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Parametric excitation of the drift wave by a modulated ion beam
Volume 95A, number 6
PHYSICS LETTERS
9 May 1983
PARAMETRIC EXCITATION OF THE DRIFT WAVE BY A MODULATED ION BEAM Mitsuyasu YATSUZUKA, Kikoh SATOH, Sadao NOBUHARA, Kiyoshi YATSUI a and Masahiro YOKOYAMA b Department of Electrical Engineering, Himeji Institute of Technology, HimejL Hyogo 671-22, Japan a Laboratory of Beam-Fusion Technology, The Technological University of Nagaoka, Nagaoka, Niigata 949-54, Japan b lnsn'tute of Laser Engineering, Osaka University, Suita, Osaka 565, Japan Received 3 June 1982 Revised manuscript received 26 January 1983
Parametric excitation of the drift wave is observed by an ion beam modulated near the lower-hybrid frequency. An rf field parallel to the magnetic field is found to play an important role in the excitation of the instability. Substantial increase of the ion and electron temperatures is observed.
Recently, there has been considerable interest in supplemental plasma heating by use of an rf electric field near the lower-hybrid (LH) frequency [ 1]. Charged particle beams modulated by an rf field are being considered to bring rf power into the interior of the plasma, leading to an effective energy transfer from beam to plasma. In fact, the injection of modulated electron beams near the LH frequency has driven parametric instabilities of the LH wave and the ion cyclotron wave or the ion quasi-mode, and shown enhanced plasma heating [ 2 - 5 ] . In these experiments, the radial electric field has been produced by the excess charge within the unneutralized electron beam, since the transit time of the beam is much less than the modulation period. A similar argument may be valid for a modulated ion beam. In this letter we wish to present the experimental identification of the parametric instability driven by a modulated ion beam. Associated plasma heating is also reported. The experiments were done in a double-plasma device in a longitudinal, uniform magnetic field. The plasma chamber (SUS) was 10.6 cm in diameter and 150 cm long. Both the target (diameter Dp = 5 cm, 0 031-9163/83/0000-0000/$ 03.00 © 1983 North-Holland
length L = 46 cm) and beam source plasmas were produced by hot cathode discharges. The target plasma was separated from the beam source by a negatively biased fine mesh grid (0.6 cm in diameter, mesh spacing (35 lines/cm) ,~ Debye length)). When the target plasma was negatively biased with respect to the beam source plasma, the ion beam was injected into the target plasma along the magnetic lines of force. By superimposing the rf pump field on the discharge current of the beam source, the beam density was modulated near the LH frequency. Typical experimental parameters were: n o (plasma density) ~ ( 1 - 5 ) × 108 c m - 3, Te 0 (electron temperature in the absence of the pump field) ~-0.2-0.3 eV, Ti0 (ion temperature in the absence of the pump field) ~O.3-0.4 eV, B 0 (magnetic field strength) ~ 0 . 5 - 1 kG, p (He gas pressure) ~2.8 × 10 - 4 Torr, r b (beam radius) ~0.3 cm, Vb (beam accelerating voltage) ~ 1 0 0 - 2 0 0 V, and n b (beam density) ~-5 X 106 cm -3. The rf power of the transmitter was less than 12 W. The electron temperature, density, and excited waves were measured or picked up by the probes movable in the r, 0, and z directions. Ion-temperature measurements were 293
Volume 95A, number 6
PHYSICS LETTERS
