Parametric Instabilities and Anomalous Heating of Plasmas near the Lower Hybrid Frequency

Abstract

It is shown both by theory and by computer experiments that a plasma subjected to a long-wavelength electric field oscillating near the lower hybrid frequency causes parametric instabilities which lead to an anomalous heating of both ions and electrons. Because the instability threshold is much lower than that for the corresponding electron plasma-wave problem, the saturation of the electric field can be much higher.Plasma heating by anomalous absorption of a large-amplitude external electromagnetic wave has been of considerable theoretical and experimental interest. 1 " 5 We show by theory and by computer simulations that an electric field perpendicular to a dc magnetic field and oscillating at a frequency above but near the lower hybrid frequency can excite, at extremely low thresholds, decay and purely growing parametric instabilities. 2 These result in short-wavelength lower hybrid waves and ion waves and lead to a substantial plasma heating. This driving field might be associated with a whistler wave, with a lower hybrid wave propagating nearly perpendicular to a magnetic field, 6 * 7 or even with grids in the plasma. Such instabilities may occur naturally in shock-heated plasmas and Earth's magnetosphere. 8 We consider the stability of a homogeneous plasma embedded in a uniform magnetic field Bjz and an oscillatory electric field JEQ^ cos(oo 0 t) in the dipole approximation; u> 0 is chosen close to the lower hybrid frequency co LH =o> /)i /(l + <*)p e 2 / tyj 2 ) 172 , where <JO PJ and fy are jth species plasma and gyrofrequencies, respectively. It is assumed that fy «co 0~ u)LH « Gl e . The linearized Vlasov equations for ion and electrons in the lab frame are of the usual form with an external acceleration term (qj/Mj)E 0 cos(oo 0 t)y. 5 The zeroth-order distribution function of the ;th species is taken as Maxwellian in its own oscillating frame and the linearized equations are solved in the usual way. 5 The coupling coefficient x = k • v 0 /co 0 is assumed less than unity where v 0 = (cE 0 /B 0 )x; ion orbits are taken as straight lines and kp e «l is assumed. Keeping only the lowest-order terms in x and taking k\ De «1 to simplify the form of the equation yields the following dispersion relation, which is of the standard form for three-wave mode cou-pling problems in the lab frame 2 ' 8 (approximately the ion frame):Xe a e 2 k 2 (co + iy n + nu 0 ) 2 -X.°*1/* 8 W, and y n are wave damping rates. Electron motion via the E mQ xB. 0 drift provides the dominant coupling here. In contrast to the high-frequency parametric instabilities where a> 0 is near w Pe or £l e , lt4 ion dynamics cannot be neglected in € ±1 , and this allows the excited highfrequency waves to heat ions directly. 9 Equation (1) exhibits both decay and purely growing or two-stream-type instabilities. Using Eqs.(1) and (2) the minimum threshold 2 for the decay of the pump at co 0 into a lower hybrid wave at ii fSfe'V? Vi/i M e 2 V e 2 X\{ l/2 and an acoustic wave at oo s = kc s is given by Above threshold where damping is not important the...

Parametrically Induced Nonlinear Wave-Particle Scattering and Plasma Heating near the Lower Hybrid Frequency

“…Previous theory considered only the resonant decay of ion acoustic modes, and the purely growing instability. 5 In what follows we shall present experimental results verifying the fundamental aspects of the nonresonant decay instability, and show that substantial plasma heating is associated with the parametrically excited modes. Thus, we believe that these modes will play an important role in future lower-hybrid rf heating of fusion plasmas.…”

Lower hybrid oscillating two-stream instability in a plasma with magnetic shear

“…the region where the solutions K(E,) are real, exists and has a finite extent only when A > y. This region reduces to the point g = |A when A = y which is the condition for the threshold of the instability in the presence of a constant magnetic field B o (Kindel et al 1972). Next we shall obtain a more complete solution of (27), first when A > y and then when A > y.…”

“…Initially, the idea was that the incident wave energy would be absorbed by linear mechanisms (Landau or collisional damping) near the lower hybrid resonance layer (Stix 1965). However, there has been experimental evidence (Hooke & Bernabei 1972;Chu, Bernabei & Motley 1973;Chang & Porkolab 1973,1974 and theoretical predictions (Kindel, Okuda & Dawson 1972) that nonlinear processes, i.e. parametric instabilities, may become effective in absorbing the incident wave energy Rogister & Hasselberg 1976).…”

“…In this paper we focus on the effect that shear has on OTSI. Both experimental (Chang & Porkolab 1974) and theoretical (Kindel et al 1972) work have shown the effectiveness of OTSI as a heating mechanism in the lower hybrid frequency range. It has been pointed out that the OTS instability is a feature of the dipole pump approximation and that finite values of the pump wavenumber k 0 introduce a finite real low frequency w (Fried et al 1976).…”

“…parametric instabilities, may become effective in absorbing the incident wave energy Rogister & Hasselberg 1976). A variety of decay channels have been investigated both for a dipole pump (Kindel et al 1972;Porkolab 1974a;Berger & Perkins 1976) and for a pump with a finite wavelength (Ott 1975). However, it is not straightforward to extrapolate results for an infinite homogeneous plasma to results for a realistic fusion-type plasma.…”