suggests that the velocity dependent collision frequency mechanism dominates the format i o n of c y c l o t r o n e c h o e s i n b o t h t y p e s of p l a s m a s . There are several additional results which t e n d to m a k e q u a n t i t a t i v e d e t e r m i n a t i o n of t h e Coulomb interaction processes difficult. As the electron density is increased one expects the electron-ion collision time to decrease with a resulting decrease in the two-pulse echo lifetime. T h i s i s not o b s e r v e d a l t h o u g h t h e n o n e x p o n e n t i a l c h a r a c t e r of t h e t w o - p u l s e e c h o d e c a y m a y t e n d to m a r k t h e o b s e r v a t i o n . In a d d i t i o n , t h e t h r e e p u l s e e c h o d e c a y s h o u l d b e a m e a s u r e of t h e e l e c t r o n e n e r g y r e l a x a t i o n [1]. F o r t h e p u r e l y C o u lomb collision this relaxation should proceed via the electron-electron interaction which has a " c o l l i s i o n " t i m e [11] Tee ~ 1.4 Tel. W e do, i n general, observe three-pulse echo lifetimes which are twice the two-pulse echo lifetime, but at the highest density n e ~ 2x 1012/cm 3 there was a weak three-pulse echo that persisted for 40 /z s e c . T h i s e x p e r i m e n t h a s p r o v i d e d o t h e r u n a n s w e r e d p r o b l e m s i n c l u d i n g t h e e x i s t e n c e of
Volume 22, number 5
PHYSICS LETTERS
a v e r y weak echo at a f r e q u e n c y of a p p r o x i m a t e l y 1.1 coc. The f r e q u e n c y f o r this echo was a l s o i n dependent of e l e c t r o n density. T h e s e o b s e r v a t i o n s a r e c u r r e n t l y u n d e r f u r t h e r study. This e x p e r i m e n t s u p p o r t s the v e l o c i t y d e p e n dent c o l l i s i o n m o d el of c y c l o t r o n echo g e n e r a t i o n and d e m o n s t r a t e s that e n e r g y and m o m e n t u m r e l a x a t i o n p r o c e s s e s and diffusion can be studied in a p u r e l y Coulomb p l a s m a u s i n g this technique. We wish to acknowledge v a l u a b l e d i s c u s s i o n s with Dr. G. F. H e r r m a n n . One of us (A. Y. W.) w i s h e s to acknowledge d i s c u s s i o n with Dr. B. D. F r i e d , Dr. R. W. Gould and D r . W. Kegel. We wish to thank the UCLA p l a s m a group, p a r t i c u l a r l y Mr. F. Hal and Mr . Z. Lucky f o r t h e i r able a s s i s tanc e.
BEAM-PLASMA
INSTABILITY
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15 September 1966
1. R.M,Hill and D.E.Kaplan, Phys.Rev. Letters 14 (1965) 1062. 2. G.F. Herrman and R.F .Whitmer, Phys. Rev. 143 (1966) 122. 3. R.W.Gould, Phys. Letters 19 (1965) 477; W.H .Kegel andR .W.Gould, Phys. Letters 19 (1965) 531. 4. J . L . Hirschfield and J.M.Wachtel, Bull.Am. Phys. S o c . l l (1966) 538. 5. F.W.CrawfordandR.S.Sharp, Phys.Lett. 21 (1966)292. 6. R.M.Hill, D.E.Kaplan and G.F.Herrmann, to b~ published. 7. The suggestion that a velocity dependent collision frequency would be a mechanism important for the formation of cyclotron echoes is due to J. P.Gordon (private communication). 8. N. Rynn and N. D'Angelo, Rev. Sci. Inst.31 (1960) 1326. 9. A.F.Kuckes and A.Y.Wong, Phys.Fluids 8 (1965) 1161; A.Y.Wongand A.F.Kuckes, Phys.Rev.Lett.13 (1964) 536. 10. R.M.Hill, D.E.Kaplan, Bull.Am.Phys.Soc.ll (1966) 496. 11. L.Spitzer, Physics of fully ionized gases, (2nd edition, Interscienee, New York) p. 132.
THE
HOLLOW
CATHODE
DISCHARGE
C. POPOVICI, M. SOME~AN and V. NISTOR Institute of Physics of the Academy of the Romanian Socialist Republic, Bucharest Received 6 August 1966
A new point of view is suggested that considers the hollow cathode effect as an expression of the plasma instabilities that arise when two antiparallel electronic beams are interacting in the plasma ("doublebeam instability").
The s t u d i e s c o n c e r n i n g the m e c h a n i s m of the glow d i s c h a r g e in a hollow cathode g e o m e t r y a g r e e about the e x i s t e n c e of two c l a s s e s of e l e c t r o n s in the glow: the group of f a s t p r i m a r y e l e c t r o n s a c c e l e r a t e d in the cathode fall r e g i o n and the group of t h e i r f i l i a t i o n in the p l a s m a . Consequently we m ay c o n s i d e r the n e g a t i v e glow of a hollow cathode d i s c h a r g e as a t h e r m a l p l a s m a through which a r e t r a v e l l i n g two b e a m s of r e l a t i v e l y f ew but e n e r g e t i c e l e c t r o n s o r i g i n a t i n g in the two cathodic d a r k s p a c e s . Such a b e a m p l a s m a m o d e l of the hollow cathode d i s c h a r g e a g r e e s with the point of v i e w a c c o r d i n g to which in a hollow cathode d i s c h a r g e , m o s t of the e x c i tation and ionization p r o c e s s e s a r e o c c u r r i n g in the n e g a t i v e glow p l a s m a [1, 2] . A b e a m of e l e c t r o n s may e x c i t e in c e r t a i n c o n ditions in the p l a s m a through which it is t r a v e l ling, longitudinal w a v e s with a p h a s e v e l o c i t y rougly equal to the m e a n v e l o c i t y of the e l e c t r o n s
of the b e a m . If two a n t i p a r a l l e l e l e c t r o n b e a m s a r e t r a v e l l i n g through the p l a s m a the o s c i l l a t i o n p a t t e r n that r e s u l t s is a standing wave [3,4]. We a s s u m e that o s c i l l a t i o n s a r e g e n e r a t e d in the s a m e m a n n e r in the negative p l a s m a of a hollow cathode d i s c h a r g e , by the two s t r e a m s of f a s t e l e c t r o n s e m e r g i n g f r o m the cathodic dark spaces. The "diffusion" of the d i s t r i b u t i o n function of the e l e c t r o n v e l o c i t i e s [5], as an e f f e c t of the w a v e - e l e c t r o n i n t e r a c t i o n , explains the p r e f e r e n t i a l e x c i t a t i o n of the m e t a l a t o m s s p u t t e r e d by the cathode as c o m p a r e d to the e x c i t a t i o n of gas a t o m s [6, 7]. The fact that p l a s m a - b e a m i n s t a b i l i t i e s r e s u l t in a s t r o n g i n c r e a s e of the ionization and e x c i t a tion p r o b a b i l i t i e s of gas a t o m s in a p l a s m a in m a g n e t i c f i el d was e m p h a s i z e d a l s o by K a r c h e n k o [8]. Such an abrupt i n c r e a s e of the ionization p r o b a b i l i t i e s e x p l a i n s the hollow cathode effect 587