carried out b y a Faraday cup (0.5 cm in diameter). A ceramically shielded double-tip probe was used to measure the rf pump field. The frequency 6o0 o f the rf pump field was chosen around the LH frequency: 6 0 0 ~ 60LH ~" Wpi (in the present experiment, 60pe/60ce '~ 5 X 1 0 - 2 ) . As the pump field was increased above a certain threshold Ve, we observed an onset o f parametric decay. The pump mode decays into the low-frequency wave 6o 1 and the high-frequency wave w 2. Typical frequencies and amplitudes of the 600, COl, and 6o2 modes are shown in figs. l a and l b , respectively. The frequency o f the w 1 mode is less than the ion cyclotron frequency 60ei (i.e., 601/60ei ~ 0 . 1 - 0 . 2 ) , and that o f the 602 mode is slightly higher than the LH frequency (w2/60Ln ~ 1.4--3.5). The frequency matching condition, 600 = 6°1 + 602, is always satisfied. Measure-
2'2-(a) ~ ~ "~
~
-
2.1
9 May 1983
ments o f the ion and electron temperatures were also carried out, and are plotted in fig. lc. At zero pump field, we see Ti0 ~ 0.3 eV and Te0 ,~ 0.2 eV. With the onset o f the decay instability, substantial heating o f ions and electrons takes place up to T i ~ 1.8 eV and T e ~ 2.9 eV. This plasma heating may be ascribed to the wave heating [6] due to the parametrically excited drift wave [7]. In the present experiment, the plasma density is inhomogeneous in the r direction. The maximum density gradient occurs around the beam edge where b o t h decay waves are strongly localized, a~ shown in fig. 2a. The density gradient coefficient was typically K n = - ( 1 / n o ) d n o / d x ~ 1 c m - 1 (KT/Kn ~ 0.4, K T
(a)
~
°°° ~ - I ~
.... ~2
j
(b)
'
-I
I
v
i
-1
I
,
0.1
o)I ,
,
,
I
I
1 r
0.05
I
0
I
--wave
2
/~Vde
(cm)
I
,
' |
o -(b) 5
:
•
"
4 "3 E "-'2
, ~
÷,
T
U
•
!
1
o
o
2
4
6
Vo (v).,
8
10
Fig. 1. (a) Frequency/'and (b) amplitude 0 of pump too, low-frequency to] and lower sideband to2 modes versus modulation voltage F0, where Vc is the threshold voltage. (c) Ion Ti and electron Te temperatures versus modulation voltage, p = 2.7 X 10 .-4 Tort, B o = 6 6 0 G, V b = 110 V, and /'o = 2.2 MHz. 294
0
0
I
I
I
I
I
1
2
3
4
5
6
kel (cm-1) Fig. 2. (a) Ion saturation current/is and wave amplitude 4,1 of the to I mode in the radial direction. (b) Signals of the to I mode picked up by two 180° -separated probe~ x = 10 #s/div. (c) Perpendicular wave number of the to I and to 2 modes, no = 3 X 108 cm -3.
=
9 May 1983
PHYSICS L E T T E R S
V o l u m e 95A, n u m b e r 6
-(llTe)dTeldx). The wave number parallel and per-
pendicular to the magnetic field was determined by measuring the phase shift of signals between a reference probe and a radially (or azimuthally) movable probe. The signals of the 601 mode from two probes azimuthally displaced by 1 80 ° are shown in fig. 2b, indicating the azimuthal mode number as m 1 = 1. By using the azimuthal traveling probe, the w 1 mode was found to propagate in the same direction as the electron diamagnetic drift, while the 602 mode in the opposite direction with m 2 = 1. As the decay waves were not observed to propagate in the r direction, the perpendicular wave number is determined by Ikil ~" Ik o I = m/r O, where r 0 is the radial position of the maximum wave amplitude, fig. 2c shows the perpendicular wave numbers of the 601 and 602 modes, satisfYing Iko 11 ~ Ik021. In the z direction, the 601 and 6o2 modes were observed to be a standing wave pattern of the axial mode number 11,2 = 1, indicating Ik,ll Ikl12[ = niL. The decay waves (601 and 6o2 modes) are considered to propagate almost perpendicularly to the magnetic field [kll/k, ~. 3(me/mi)l/2]. We have also studied the phase shift of the 600 mode in the r, 0, and z directions by using an interferometer technique. We have not observed the phase shift of the 600 mode in any direction. Thus, we may conclude that [k01 ~ 0 (dipole approximation). These experimental studies demonstrate that the momentum-conservation law can be satisfied as k 1 + k 2 = k 0 ~ 0. From the wave characteristics mentioned above, the 601 mode seems to be the drift wave. Furthermore, we study the dispersion relation of the drift wave in an external LH frequency electric field. If the rf field is oriented parallel to the magnetic field, the dispersion relation of the drift wave is given by refs. [8,9]
