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Parametric excitation of cyclotron harmonic waves in plasmas
Volume 28A, number 9
PARAMETRIC
PHYSICS
EXCITATION IN
LETTERS
10 February 1969
OF CYCLOTRON PLASMAS
HARMONIC
WAVES
S. TANAKA, R. SUGAYA and K. M I Z U N O Department o f P h y s i c s , Faculty of Science, University o f Kyoto, Kyoto. Japan Received 8 January 1969
The p a r a m e t r i c excitation of electrostatic cyclotron harmonic waves (Bernstein mode) by means of an electromagnetic wave at the pump frequency twice the excited one are observed experimentally.
There has been considerable interest, both t h e o r e t i c a l [1] and e x p e r i m e n t a l [2], in the p a r a m e t r i c r e s o n a n c e s in p l a s m a s . R e c e n t l y , it i s s h o w n t h e o r e t i c a l l y by T a k e o [3] and A m a n o e t al. [4] t h a t the p a r a m e t r i c c o u p l i n g v i a a d e n s i t y g r a d i e n t i s i m p o r t a n t and it w a s a l s o p r o p o s e d [4] t h a t a p a r a m e t r i c e x c i t a t i o n of the u p p e r h y b r i d m o d e i s p o s s i b l e . In t h i s l e t t e r , e x p e r i m e n t a l r e s u l t s a r e p r e s e n t e d , w h i c h show the p a r a m e t r i c e n h a n c e m e n t of the f l u c t u a t i o n s at the h y b r i d (Coh = (cod 2 + Wc2)½) and the e l e c t r o n c y c l o t r o n h a r m o n l c f r e q u e n c i e s (Co = nCoc; n = 2 , 3 , . . ) and a low t h r e s h o l d d e p e n d e n t on the d e n s i t y gradient. Experiments have been performed using a pos i t i v e c o l u m n in a d i s c h a r g e tube, w h e r e two 15 m m din d i s k a n t e n n a s a r e p l a c e d s y m m e t r i c a l l y a b o u t the tube a x i s (its s e p a r a t i o n D = 15 m m ) and a l i g n e d p a r a l l e l to a m a g n e t i c field. T h e p u m p f i e l d Vpump f r o m an e x t e r n a l o s c i l l a t o r i s a p p l i e d to one of the two a n t e n n a s , the o t h e r b e i n g g r o u n d e d . T h e output s i g n a l V s is p i c k e d up by a n e e d l e p r o b e i n s e r t e d b e t w e e n the two a n t e n n a s and fed to a f i e l d - i n t e n s i t y - m e t e r tuned to a half 1 of the p u m p f r e q u e n c y , Cod ~ ~Copump, and i s p l o t t e d a s a f u n c t i o n of Coc/Cod . A s shown in the e m i s s i o n s p e c t r a in fig. l a , w h e n V_ _ _ e x c• e e d s a t h r e s h o l d v a l u e , Vth, a puL~p l a r g e i n c r e a s e tpeak C2, C 3 and C4) in the e m i t ted s i g n a l o c c u r s at a c r i t i c a l m a g n e t i c field, though t h e r e a r e no p e a k s f o r Vpump < Vth. M e a s u r i n g e m i s s i o n s p e c t r a f o r the v a r i o u s v a l u e s of Id, w e c a n o b t a i n the (Coc/Cod) - (Cop/Cod) 2 d i a g r a m of fig. lb. T h e s e r i e s of the e x p e r i m e n t a l p l o t s H, C2 . . . . . a r e o b s e r v e d n e a r Co = Coh and Co = nCoc, r e s p e c t i v e l y . S u b s t i t u t i n g the w a v e l e n g t h of e x c i t e d s i g n a l , w h i c h i s a s s u m e d to be t w i c e D, T e = 2 eV and (Wp/Cod)2 = 1.5 into the 650
dispersion relation for perpendicularly propagating c y c l o t r o n h a r m o n i c w a v e s in a M a x w e l l i a n p l a s m a , w e can o b t a i n Coc/Cod = 0.65, w h i c h agrees well with experiments. Therefore, these p e a k s c a n be e x p l a i n e d a s a m a n i f e s t a t i o n of the p a r a m e t r i c e x c i t a t i o n of B e r n s t e i n m o d e s * . * See footnote on next page.
3
0
v
DISCHARGE CURRENT Id(mA) 5 I0 , 1 '~a} ' '~c'~
rr, t,
,,-d
I
TI 2L
", ,.
