A study of quasi-mode parametric excitations in lower-hybrid heating of tokamak plasmas

Abstract

A detailed linear and nonlinear analysis of quasimode parametric excitations relevant to experiments in supplementary heating of tokamak plasmas is presented. The linear analysis includes the full ion-cyclotron harmonic quasimode spectrum. The nonlinear analysis, considering depletion of the pump electric field, is applied to the recent Alcator A heating experiment. Because of the very different characteristics of a tokamak plasma near the wall (in the shadow of the limiter) and inside, t-he quasimode excitations are studied independently for the plasma edge and the main bulk of tFle plasma, and for two typical regimes in overall d&nsity, the low (peak in density, ne = 1.5 x 1 0 H cM~?) and high (7o = _ x 10 ~M3) density regimes. At the edge of the plasma and for the low density regime, it is found that higher Pz 's (nz = c kz'o) than those predicted by the linear theory are strcngly excited. Inside the plasma,. the excitation of higher wave-numbers is also signiftcant. These results' indicate that a large amount of the rf-power may not penetrate to the plasma center, but will rather be either Landau-damped on the electrons or modeconverted into thermal modes, close to the plasma edge . Moreover, for sufficiently high peaks in density it is found that all the rf-power is modeconverted before reaching the plasma center. Inside the plasma the power density of the excited sideband fields is shown to be always very small in comparasion with their excitation at the plasma edge.

Excitation of ion-cyclotron harmonic waves in lower-hybrid heating

“…Also, k 21 as given in Eq. 3 formulate the parametric decay assuming that the low frequency mode is non-resonant (i.e., it is a quasi-mode) (2]. This means that the wavenumber of the low frequency quasi-mode is to be chosen at any point in the plasma such that it matches the wavenumbers of the lower-hybrid waves.…”

“…where E 0 is the constant pump electric field which is related to ao as, Eoao, 2 the coordinates that lie respectively along and perpendicular to the pump propagation cone. We define a new coordinate system as,…”

Saturation of parametric instabilities in lower hybrid heating of tokamak plasmas

“…The linear theory of various parametric processes at the lower hybrid frequency range is well explored [2], and it predicts roughly the same density limit for their existence as experimental observations do. A detailed comparison with the theory and the experiment, recently made for the Alcator lower hybrid experiments [3,4], emphasizes the importance of a precise knowledge of density and temperature profiles as well as of wavenumber and frequency spectra of pump and decay waves in evaluating the role of parametric decay upon pump wave penetration. In addition, various non-linear mechanisms may modify the linear growth of parametric instabilities.…”

“…The spatial growth factor A has been calculted in Ref. [4] for a variety of tokamak parameters and for a broad spectrum of Ej. It was found that A is large at the edge of the plasma, and the excited spectrum has a frequency very close to the initial pump frequency, while the wavenumber spectrum may be very different from the initial linear spectrum (i.e.…”

“…In Section 3, we shall make a similar survey as in Ref. [4], but include the harmonic generation leading to the modified growth factors. We also preserve the spatial derivatives, which allow us to study the convective growth in the rj direction possible for resonant modes at high pump intensity.…”