The threshold condition for stochastic diffusion of energetic ions due to lower hybrid waves

Abstract

In the present paper we consider the interaction between energetic ions and lower hybrid waves in tokamak plasmas and study the parametric dependence of the threshold condition for stochastic ion di usion. It is shown that the threshold condition as obtained in the work by Karney C. F. F. Karney, P h ys. Fluids 22, 2188 1979 may be not easily satis ed in present d a y large tokamaks, but can attained in small tokamaks with relatively modest levels of wave p o wer. I IntroductionIn a series of two papers published in 1978 and 1979, it has been shown that the movement of an ion in a uniform magnetic eld becomes stochastic in the presence of a perpendicularly propagating coherent electrostatic wave, if the wave amplitude exceeds a threshold 1, 2 . Due to the stochasticity the ion di uses in velocity space, and this di usion may be described by a di usion equation which also applies to the case of lower hybrid waves in the slow mode non-vanishing k k k ? , propagating in a weakly inhomogeneous magnetic eld 2 . The possibility of this di usion mechanism raised important questions related to the e ciency of proposed RF current drive s c hemes using lower hybrid LH waves 3, 4, 5 . In particular, it has been argued that in fusion reactors the presence of particles originated from fusion reactions would contribute to decrease the e ciency of the lower hybrid current drive, since part of the energy of the LH waves would be absorbed by the particles 1 . The potential importance of this interaction between LH waves and particles has motivated subsequent i n vestigations, and many examples may be found in the recent literature 6, 7 , 8 , 9 , 1 0 , 11, 12, 13 . Investigations have also been made by considering other kind of possible interactions, as the interaction between LH waves and a population of energetic ions generated by neutral beam injection 14, 1 5 , 16, 17 , and the interaction between LH waves and fast ions generated by I C w aves utilized for ion heating. Some experimental results on this subject are available, as those originated from relatively recent experiments conducted in the JET tokamak Joint European Torus 18, 1 9 . The results of these experiments provide evidence of signi cant absorption of LH waves by fast ions, and therefore con rm the convenience of further investigations on this important issue concerning the dynamics of particles or other energetic ions in the environment of a reactor, and the e ciency of the LH waves for radio frequency current drive.In the present paper we study particular features of the subject, considering the threshold condition for stochastic di usion of energetic ions, in a tokamak environment modelated by a plasma slab. We utilize the formalism proposed by Karney 2 , discussing the dependence of the threshold condition on some wave and plasma parameters, for large present d a y tokamaks and for small scale tokamaks, and compare the value of the electric eld predicted by the threshold condition with the wave electric eld inside the tokamak.

Interaction between lower hybrid waves and energetic ions in a tokamak system

“…For the LH waves we consider parameters already utilized in our previous analysis about the threshold condition [17], namely wave power W 0 (a) = 1.0 MW, N chosen such that the resonance condition between the wave at the centre of the LH spectrum and the electrons is satisfied at position x = 0 m for u = 3.5 (this condition is expected to assure good efficiency in current generation), and N = 0.2. For practical reasons, the Gaussian spectra is assumed to be non-vanishing between N − 2 N and N + 2 N , vanishing outside these limits.…”

“…We have already investigated some features of this subject, starting with a discussion on the threshold condition for stochastic ion diffusion due to LH waves, originated from the analysis by Karney [2], and continuing by the application of a two-dimensional quasilinear formulation which was able to follow the time evolution of the electron and ion distribution functions under the action of LH and IC waves, and collisions [17,18]. In this investigation the LH spectrum was assumed to be very narrow, such that a monochromatic wave could be assumed for the evaluation of the LH diffusion coefficient, according to the Karney proposal [2].…”