I.,I_ (.) l-ILl Z
t tt 2-'
\
b)
a l.IJ N
0 Z
w:w h
i
I
1
i
,
0.5 1.0 1.5 NORMALIZED ELECTRON DENSITY (Wp/Wd) 2
Fig. 1. (a) Emission spectra as a function of (We/COd) in the absence (dotted curve) and in the presence (solid curve) of Vpump. with Id = 19 mA. (b) (C0o/COd) - (wp/cod)2 diagram. The normalized magnetic field (Coe/cod), at which the excited peaks H, C2, C 3 . . . appear in emission spectra, is plotted as a function of the discharge current Id, or the normalized electron density (cop/cod) 2. Enhanced emissions are observed in the region of the magnetic field denoted by the v e r t i c a l bar and become maximum at the field d e noted by the circle. Experimental conditions are: H g , p = 1.5 m T o r r , Te = 2 eV, VDump = 0.9 V / c m , COpump/2n = 248 and ~Od/2n = 120 MHz.
Volume 28A, number 9
PHYSICS
It i s r e m a r k a b l e t h a t Vth i s of the o r d e r of 0.1 V / c m , w h i c h i s s m a l l e r by a few o r d e r s t h a n t h a t p r e d i c t e d t h e o r e t i c a l l y [1], and d e p e n d s on p l a s m a p a r a m e t e r s . A s r e g a r d s to a d e p e n d e n c e of Vth on Wp 2 in the H and C2 m o d e s , Vth a t t a i n s a m i n i m u m v a l u e n e a r the double r e s o n a n c e , wh = 2Wc, and i n c r e a s e s b o t h a b o v e and b e l o w the e l e c t r o n d e n s i t y c o r r e s p o n d i n g to t h i s r e s o n a n c e v a l u e . T h e t h r e s h o l d Vth d e c r e a s e s s h a r p l y and a t t a i n s a c o n s t a n t v a l u e , a s a n e g a t i v e v a l u e of the p o t e n t i a l of the d i s k r e l a t i v e to the s p a c e one i s i n c r e a s e d . T h i s f a c t s e e m s to b e due to the i n c r e a s e of the d e n s i t y g r a d i e n t in the s h e a t h r e g i o n , a s s u m i n g t h a t the p a r a m e t r i c e x c i t a t i o n o c c u r s in t h a t r e g i o n . T h e e l e c t r o n d e n s i t y Wp2, f r o m w h i c h w = w h i s c a l c u l a t e d and p l o t t e d in fig. l b , i s not o b t a i n e d by the n e e d l e p r o b e , but by the d i s k one, w h i c h s h o w s that the p a r a m e t r i c e x c i t a t i o n o c c u r s n e a r the d i s k r a t h e r t h a n in c e n t r a l p a r t of the p o s i t i v e c o l u m n . T h e s e e x p e r i m e n t a l r e s u l t s a r e i m p l i e d by t h e t h e o r y
[4]. F o r the i n t e n s e p u m p f i e l d , n o n l i n e a r e f f e c t s * As p d e c r e a s e s the peak C2~splits into several sharp ones. For the fixed ¢oc. COp~ and p ~ 0.5 mTorr, these sharp peaks satisfy ¢Opump = 2¢0d and ¢o~i+ w~, while the conservation of wave numbers being under study.
LETTERS
10 February 1969
a r e o b s e r v e d . A s Vpump i n c r e a s e s , Vs i n c r e a s e s at f i r s t , r e a c h e s a s a t u r a t i o n v a l u e , t h e n d e c r e a s e s and, at l a s t , the e n h a n c e d e m i s s i o n d i s a p p e a r s . C o r r e s p o n d i n g l y , the h a l f - w i d t h of the e x c i t e d s i g n a l b e c o m e s b r o a d and i t s r e s o n a n c e f r e q u e n c y (its c r i t i c a l m a g n e t i c field) d e c r e a s e s ( i n c r e a s e s ) s l i g h t l y w h e n Vpump b e c o m e s so i n t e n s e t h a t the n o n l i n e a r s a t u r a t i o n occurs. T h e a u t h o r s w i s h to e x p r e s s t h e i r t h a n k s to D r s . T. A m a n o and K. N i s h i k a w a f o r t h e i r h e l p ful d i s c u s s i o n s . References 1. E.A. Jackson, Phys. Rev. 153 (1967} 110. D. F. Du Bois and M. V. Goldman, Phys. Rev. 164 (1967) 207. K. Nishikawa. J. Phys. Soc. Japan 24 (1968) 916 and 1152. 2, K. Kato. M. Yoseli, S. Kiyama and S. Watanabe. J. Phys. Soc. Japan 20 (1965) 2097. S. Hiroe and H. Ikegami, Phys. Rev. Letters 19 (1967) 1414. A. Y. Wong, M.V. Goldman. F. Hai and R. Rowberg, Phys. Rev. Letters 21 (1968) 518. 3. A. Takeo, J . P h y s . Soc. Japan 22 (1967) 1282. 4. T. Amano and M. Okamoto. J. Phys. Soc. Japan 23 {1967} 1432 and ibid. to be published.
