Perpendicular Shear Research Articles

Shear Wave Dissipation in Planar MagneticX‐Points

The resistive dissipation of nonlinear shear wave disturbances is discussed. We consider an incom- pressible, open II X-point geometry, in which mass and energy are free to enter and leave the reconnec- tion region. An analytic treatment is possible which uni-es many of the dynamic and steady-state X-point solutions obtained previously. We show that while -eld disturbances in the plane of the X-point have the potential for rapid energy release when suitably driven, perpendicular shear disturbances dissi- pate slowly, at a rate Dg1@2, where g is the plasma resistivity. This behavior can be understood in terms of the absence of Nux pileup in nonplanar shear wave disturbances. We conclude that only planar shear waves have the potential for fast magnetic energy release. Subject headings: MHD E plasmas

Finite-amplitude Alfvén waves in a dissipative inhomogeneous plasma

The effects of an inhomogeneous background magnetic field and resistivity on finite-amplitude Alfvén waves are studied in terms of the derivative nonlinear Schrödinger equation. It is shown that a weak inhomogeneity in the background magnetic field introduces a perpendicular shear in the resulting waves. This causes the waves to split apart, and a longitudinal current, which increases linearly in time, is produced as a consequence. Resistivity, however, restricts this unbounded growth of current and causes the waves and the current to decay exponentially at later times. The connection of these results to previous results on the Alfvén continuum and low-frequency current drive are discussed in the paper. In the paper the effects of resistivity on the modulational instability of time harmonic solutions of the derivative nonlinear Schrödinger equation are also explored. Both numerical and analytical results indicate that resistivity will decrease the growth rate of envelope perturbations. At large enough values, it can even suppress the perturbations.

Integral eigenmode analysis of shear flow effects on the ion temperature gradient mode

Previous numerical and analytic kinetic studies have investigated the influence of velocity shear on the ion temperature gradient (ITG) mode. These studies relied on a differential approximation to study mode structures with k⊥ρi≪1. A recently developed gyrokinetic integral code is here used to explore the effects of sheared flows on the ITG mode for arbitrary values of k⊥ρi in sheared slab geometry. It is found that both the mode structure and eigenfrequencies predicted by the integral code can differ from the results obtained by the differential approach, even in the kyρi≪1 limit. Although some trends predicted by the differential approximation are recovered by the integral approach, there are some significant differences. For example, the slight destabilizing effect observed for small values of the perpendicular velocity shear at k⊥ρi≪1 is amplified when the integral approach is applied. In dealing with the higher radial eigenmodes, which can often exhibit the largest growth rates, it is emphasized that their finer radial structure usually dictates that the integral equation analysis is required. Results from the integral code are presented together with comparisons with results from the differential approach.

Anomalous momentum transport from drift wave turbulence

A sheared slab magnetic field model B=B0[ẑ+(x/Ls)ŷ], with inhomogeneous flows in the ŷ and ẑ directions, is used to perform a fully kinetic stability analysis of the ion temperature gradient (ITG) and dissipative trapped electron (DTE) modes. The concomitant quasilinear stress components that couple to the local perpendicular (y component) and parallel (z component) momentum transport are also calculated and the anomalous perpendicular and parallel viscous stresses obtained. A breakdown of the ITG-induced viscous stresses are generally observed at moderate values of the sheared perpendicular flow. Even in the absence of external momentum sources, ion diamagnetic effects can generate an inhomogeneous radial electric field which gives rise to a sheared perpendicular flow which can sustain a sheared parallel flow. The effect of the perpendicular stress component in the momentum balance equations is generally small while the parallel stress component, which is primarily determined by the perpendicular flow shear, can dominate the usual neoclassical viscous stress terms. The large anomalous effect suggests that the neoclassical explanation of poloidal flows in tokamaks may be incorrect. The present results are in general agreement with existing experimental observations on momentum transport in tokamaks.

Kinetic quasitoroidal ion temperature gradient instability in the presence of sheared flows

The gyrokinetic integral equations for the study of the ion temperature gradient driven mode (ηi mode) in toroidal geometry, at low plasma pressure, are extended to include equilibrium ion parallel v0∥(r) and perpendicular vE(r) sheared flows, where r is the minor radius of the flux surface. Magnetic gradient and curvature drifts of the ions, as well as finite ion Larmor radius effects, are included. The parallel sheared flow is shown to be destabilizing. The perpendicular sheared flow is a stabilizing mechanism. Mixing length estimates show that the ηi-mode induced ion thermal transport increases with increasing parallel flow shear, and decreases with perpendicular flow shear. The decrease of the ion transport is due not only to the decrease of the mode growth rate, but also to the shrinking of the mode width. Using the mixing length formulas for the thermal transport associated with the unstable modes, it is shown that the results are consistent with the experimental observations concerning the improvement of confinement in H-mode discharges coincident with the increase of cross-field sheared flows.