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1063-780X/00/2604- $20.00 © 2000 MAIK “Nauka/Interperiodica” 0366 Plasma Physics Reports, Vol. 26, No. 4, 2000, pp. 366–368. Translated from Fizika Plazmy, Vol. 26, No. 4, 2000, pp. 393–395. Original Russian Text Copyright © 2000 by Ivanov, Knyazev, Luk’yanov, Murav’ev, Serov, Fedotov. A low-pressure steady-state beam–plasma dis- charge (BPD) in a longitudinal magnetic field is an effi- cient tool for producing plasmochemical dissociation reactions [1, 2]. It can also be used in technology for surface treating. The efficiency of surface treating increases in the presence of flows of high-energy ions, which can be produced by combining a BPD with an RF discharge (combined BPD–RF discharge). The interaction of an RF electric field with a magnetized plasma is also of great interest for heating plasma elec- trons and ions. In this paper, we consider a combined BPD–RF dis- charge, in which a potential RF electric field (= 8.5 × 10 7 s –1 ) perpendicular to the magnetic field is applied to a conventional BPD. The schematic of the experiment is presented in Fig. 1 (see [3] for details). The plasma was produced in argon at a pressure of 10 –4 –10 –3 torr by a sheetlike electron beam with an energy of 2 keV and current of 0.05–1 A and was con- fined by a 300- to 500-G magnetic field. An electron beam propagated along the magnetic field. In the absence of an RF field, the shape of the beam-electron distribution function (BEDF) on the whole varied according to the one-dimensional quasilinear theory (Fig. 2). However, in developed BPDs, the relaxation length was several times greater than that predicted by the theory. (This well-known discrepancy has led to the development of the theory of strong turbulence, which, however, predicts a relaxation length substantially larger than that observed in experiments [4].) In some cases, when an external RF field was applied to a BPD plasma, the discharge was quenched. This occurred when the plasma density and tempera- ture were low, n < (2–3) × 10 11 cm –3 and T e < 2–3 eV. The quenching manifested itself in a decrease in the plasma density by more than one order of magnitude when the RF field was switched on. In this case, near the electron beam, at distances more than several elec- tron cyclotron radii from the field source, the electric field was 1–2 V/cm. The plasma parameters and the Effect of an External RF Field on the Beam–Plasma Discharge in a Magnetic Field A. A. Ivanov, L. N. Knyazev, A. A. Luk’yanov, S. V. Murav’ev, A. A. Serov, and V. Yu. Fedotov Russian Research Centre Kurchatov Institute, pl. Kurchatova 1, Moscow, 123182 Russia Received April 27, 1999 Abstract—The effect of an RF field on a steady-state beam–plasma discharge with a plane electrode placed parallel to a sheetlike electron beam is studied experimentally. The plasma parameters were measured by a sin- gle probe, and the electron distribution function was determined with the use of an electrostatic analyzer. The energy and current of the electron beam were E B = 2.5 keV and J B = 0.05–1.5 A, respectively. The working pressure was p = 2 × 10 –5 –10 –3 torr. The frequency of the external RF field was 13.56 MHz. Both the steady- state regimes in which the RF field had no effect on the plasma parameters and regimes with a pronounced effect of the RF field were observed. The experiments show that the regime of the discharge depends strongly on the plasma density and the magnetic field. The parametric instability is studied theoretically in the weak-turbulence approximation. It is shown that, due to the decay nature of the spectrum of plasma oscillations, the onset of instability is accompanied by the transfer of the energy of fluctuations over the spectrum, from the pump fre- quency toward its harmonics. © 2000 MAIK “Nauka/Interperiodica”. Electric field Magnetic field Electron beam B E B Fig. 1. Beam–plasma discharge device with a sheetlike beam. PLASMA ELECTRONICS AND NEW ACCELERATION METHODS

Effect of an external RF field on the beam-plasma discharge in a magnetic field

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Plasma Physics Reports, Vol. 26, No. 4, 2000, pp. 366–368. Translated from Fizika Plazmy, Vol. 26, No. 4, 2000, pp. 393–395.Original Russian Text Copyright © 2000 by Ivanov, Knyazev, Luk’yanov, Murav’ev, Serov, Fedotov.