P L A N A R BLOCKING I N T E N S I T I E S : A C O R R E L A T I O N WITH CONTINUUM P O T E N T I A L S W. W H I T E and R. M. M U E L L E R Nuclear-Chicago Corporation. Des Plaines, Illinois, 60018, USA
Received 1 January 1969
Experimental planar blocking intensities for diamond cubic, hcp, and wurtzite crystals are compared with continuum potentials calculated by summing the contributions of neighboring planes. Structure of the interplanar potential well, in addition to b a r r i e r height, is shown to be important in determining blocking effects.
Blocking phenomena for energetic heavy charg e d p a r t i c l e s in c r y s t a l s a r e u s u a l l y d e s c r i b e d in t e r m s of the i n t e r a c t i o n of a p a r t i c l e w i t h the a v e r a g e o r c o n t i n u u m p o t e n t i a l of a single r o w o r p l a n e of a t o m s [1,2]. S u c h a m o d e l i s in s u b s t a n t i a l a c c o r d w i t h e x p e r i m e n t [3,4] f o r m o n a t o m i c c r y s t a l s of u n i f o r m i n t e r p l a n a r s p a c i n g s , but f a i l s to p r e d i c t t h e r e l a t i v e i n t e n s i t i e s of p l a n a r b l o c k -
ing lines for crystals with staggered interplanar spacings [4]. In this letter we present selected examples, from a more extensive investigation [5], which demonstrate the effects of neighboring planes. The need for such studies has been noted by other [6-8]. Barrett [9] has shown a correlation of planar blocking intensities with structure factor computations. 651
PARAMETRIC
PHYSICS
EXCITATION IN
LETTERS
10 February 1969
OF CYCLOTRON PLASMAS
HARMONIC
WAVES
S. TANAKA, R. SUGAYA and K. M I Z U N O Department o f P h y s i c s , Faculty of Science, University o f Kyoto, Kyoto. Japan Received 8 January 1969
The p a r a m e t r i c excitation of electrostatic cyclotron harmonic waves (Bernstein mode) by means of an electromagnetic wave at the pump frequency twice the excited one are observed experimentally.
There has been considerable interest, both t h e o r e t i c a l [1] and e x p e r i m e n t a l [2], in the p a r a m e t r i c r e s o n a n c e s in p l a s m a s . R e c e n t l y , it i s s h o w n t h e o r e t i c a l l y by T a k e o [3] and A m a n o e t al. [4] t h a t the p a r a m e t r i c c o u p l i n g v i a a d e n s i t y g r a d i e n t i s i m p o r t a n t and it w a s a l s o p r o p o s e d [4] t h a t a p a r a m e t r i c e x c i t a t i o n of the u p p e r h y b r i d m o d e i s p o s s i b l e . In t h i s l e t t e r , e x p e r i m e n t a l r e s u l t s a r e p r e s e n t e d , w h i c h show the p a r a m e t r i c e n h a n c e m e n t of the f l u c t u a t i o n s at the h y b r i d (Coh = (cod 2 + Wc2)½) and the e l e c t r o n c y c l o t r o n h a r m o n l c f r e q u e n c i e s (Co = nCoc; n = 2 , 3 , . . ) and a low t h r e s h o l d d e p e n d e n t on the d e n s i t y gradient. Experiments have been performed using a pos i t i v e c o l u m n in a d i s c h a r g e tube, w h e r e two 15 m m din d i s k a n t e n n a s a r e p l a c e d s y m m e t r i c a l l y a b o u t the tube a x i s (its s e p a r a t i o n D = 15 m m ) and a l i g n e d p a r a l l e l to a m a g n e t i c field. T h e p u m p f i e l d Vpump f r o m an e x t e r n a l o s c i l l a t o r i s a p p l i e d to one of the two a n t e n n a s , the o t h e r b e i n g g r o u n d e d . T h e output s i g n a l V s is p i c k e d up by a n e e d l e p r o b e i n s e r t e d b e t w e e n the two a n t e n n a s and fed to a f i e l d - i n t e n s i t y - m e t e r tuned to a half 1 of the p u m p f r e q u e n c y , Cod ~ ~Copump, and i s p l o t t e d a s a f u n c t i o n of Coc/Cod . A s shown in the e m i s s i o n s p e c t r a in fig. l a , w h e n V_ _ _ e x c• e e d s a t h r e s h o l d v a l u e , Vth, a