No abstract

The local dispersion relation for the lower-hybrid-drift isntability is derived in a fully self-consistent manner including the finite-beta effects associated with (a) transverse electromagnetic perturbations (δB≠0), and (b) resonant and nonresonant h/B0 electron orbit modifications. Moreover, the analysis is carried out for arbitrary values of local β=8πn (Te+Ti)/B02, Te/Ti, ω2pe/ω2ce, and VE/vi. (Here, VE is the cross-field E×B velocity, and vi is the ion thermal speed.) For all parameter regimes studied, the net effect of finite plasma beta is to reduce the maximum growth rate γm of the lower-hybrid-drift instability. The details, however, vary, depending on plasma parameters. For example, if Te≪Ti and VE<vi, then the maximum growth rate is reduced by a factor (1+βi/2)−1/2, relative to the value obtained when βi=8πnTi/B20→0. On the other hand, for Te≈Ti, there exists a critical value of plasma beta (βcr) such that the lower-hybrid-drift instability is completely stabilized (γ<0) for β≳βcr.

The linear stability behavior and anomalous transport properties associated with the lower-hybrid-drift instability are studied assuming flute-like perturbations with k⋅B0=0. Primary emphasis is placed on the low-drift-velocity regime with VE≲vThi (here, VE is the cross-field electron E×B drift velocity), which pertains to the late stages of implosion and the post-implosion phase of high-density pinch experiments. Nonlinear estimates of the instantaneous heating rates and rate of momentum transfer are made, and the results are studied numerically to determine the parametric dependence on VE/vThi and the level of turbulent field fluctuation energy ℰF. It is shown that the lower-hybrid-drift instability can result in substantial resistivity and plasma heating for VE≲vThi, as well as for the large-drift-velocity regime (VE≳vThi). For example, when Ti/Te≫1 and ω2pe/ω2ce≫1, the bound on anomalous resistivity for VE≲vThi is [nan]max≃4π√π/2(VE/vThi)2 ωLH/ω2ce, where ωLH = (ωciωce)1/2 is the lower-hybrid frequency. This large value of resistivity is consistent with observations made during the post-implosion phase of the ZT-1 experiment.

An analytical and numerical study of the stability of tearing modes is carried out using the Braginskii fluid equations. An electron temperature gradient coupled with finite (nonzero) parallel thermal conductivity causes large parallel currents to flow in the vicinity of the singular layer (where k⋅B=0). The pressure-driven currents are stabilizing and in the limit βL2s/L2n>1, where β is the ratio of the thermal to magnetic pressure and Ls and Ln are the magnetic shear and density scale lengths, the linear tearing mode no longer exists. In this high-β limit, the magnetic perturbation of the tearing mode is completely shielded from the singular layer so that no reconnection of the magnetic field can take place. The relationship between the tearing mode and previously investigated temperature-gradient-driven modes and the implications of the results for resistive modes in present and future tokamak discharges is discussed.