A
_
1
[eEllkl, ~2[
1 - co2[60 2
2k2d2 ~me6021 !~(1 -'~2/6020)----~+ ~2]' lr 1/2
= k2d---~
6°0
kllu---~
exp(-602/k~,u2),
COA 2 = COL2H[1 + (k~/k2)mi/me], 2 2 b~ _- k±2 vt//260c/,
ut/2 -_ 2T/ /m/, T - Te/Ti, A 0 = exp(-bi)Io(bi),Io(bi) is the modified Bessel func-
tion, Eli is the amplitude of the rf electric field parallel to the magnetic field, co/* is the drift frequency, a n d / d e n o t e s the species of the particle [electron (e) and ion (i)]. The dispersion relations for the drift and LH waves are compared with experimental values of the 6o 1 and 60 2 modes in fig. 3, where the ordinate is enlarged in the region of the drift wave. Here, the ex. perimental values of frequencies (e) are determined by subtraction of the effect of plasma rotation due to the E r X B 0 drift (typically, the radial electric field is E r 0.1 V/cm). In fig. 3, the theoretical curve of the LH wave is calculated from the dispersion relation of the LH wave in an irdaomogeneous plasma (602/602u = 1 +2 • 222 • ~'= kll milk 2 m e - cO60e/k de60~i ). As seen m fig. 3, reasonable agreement is obtainedbetween the theoretical curves and the experimental results. From these studies, the 601 mode may be identified as the drift wave, while the 602 mode the LH wave in the inhomogeneous plasma. In fig. 3, the experimental data of the 601
k "° 2
(T + A)A060 l 1 + ( T + A ) ( 1 - At) ) '
lrl/l~r 7 = 1 + (1 - A 0 ) ( T + A ) \
/
oLI
t.../
0
2 uti)(~i 2 • - ~r) ) ' A0 r exp(--60r/k{l
where
LH wave
~vmode 006~-
0 r
kllvti
o
drift
o
k,Vte
I
G2
I
I
T wave _~ r. / '' evl I
04 06 0.8 1/2 kl/h,(me/m i ) •
(2)
I
°
(1)
(60_~ - ~ r
I
~2.mode
•
f
60r--
I
I
1
"
Fig. 3. Dispersion relations for drift and LH waves together with experimental values o f co I a n d to 2 modes. WLH/2*r = 1.8 MHz, T i= 1 eV, and B o = 6 5 0 G.
295
Volume 95A, number 6
PHYSICS LETTERS
and 60.02 modes for co0/60LH = 2.3 are indicated by the sign (o). These data demonstrate that the 60- and k-matching conditions are satisfied. In addition, we consider the threshold electric field. F r o m the condition ? = 0 in eq. (2), the threshold field, E,c may be written as
9 May 1983 I
1
Experi.
-~ ~
~,
~Sfe
•
w
toO. 1 "IAl~t,H 2 ~AI(~ 0
where we have assumed A 0 ~ 1 - b i (typically, b i 0.25) a n d A b i "~ 1 and or-
T)(Tmi/me)l/2exp(-602/~o 2)
1 + (Tmi/me)l/2Texp(-w2/k2o2i)
(4)
Using typical experimental parameters, the threshold field Eli c is theoretically evaluated and is shown in fig. 4, where the dotted points represent the experimental threshold determined by the calibrated doubletip probe. Fig. 4 shows reasonable agreement between the theoretical threshold and the experimental measurements except in the region WA/W 0 > 1.8. In the region 60A/600 >~1.8, we see that the experimental thresholds are larger than the theoretical ones. This may be due to the frequency mismatch [10] which is caused by the deviation o f the excited modes from the natural modes. The rf pump field component across the magnetic field was observed, but is not shown here. However, the experimental radial rf field at the onset o f the instability was approximately 10 times less than the theoretical threshold Exc* 1. Then, the rf field parallel to the magnetic field is considered to play an important role in the excitation of the instability. In summary, the modulated ion beam near the LH * t When the rf field is directed perpendicular to the magnetic field, the threshold field E.Lc is given by E.Lc = (2a) 1/2 (kdiBowo/k.L) X ,.[ ~ + (1 - ~ / o a ~ ) 2 ]/11 - o)~l/~(~l } '/2 .