puL~p l a r g e i n c r e a s e tpeak C2, C 3 and C4) in the e m i t ted s i g n a l o c c u r s at a c r i t i c a l m a g n e t i c field, though t h e r e a r e no p e a k s f o r Vpump < Vth. M e a s u r i n g e m i s s i o n s p e c t r a f o r the v a r i o u s v a l u e s of Id, w e c a n o b t a i n the (Coc/Cod) - (Cop/Cod) 2 d i a g r a m of fig. lb. T h e s e r i e s of the e x p e r i m e n t a l p l o t s H, C2 . . . . . a r e o b s e r v e d n e a r Co = Coh and Co = nCoc, r e s p e c t i v e l y . S u b s t i t u t i n g the w a v e l e n g t h of e x c i t e d s i g n a l , w h i c h i s a s s u m e d to be t w i c e D, T e = 2 eV and (Wp/Cod)2 = 1.5 into the 650
dispersion relation for perpendicularly propagating c y c l o t r o n h a r m o n i c w a v e s in a M a x w e l l i a n p l a s m a , w e can o b t a i n Coc/Cod = 0.65, w h i c h agrees well with experiments. Therefore, these p e a k s c a n be e x p l a i n e d a s a m a n i f e s t a t i o n of the p a r a m e t r i c e x c i t a t i o n of B e r n s t e i n m o d e s * . * See footnote on next page.
3
0
v
DISCHARGE CURRENT Id(mA) 5 I0 , 1 '~a} ' '~c'~
rr, t,
,,-d
I
TI 2L
", ,.
I.,I_ (.) l-ILl Z
t tt 2-'
\
b)
a l.IJ N
0 Z
w:w h
i
I
1
i
,
0.5 1.0 1.5 NORMALIZED ELECTRON DENSITY (Wp/Wd) 2
Fig. 1. (a) Emission spectra as a function of (We/COd) in the absence (dotted curve) and in the presence (solid curve) of Vpump. with Id = 19 mA. (b) (C0o/COd) - (wp/cod)2 diagram. The normalized magnetic field (Coe/cod), at which the excited peaks H, C2, C 3 . . . appear in emission spectra, is plotted as a function of the discharge current Id, or the normalized electron density (cop/cod) 2. Enhanced emissions are observed in the region of the magnetic field denoted by the v e r t i c a l bar and become maximum at the field d e noted by the circle. Experimental conditions are: H g , p = 1.5 m T o r r , Te = 2 eV, VDump = 0.9 V / c m , COpump/2n = 248 and ~Od/2n = 120 MHz.
Volume 28A, number 9
PHYSICS
It i s r e m a r k a b l e t h a t Vth i s of the o r d e r of 0.1 V / c m , w h i c h i s s m a l l e r by a few o r d e r s t h a n t h a t p r e d i c t e d t h e o r e t i c a l l y [1], and d e p e n d s on p l a s m a p a r a m e t e r s . A s r e g a r d s to a d e p e n d e n c e of Vth on Wp 2 in the H and C2 m o d e s , Vth a t t a i n s a m i n i m u m v a l u e n e a r the double r e s o n a n c e , wh = 2Wc, and i n c r e a s e s b o t h a b o v e and b e l o w the e l e c t r o n d e n s i t y c o r r e s p o n d i n g to t h i s r e s o n a n c e v a l u e . T h e t h r e s h o l d Vth d e c r e a s e s s h a r p l y and a t t a i n s a c o n s t a n t v a l u e , a s a n e g a t i v e v a l u e of the p o t e n t i a l of the d i s k r e l a t i v e to the s p a c e one i s i n c r e a s e d . T h i s f a c t s e e m s to b e due to the i n c r e a s e of the d e n s i t y g r a d i e n t in the s h e a t h r e g i o n , a s s u m i n g t h a t the p a r a m e t r i c e x c i t a t i o n o c c u r s in t h a t r e g i o n . T h e e l e c t r o n d e n s i t y Wp2, f r o m w h i c h w = w h i s c a l c u l a t e d and p l o t t e d in fig. l b , i s not o b t a i n e d by the n e e d l e p r o b e , but by the d i s k one, w h i c h s h o w s that the p a r a m e t r i c e x c i t a t i o n o c c u r s n e a r the d i s k r a t h e r t h a n in c e n t r a l p a r t of the p o s i t i v e c o l u m n . T h e s e e x p e r i m e n t a l r e s u l t s a r e i m p l i e d by t h e t h e o r y
[4]. F o r the i n t e n s e p u m p f i e l d , n o n l i n e a r e f f e c t s * As p d e c r e a s e s the peak C2~splits into several sharp ones. For the fixed ¢oc. COp~ and p ~ 0.5 mTorr, these sharp peaks satisfy ¢Opump = 2¢0d and ¢o~i+ w~, while the conservation of wave numbers being under study.