PLASMA ELECTRONICSAND NEW ACCELERATION METHODS

Effect of an External RF Field on the Beam–Plasma Dischargein a Magnetic Field

A. A. Ivanov, L. N. Knyazev, A. A. Luk’yanov, S. V. Murav’ev, A. A. Serov, and V. Yu. Fedotov

Russian Research Centre Kurchatov Institute, pl. Kurchatova 1, Moscow, 123182 RussiaReceived April 27, 1999

Abstract—The effect of an RF field on a steady-state beam–plasma discharge with a plane electrode placedparallel to a sheetlike electron beam is studied experimentally. The plasma parameters were measured by a sin-gle probe, and the electron distribution function was determined with the use of an electrostatic analyzer. Theenergy and current of the electron beam were EB = 2.5 keV and JB = 0.05–1.5 A, respectively. The workingpressure was p = 2 × 10–5–10–3 torr. The frequency of the external RF field was 13.56 MHz. Both the steady-state regimes in which the RF field had no effect on the plasma parameters and regimes with a pronounced effectof the RF field were observed. The experiments show that the regime of the discharge depends strongly on theplasma density and the magnetic field. The parametric instability is studied theoretically in the weak-turbulenceapproximation. It is shown that, due to the decay nature of the spectrum of plasma oscillations, the onset ofinstability is accompanied by the transfer of the energy of fluctuations over the spectrum, from the pump fre-quency toward its harmonics. © 2000 MAIK “Nauka/Interperiodica”.

A low-pressure steady-state beam–plasma dis-charge (BPD) in a longitudinal magnetic field is an effi-cient tool for producing plasmochemical dissociationreactions [1, 2]. It can also be used in technology forsurface treating. The efficiency of surface treatingincreases in the presence of flows of high-energy ions,which can be produced by combining a BPD with anRF discharge (combined BPD–RF discharge). Theinteraction of an RF electric field with a magnetizedplasma is also of great interest for heating plasma elec-trons and ions.

In this paper, we consider a combined BPD–RF dis-charge, in which a potential RF electric field (Ω = 8.5 ×107 s–1) perpendicular to the magnetic field is applied toa conventional BPD. The schematic of the experimentis presented in Fig. 1 (see [3] for details).

The plasma was produced in argon at a pressure of10–4–10–3 torr by a sheetlike electron beam with anenergy of 2 keV and current of 0.05–1 A and was con-fined by a 300- to 500-G magnetic field. An electronbeam propagated along the magnetic field. In theabsence of an RF field, the shape of the beam-electrondistribution function (BEDF) on the whole variedaccording to the one-dimensional quasilinear theory(Fig. 2). However, in developed BPDs, the relaxationlength was several times greater than that predicted bythe theory. (This well-known discrepancy has led to thedevelopment of the theory of strong turbulence, which,however, predicts a relaxation length substantiallylarger than that observed in experiments [4].)

In some cases, when an external RF field wasapplied to a BPD plasma, the discharge was quenched.

1063-780X/00/2604- $20.00 © 20366

This occurred when the plasma density and tempera-ture were low, n < (2–3) × 1011 cm–3 and Te < 2–3 eV.The quenching manifested itself in a decrease in theplasma density by more than one order of magnitudewhen the RF field was switched on. In this case, nearthe electron beam, at distances more than several elec-tron cyclotron radii from the field source, the electricfield was 1–2 V/cm. The plasma parameters and the

Electric field

Magnetic field

Electron beam

B

E

B

Fig. 1. Beam–plasma discharge device with a sheetlikebeam.

000 MAIK “Nauka/Interperiodica”

Page 2: Effect of an external RF field on the beam-plasma discharge in a magnetic field

EFFECT OF AN EXTERNAL RF FIELD ON THE BEAM–PLASMA DISCHARGE 367

local potential of the RF field were measured by aLangmuir probe. To measure the plasma density np andthe electron temperature Te, a high-frequency filter wasintroduced into the probe circuit. The probe could bemoved in the direction perpendicular to the direction ofelectron-beam propagation, which allowed us to mea-sure the spatial distributions of the plasma parameters.

The RF potential was measured by the shift of theprobe floating potential VS according to the expression

VS = –(Te/e)ln(e /Te) [5]. The beam-electron energyanalyzer based on the retarding-field method was posi-tioned at the end of the experimental chamber and mea-sured the BEDF. The spectra of plasma oscillationsexcited under the parametric action of the RF field werealso analyzed (Fig. 3). The spectrum consisted of aseries of peaks localized near harmonics of the pumpfrequency. This is evidence of the transfer of the energyof fluctuations to the high-frequency region of the spec-trum.

Such a spectrum is very different from that pre-dicted by the well-known theoretical models (see, e.g.,[6, 7]). According to those models, the energy of fluc-tuations must be transferred toward low frequencies(down to the lower hybrid frequency ΩLH) and smallwavenumbers k ≈ 0. After that, the plasma should cometo a highly turbulent state, which should be accompa-nied by the formation of a Langmuir condensate. In theabove papers, the basic nonlinear process leading tosaturation of the parametric instability is the inducedscattering of plasma waves by ions.