296
**
~
me6002 {~2 + (1 -- 602/602)211/2 EIIc=(2a)l/2kdi--~ll \ I 1 - - ,2/60 21 _/ , (3) '~A ~ 0 ~
Tbi(1 + T ) - T(1 +
I
Fig. 4. Threshold field versus pump frequency normalized by
)1/2.'. The theoretical threshold to A = COLH(l + k~mi/k2me field Elic is evaluated from eq. (3) by using experimental parameters. The dotted points denote the experimental threshold. T = Te/Ti, Te = 0.3 eV, WA/COLH= 2.59, and n o = 3 X 10s cm-3. frequency excites a parametric decay into a drift wave and a LH wave. The rf field parallel to the magnetic field is found to play an important role in the excitation o f the instability. Substantial increase o f the ion and electron temperatures has been observed with the growth o f the instability.
References [1] M. Porkolab, S. Bernabei, W.M. Hooke and R.W. Motley, Phys. Rev. Lett. 38 (1977) 230. [2] K. Yatsui and T. Imai, Phy~ Rev. Lett. 35 (1975) 1279. [3] K. Yatsui et al., Phys. Lett. 73A (1979) 321. [4] G.R. Alien et al., Phys. Rev. Lett. 41 (1978) 1045. [5] H. Fujiyama, Y. Watanabe and M. Akazaki, Jpn. J. Appl. Phys. 20 (1981) 1715. [6] S. Ichimaru, J. Phys. Soc. Japan 39 (1975) 1373. [7] M. Yatsuzuka et al., J. Phys. Soc. Japan, to be published. [8] M. Okamoto, T. Amano and K. Kitao, J. Phys. Soc. Japan 29 (1970) 1041. [9] A.K. Sundaram and P.K. Kaw, Nucl. Fusion 13 (1973) 901. [10] K. Nishikawa, J. Phys. Soc. Japan 24 (1968) 916.
PHYSICS LETTERS
9 May 1983
PARAMETRIC EXCITATION OF THE DRIFT WAVE BY A MODULATED ION BEAM Mitsuyasu YATSUZUKA, Kikoh SATOH, Sadao NOBUHARA, Kiyoshi YATSUI a and Masahiro YOKOYAMA b Department of Electrical Engineering, Himeji Institute of Technology, HimejL Hyogo 671-22, Japan a Laboratory of Beam-Fusion Technology, The Technological University of Nagaoka, Nagaoka, Niigata 949-54, Japan b lnsn'tute of Laser Engineering, Osaka University, Suita, Osaka 565, Japan Received 3 June 1982 Revised manuscript received 26 January 1983
Parametric excitation of the drift wave is observed by an ion beam modulated near the lower-hybrid frequency. An rf field parallel to the magnetic field is found to play an important role in the excitation of the instability. Substantial increase of the ion and electron temperatures is observed.