LETTERS
10 February 1969
a r e o b s e r v e d . A s Vpump i n c r e a s e s , Vs i n c r e a s e s at f i r s t , r e a c h e s a s a t u r a t i o n v a l u e , t h e n d e c r e a s e s and, at l a s t , the e n h a n c e d e m i s s i o n d i s a p p e a r s . C o r r e s p o n d i n g l y , the h a l f - w i d t h of the e x c i t e d s i g n a l b e c o m e s b r o a d and i t s r e s o n a n c e f r e q u e n c y (its c r i t i c a l m a g n e t i c field) d e c r e a s e s ( i n c r e a s e s ) s l i g h t l y w h e n Vpump b e c o m e s so i n t e n s e t h a t the n o n l i n e a r s a t u r a t i o n occurs. T h e a u t h o r s w i s h to e x p r e s s t h e i r t h a n k s to D r s . T. A m a n o and K. N i s h i k a w a f o r t h e i r h e l p ful d i s c u s s i o n s . References 1. E.A. Jackson, Phys. Rev. 153 (1967} 110. D. F. Du Bois and M. V. Goldman, Phys. Rev. 164 (1967) 207. K. Nishikawa. J. Phys. Soc. Japan 24 (1968) 916 and 1152. 2, K. Kato. M. Yoseli, S. Kiyama and S. Watanabe. J. Phys. Soc. Japan 20 (1965) 2097. S. Hiroe and H. Ikegami, Phys. Rev. Letters 19 (1967) 1414. A. Y. Wong, M.V. Goldman. F. Hai and R. Rowberg, Phys. Rev. Letters 21 (1968) 518. 3. A. Takeo, J . P h y s . Soc. Japan 22 (1967) 1282. 4. T. Amano and M. Okamoto. J. Phys. Soc. Japan 23 {1967} 1432 and ibid. to be published.
P L A N A R BLOCKING I N T E N S I T I E S : A C O R R E L A T I O N WITH CONTINUUM P O T E N T I A L S W. W H I T E and R. M. M U E L L E R Nuclear-Chicago Corporation. Des Plaines, Illinois, 60018, USA
Received 1 January 1969
Experimental planar blocking intensities for diamond cubic, hcp, and wurtzite crystals are compared with continuum potentials calculated by summing the contributions of neighboring planes. Structure of the interplanar potential well, in addition to b a r r i e r height, is shown to be important in determining blocking effects.
Blocking phenomena for energetic heavy charg e d p a r t i c l e s in c r y s t a l s a r e u s u a l l y d e s c r i b e d in t e r m s of the i n t e r a c t i o n of a p a r t i c l e w i t h the a v e r a g e o r c o n t i n u u m p o t e n t i a l of a single r o w o r p l a n e of a t o m s [1,2]. S u c h a m o d e l i s in s u b s t a n t i a l a c c o r d w i t h e x p e r i m e n t [3,4] f o r m o n a t o m i c c r y s t a l s of u n i f o r m i n t e r p l a n a r s p a c i n g s , but f a i l s to p r e d i c t t h e r e l a t i v e i n t e n s i t i e s of p l a n a r b l o c k -
ing lines for crystals with staggered interplanar spacings [4]. In this letter we present selected examples, from a more extensive investigation [5], which demonstrate the effects of neighboring planes. The need for such studies has been noted by other [6-8]. Barrett [9] has shown a correlation of planar blocking intensities with structure factor computations. 651