Here, we propose another scenario of the onset ofthe instability. In the magnetic field, the plasma oscilla-tions in the frequency range under study are described

V

V

BEDF, 104 eV–1

10

5

0 1 2 3 4E, keV

1 2

3

4

3' 2'

Fig. 2. (1) Initial BEDF and (2–4) BEDFs measured at thedevice output in the absence of an RF field for the beam cur-rents I = (2) 0.05, (3) 0.25, and (4) 0.7 A. The arrows showthe lower beam energy calculated by the quasilinear theory.

PLASMA PHYSICS REPORTS Vol. 26 No. 4 2000

by the following dispersion relation [8]:

(1)

where ΩLH ≤ ω < ωce, ωce is the electron cyclotron fre-

quency; A0 = I0( )exp(– ), ρe is the electroncyclotron radius; I0(x) is the modified Bessel function;

y = (kz/k) , M and m are the ion and electron masses,

respectively; ω/|kz| > vTe; k = |k|; and k⊥ is the wave-vec-tor component perpendicular to the magnetic field. Themagnetic field is directed along the z-axis.

The dispersion curve ω(k) can be conventionallydivided into two regions: the electron region (k ! 1 andthe ion-acoustic region (k > 1).

The external RF field drives the parametric instabil-ity with the maximum growth rates

in the electron region and

in the ion region (here, ue is the electron drift velocityand cs is the speed of sound), which results in the exci-tation of the wave packets P1e and P1i in the electron andion-acoustic regions, respectively. Two waves bothbelonging to any of these packets and having the fre-quencies ω1 ≈ ω2 ≈ Ω generate long-wavelength oscilla-

ω2 k( )ωpi

21 y

2A0+( )

1 1 A0–( )/k2ρDe

2+

---------------------------------------------,=

k⊥2 ρe

2k ⊥

2 ρe2

Mm-----

γmax18---

ue2ΩLH

2

cs2Ω

----------------=

γmax18---

ue2

cs2

-----Ω=

Amplitude, arb. units9

0 1 2 3 4Frequency, rad/s × 108

8

7

6

5

4

3

2

1

5 6 7 8

Fig. 3. The spectrum of plasma oscillations excited underthe parametric action of an external RF field.

Page 3: Effect of an external RF field on the beam-plasma discharge in a magnetic field

368 IVANOV et al.

tions with the frequency ω in the electron region suchthat

ω = ω1 + ω2, k = k1 + k2.

These conditions, which are usually referred to asthe decay conditions, are consistent with equation (1).Evidently, ω ≈ 2Ω; thus, a packet P2 emerges near thesecond harmonic of the pump frequency. Similarly, twowaves belonging to the packets P1e and P2 generate thewave with frequency ≈3Ω , etc. Thus, we obtain the setof packets near the harmonics of the pump frequency.Since these packets relate to the long-wavelength elec-tron region, they can be easily recorded in the experi-ment.

As for short-wavelength oscillations excited in theion-acoustic region, it is difficult to observe themdirectly. Nevertheless, they manifest themselves indi-rectly through their strong effect on the beam–plasmainstability. Since the growth rate of the instability is

proportional to /Ω2u2 ~ (where u is thebeam velocity), it strongly decreases in the presence ofshort-wavelength oscillations, so that the beam relax-ation is suppressed.

ωpe2

cs2

ki2 k ⊥

2⁄

REFERENCES1. A. A. Ivanov and T. K. Soboleva, Nonequilibrium Plas-

mochemistry (Atomizdat, Moscow, 1978).2. Yu. F. Nasedkin, L. N. Knyazev, A. N. Korukov, and

A. A. Serov, Proceedings of Interindustry Seminar onPhysical Principles of Innovative Plasma Technologiesin Microelectronics, Kharkov, 1991, p. 51.

3. V. M. Atamanov, G. B. Levadnyi, A. A. Ivanov, et al.,Beitr. Plasmaphys. 22, 509 (1982).

4. A. K. Berezin, E. V. Lifshits, Ya. B. Fainberg, et al., Fiz.Plazmy 21, 241 (1995) [Plasma Phys. Rep. 21, 227(1995)].

5. V. A. Godyak, A. N. Ivanov, and A. A. Kuzovnikov, Zh.Tekh. Fiz. 37, 1063 (1967) [Sov. Phys. Tech. Phys. 12,766 (1967)].

6. S. L. Musher, A. M. Rubenchik, and B. I. Sturman,Plasma Phys. 20, 1131 (1978).

7. B. D. Ogirov and A. M. Rubenchik, Zh. Éksp. Teor. Fiz.81, 159 (1981) [Sov. Phys. JETP 54, 79 (1981)].

8. A. B. Mikhaœlovskiœ, Theory of Plasma Instabilities(Atomizdat, Moscow, 1971; Consultants Bureau, NewYork, 1974).

Translated by A. D. Smirnova†

† Now deceased.

PLASMA PHYSICS REPORTS Vol. 26 No. 4 2000