Recently, there has been considerable interest in supplemental plasma heating by use of an rf electric field near the lower-hybrid (LH) frequency [ 1]. Charged particle beams modulated by an rf field are being considered to bring rf power into the interior of the plasma, leading to an effective energy transfer from beam to plasma. In fact, the injection of modulated electron beams near the LH frequency has driven parametric instabilities of the LH wave and the ion cyclotron wave or the ion quasi-mode, and shown enhanced plasma heating [ 2 - 5 ] . In these experiments, the radial electric field has been produced by the excess charge within the unneutralized electron beam, since the transit time of the beam is much less than the modulation period. A similar argument may be valid for a modulated ion beam. In this letter we wish to present the experimental identification of the parametric instability driven by a modulated ion beam. Associated plasma heating is also reported. The experiments were done in a double-plasma device in a longitudinal, uniform magnetic field. The plasma chamber (SUS) was 10.6 cm in diameter and 150 cm long. Both the target (diameter Dp = 5 cm, 0 031-9163/83/0000-0000/$ 03.00 © 1983 North-Holland
length L = 46 cm) and beam source plasmas were produced by hot cathode discharges. The target plasma was separated from the beam source by a negatively biased fine mesh grid (0.6 cm in diameter, mesh spacing (35 lines/cm) ,~ Debye length)). When the target plasma was negatively biased with respect to the beam source plasma, the ion beam was injected into the target plasma along the magnetic lines of force. By superimposing the rf pump field on the discharge current of the beam source, the beam density was modulated near the LH frequency. Typical experimental parameters were: n o (plasma density) ~ ( 1 - 5 ) × 108 c m - 3, Te 0 (electron temperature in the absence of the pump field) ~-0.2-0.3 eV, Ti0 (ion temperature in the absence of the pump field) ~O.3-0.4 eV, B 0 (magnetic field strength) ~ 0 . 5 - 1 kG, p (He gas pressure) ~2.8 × 10 - 4 Torr, r b (beam radius) ~0.3 cm, Vb (beam accelerating voltage) ~ 1 0 0 - 2 0 0 V, and n b (beam density) ~-5 X 106 cm -3. The rf power of the transmitter was less than 12 W. The electron temperature, density, and excited waves were measured or picked up by the probes movable in the r, 0, and z directions. Ion-temperature measurements were 293
Volume 95A, number 6
PHYSICS LETTERS
carried out b y a Faraday cup (0.5 cm in diameter). A ceramically shielded double-tip probe was used to measure the rf pump field. The frequency 6o0 o f the rf pump field was chosen around the LH frequency: 6 0 0 ~ 60LH ~" Wpi (in the present experiment, 60pe/60ce '~ 5 X 1 0 - 2 ) . As the pump field was increased above a certain threshold Ve, we observed an onset o f parametric decay. The pump mode decays into the low-frequency wave 6o 1 and the high-frequency wave w 2. Typical frequencies and amplitudes of the 600, COl, and 6o2 modes are shown in figs. l a and l b , respectively. The frequency o f the w 1 mode is less than the ion cyclotron frequency 60ei (i.e., 601/60ei ~ 0 . 1 - 0 . 2 ) , and that o f the 602 mode is slightly higher than the LH frequency (w2/60Ln ~ 1.4--3.5). The frequency matching condition, 600 = 6°1 + 602, is always satisfied. Measure-
2'2-(a) ~ ~ "~
~
-
2.1
9 May 1983
ments o f the ion and electron temperatures were also carried out, and are plotted in fig. lc. At zero pump field, we see Ti0 ~ 0.3 eV and Te0 ,~ 0.2 eV. With the onset o f the decay instability, substantial heating o f ions and electrons takes place up to T i ~ 1.8 eV and T e ~ 2.9 eV. This plasma heating may be ascribed to the wave heating [6] due to the parametrically excited drift wave [7]. In the present experiment, the plasma density is inhomogeneous in the r direction. The maximum density gradient occurs around the beam edge where b o t h decay waves are strongly localized, a~ shown in fig. 2a. The density gradient coefficient was typically K n = - ( 1 / n o ) d n o / d x ~ 1 c m - 1 (KT/Kn ~ 0.4, K T
(a)
~
°°° ~ - I ~
.... ~2
j
(b)
'
-I
I
v
i
-1
I
,
0.1
o)I ,
,
,
I
I
1 r
0.05
I
0
I
--wave
2
/~Vde
(cm)
I
,
' |
o -(b) 5
:
•
"
4 "3 E "-'2
, ~
÷,
T
U
•
!
1
o
o
2
4
6
Vo (v).,
8
10
Fig. 1. (a) Frequency/'and (b) amplitude 0 of pump too, low-frequency to] and lower sideband to2 modes versus modulation voltage F0, where Vc is the threshold voltage. (c) Ion Ti and electron Te temperatures versus modulation voltage, p = 2.7 X 10 .-4 Tort, B o = 6 6 0 G, V b = 110 V, and /'o = 2.2 MHz. 294
0
0
I
I
I
I
I
1
2
3
4
5
6
kel (cm-1) Fig. 2. (a) Ion saturation current/is and wave amplitude 4,1 of the to I mode in the radial direction. (b) Signals of the to I mode picked up by two 180° -separated probe~ x = 10 #s/div. (c) Perpendicular wave number of the to I and to 2 modes, no = 3 X 108 cm -3.
