N. T. Gladd

Effects of finite plasma beta on the lower-hybrid-drift instability

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.

Lower‐hybrid‐drift instability in field reversed plasmas

The nonlocal structure of the lower‐hybrid‐drift instability is investigated in a reversed field configuration. The calculation includes electromagnetic effects and ∇B electron orbit modifications, which must be considered in the high β region of the current sheet. The eigenmodes are trapped in a potential well centered symmetrically on either side of the neutral layer at ‖x‖∼λ (λ is the scale length of the current sheet). The fundamental mode is well localized away from the neutral line with a half‐width Δx∼ (λ/ky)1/2<<λ, where ky∼Ωe(Ti/me)1/2 for the fastest growing mode. Higher order modes, however, have growth rates comparable to the fundamental mode and are much more global. In the cold electron limit (Te=0), the higher order modes with ∂/∂x∼ky can propagate throughout the entire sheet. In the warm electron limit (Te≠0), the electron ∇B drift‐wave resonance damps the mode and prevents the penetration of the mode closer than ‖x‖p∼λ (Te/2Ti) 1/2 of the neutral line. The effects of this instability on m...

Stabilization of the tearing mode in high‐temperature plasma

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.

Electron temperature gradient driven microtearing mode

The linear stability theory of an electron temperature gradient driven microtearing mode, an instability recently proposed as a possible cause for anomalous electron thermal transport in tokamaks, is considered. The theory is electromagnetic and is carried out within the context of a slab model with a sheared magnetic field. In contrast to the linear theory of drift waves, where any magnetic shear is completely stabilizing, shear may actually increase the growth rate of microtearing modes. The crucial feature required for instability is the energy dependence of electron‐ion collisions. The mode is shown to be unstable for electron temperature gradients and degrees of collisionality typical of present day tokamaks. It is found that previous theories of these modes were based on assumptions which are not, in general, justified; a case in point being the fact that the usually neglected electrostatic effects are actually quite important in producing instability.

‘‘Stabilization’’ of the lower‐hybrid‐drift instability in finite‐β plasmas

The stability properties of the lower‐hybrid‐drift instability are reexamined for finite‐β plasmas. In contrast to previous results, it is found that finite‐β does not stabilize the instability in the sense that the growth rate becomes negative. Rather, as β increases, the fastest growing mode shifts to longer wavelengths and makes a transition to an ion‐cyclotron mode when the growth rate falls below the ion‐cyclotron frequency.

Finite beta effects on the drift-cyclotron instability

The local dispersion equation for the drift‐cyclotron instability is derived and solved in order to examine the effects of finite beta associated with (a) transverse electromagnetic perturbations (δB≠0), and (b) resonant and nonresonant ∇B orbit modifications of both electrons and ions. Moreover, a formalism is chosen which allows consideration of variable density gradients, (me/mi)1/2≲rLi/LN≲1, on the ions. A detailed numerical study of the effects of finite beta on the general dispersive character and unstable spectrum is presented as well as a consideration of the effects of finite beta on the most rapidly growing mode. It is found that finite beta, in general, increases the frequency and reduces the growth rate but does not completely stabilize the drift‐cyclotron instability. The transition of the drift‐cyclotron instability into the lower‐hybrid‐drift instability which occurs for rLi/LN≃ (me/mi)1/4 is also discussed.

Current‐driven drift modes in sheared magnetic field

The radial eigenmode problem for current‐driven drift modes in a plasma slab with sheared magnetic field is solved including the full electron dynamics and effects of electron temperature gradient and electron‐ion collisions. Particular attention is given to the eigenmode structure and comparisons with the universal drift mode are made. The threshold current for the onset of current‐driven drift mode is found to be close to that predicted by analytic theory and not greatly affected by electron temperature gradient or collisionality.

Warm plasma effects on drift cyclotron loss cone mode

Although plasma density gradients in mirror machines are larger than the theoretical threshold for the drift cyclotron loss cone instability, turbulence is experimentally observed only at low harmonics of the ion cyclotron frequency. The evolution of the drift cyclotron loss cone instability as the loss cone velocity distribution is progressively filled with a warm Maxwellian component is studied. The addition of the warm plasma results in both a lowering of the growth rate and a distortion and narrowing of the frequency spectrum. Under conditions typical of an almost filled loss cone, the numerical result shows that the growth rate is largest for the lower ion cyclotron harmonics and is quite consistent with experimental observations.

Influence of strong inhomogeneities and magnetic shear on microstability properties of the Tormac sheath

Microstability properties of the Tormac sheath are discussed with particular emphasis on the influence of strong inhomogeneities and magnetic shear on the lower‐hybrid‐drift and mirror‐drift‐cone instabilities. It is found that magnetic shear can completely stabilize the lower‐hybrid‐drift instability (Maxwellian ions), and lead to a reduction in growth rate of the mirror‐drift‐cone instability (loss‐cone ions). The persistence of the mirror‐drift‐cone instability (at a reduced growth rate) in the presence of moderate magnetic shear suggests that the addition of a cold plasma component (as in the 2X‐IIB mirror experiment) may be desirable to further reduce the instability growth rate and suppress the associated anomalous transport.

Universal instability in a plasma sheath

Low‐frequency drift waves are considered in a planar sheath of neutral plasma with thickness on the order of the ion gyroradius. An integral eigenmode equation is derived and solved numerically using fast Fourier transforms. The analysis is valid for arbitrary wavenumbers and accounts for shear in the equilibrium magnetic field. It is found that unstable universal drift modes can exist in this strongly localized plasma. In contrast to what has been found previously in connection with weakly inhomogeneous plasmas, it is observed here that shear can have a destabilizing influence. The relevance of this idealized model to experiments is also discussed.