=
9 May 1983
PHYSICS L E T T E R S
V o l u m e 95A, n u m b e r 6
-(llTe)dTeldx). The wave number parallel and per-
pendicular to the magnetic field was determined by measuring the phase shift of signals between a reference probe and a radially (or azimuthally) movable probe. The signals of the 601 mode from two probes azimuthally displaced by 1 80 ° are shown in fig. 2b, indicating the azimuthal mode number as m 1 = 1. By using the azimuthal traveling probe, the w 1 mode was found to propagate in the same direction as the electron diamagnetic drift, while the 602 mode in the opposite direction with m 2 = 1. As the decay waves were not observed to propagate in the r direction, the perpendicular wave number is determined by Ikil ~" Ik o I = m/r O, where r 0 is the radial position of the maximum wave amplitude, fig. 2c shows the perpendicular wave numbers of the 601 and 602 modes, satisfYing Iko 11 ~ Ik021. In the z direction, the 601 and 6o2 modes were observed to be a standing wave pattern of the axial mode number 11,2 = 1, indicating Ik,ll Ikl12[ = niL. The decay waves (601 and 6o2 modes) are considered to propagate almost perpendicularly to the magnetic field [kll/k, ~. 3(me/mi)l/2]. We have also studied the phase shift of the 600 mode in the r, 0, and z directions by using an interferometer technique. We have not observed the phase shift of the 600 mode in any direction. Thus, we may conclude that [k01 ~ 0 (dipole approximation). These experimental studies demonstrate that the momentum-conservation law can be satisfied as k 1 + k 2 = k 0 ~ 0. From the wave characteristics mentioned above, the 601 mode seems to be the drift wave. Furthermore, we study the dispersion relation of the drift wave in an external LH frequency electric field. If the rf field is oriented parallel to the magnetic field, the dispersion relation of the drift wave is given by refs. [8,9]
A
_
1
[eEllkl, ~2[
1 - co2[60 2
2k2d2 ~me6021 !~(1 -'~2/6020)----~+ ~2]' lr 1/2
= k2d---~
6°0
kllu---~
exp(-602/k~,u2),
COA 2 = COL2H[1 + (k~/k2)mi/me], 2 2 b~ _- k±2 vt//260c/,
ut/2 -_ 2T/ /m/, T - Te/Ti, A 0 = exp(-bi)Io(bi),Io(bi) is the modified Bessel func-
tion, Eli is the amplitude of the rf electric field parallel to the magnetic field, co/* is the drift frequency, a n d / d e n o t e s the species of the particle [electron (e) and ion (i)]. The dispersion relations for the drift and LH waves are compared with experimental values of the 6o 1 and 60 2 modes in fig. 3, where the ordinate is enlarged in the region of the drift wave. Here, the ex. perimental values of frequencies (e) are determined by subtraction of the effect of plasma rotation due to the E r X B 0 drift (typically, the radial electric field is E r 0.1 V/cm). In fig. 3, the theoretical curve of the LH wave is calculated from the dispersion relation of the LH wave in an irdaomogeneous plasma (602/602u = 1 +2 • 222 • ~'= kll milk 2 m e - cO60e/k de60~i ). As seen m fig. 3, reasonable agreement is obtainedbetween the theoretical curves and the experimental results. From these studies, the 601 mode may be identified as the drift wave, while the 602 mode the LH wave in the inhomogeneous plasma. In fig. 3, the experimental data of the 601
k "° 2
(T + A)A060 l 1 + ( T + A ) ( 1 - At) ) '
lrl/l~r 7 = 1 + (1 - A 0 ) ( T + A ) \
/
oLI
t.../
0
2 uti)(~i 2 • - ~r) ) ' A0 r exp(--60r/k{l
where
LH wave
~vmode 006~-
0 r
kllvti
o
drift
o
k,Vte
I
G2
I
I
T wave _~ r. / '' evl I
04 06 0.8 1/2 kl/h,(me/m i ) •
(2)
I
°
(1)
(60_~ - ~ r
I
~2.mode
•
f
60r--
I
I
1
"
Fig. 3. Dispersion relations for drift and LH waves together with experimental values o f co I a n d to 2 modes. WLH/2*r = 1.8 MHz, T i= 1 eV, and B o = 6 5 0 G.
295
Volume 95A, number 6
PHYSICS LETTERS
and 60.02 modes for co0/60LH = 2.3 are indicated by the sign (o). These data demonstrate that the 60- and k-matching conditions are satisfied. In addition, we consider the threshold electric field. F r o m the condition ? = 0 in eq. (2), the threshold field, E,c may be written as
9 May 1983 I
1
Experi.
-~ ~
~,
~Sfe
•
w
toO. 1 "IAl~t,H 2 ~AI(~ 0
where we have assumed A 0 ~ 1 - b i (typically, b i 0.25) a n d A b i "~ 1 and or-
T)(Tmi/me)l/2exp(-602/~o 2)
1 + (Tmi/me)l/2Texp(-w2/k2o2i)
(4)
Using typical experimental parameters, the threshold field Eli c is theoretically evaluated and is shown in fig. 4, where the dotted points represent the experimental threshold determined by the calibrated doubletip probe. Fig. 4 shows reasonable agreement between the theoretical threshold and the experimental measurements except in the region WA/W 0 > 1.8. In the region 60A/600 >~1.8, we see that the experimental thresholds are larger than the theoretical ones. This may be due to the frequency mismatch [10] which is caused by the deviation o f the excited modes from the natural modes. The rf pump field component across the magnetic field was observed, but is not shown here. However, the experimental radial rf field at the onset o f the instability was approximately 10 times less than the theoretical threshold Exc* 1. Then, the rf field parallel to the magnetic field is considered to play an important role in the excitation of the instability. In summary, the modulated ion beam near the LH * t When the rf field is directed perpendicular to the magnetic field, the threshold field E.Lc is given by E.Lc = (2a) 1/2 (kdiBowo/k.L) X ,.[ ~ + (1 - ~ / o a ~ ) 2 ]/11 - o)~l/~(~l } '/2 .
296
**
~
me6002 {~2 + (1 -- 602/602)211/2 EIIc=(2a)l/2kdi--~ll \ I 1 - - ,2/60 21 _/ , (3) '~A ~ 0 ~
Tbi(1 + T ) - T(1 +
I
Fig. 4. Threshold field versus pump frequency normalized by
)1/2.'. The theoretical threshold to A = COLH(l + k~mi/k2me field Elic is evaluated from eq. (3) by using experimental parameters. The dotted points denote the experimental threshold. T = Te/Ti, Te = 0.3 eV, WA/COLH= 2.59, and n o = 3 X 10s cm-3. frequency excites a parametric decay into a drift wave and a LH wave. The rf field parallel to the magnetic field is found to play an important role in the excitation o f the instability. Substantial increase o f the ion and electron temperatures has been observed with the growth o f the instability.
References [1] M. Porkolab, S. Bernabei, W.M. Hooke and R.W. Motley, Phys. Rev. Lett. 38 (1977) 230. [2] K. Yatsui and T. Imai, Phy~ Rev. Lett. 35 (1975) 1279. [3] K. Yatsui et al., Phys. Lett. 73A (1979) 321. [4] G.R. Alien et al., Phys. Rev. Lett. 41 (1978) 1045. [5] H. Fujiyama, Y. Watanabe and M. Akazaki, Jpn. J. Appl. Phys. 20 (1981) 1715. [6] S. Ichimaru, J. Phys. Soc. Japan 39 (1975) 1373. [7] M. Yatsuzuka et al., J. Phys. Soc. Japan, to be published. [8] M. Okamoto, T. Amano and K. Kitao, J. Phys. Soc. Japan 29 (1970) 1041. [9] A.K. Sundaram and P.K. Kaw, Nucl. Fusion 13 (1973) 901. [10] K. Nishikawa, J. Phys. Soc. Japan 24 (1968) 916.