Electromagnetic effects in the stabilization of turbulence by sheared flow

Abstract

Abstract.We have extended our study of the competition between the drive and stabilization of plasma microinstabilities by sheared flow to include electromagnetic effects at low plasma β (the ratio of plasma to magnetic pressure). The extended system of characteristic equations is formulated, for a dissipative fluid model developed from the gyrokinetic equation, using a twisting mode representation in sheared slab geometry and focusing on the ion temperature gradient mode. Perpendicular flow shear convects perturbations along the field at the speed we denote as M cs (where cs is the sound speed). M > 1/ √ β is required to make the system characteristics unidirectional and inhibit eigenmode formation, leaving only transitory perturbations in the system. This typically represents a much larger flow shear than in the electrostatic case, which only needs M > 1. Numerical investigation of the region M < 1/ √ β shows the driving terms can conflict, as in the electrostatic case, giving low growth rates over a range of parameters. Also, at modest drive strengths and low β values typical of experiments, including electromagnetic effects does not significantly alter the growth rates. For stronger flow shear and higher β, geometry characteristic of the spherical tokamak mitigates the effect of an instability of the shear Alfvén wave, driven by the parallel flow shear.

Magnetic compressibility and ion-temperature-gradient-driven microinstabilities in magnetically confined plasmas

“…In Fig. (10) we see that, for the ŝ − α equilibium, the magnetic shear is stabilizing whereas, as expected, α has a destabilizing effect. The critical α for destabilization is a growing function of the local shear.…”

“…).In Figs (10)-(11),. we plot the contour of ℑ[δω] = 0 for a Tokamak ŝ − α equilibrium[18], and for a general equilibrium with arbitrary a[21].…”

“…Most kinetic investigations of ion-temperature-gradient (ITG) instabilities in plasmas rely on the simplifying assumption that perturbations are electrostatic [1][2][3]. With some notable exceptions [4][5][6][7][8][9][10], electromagnetic perturbations have been considered mainly from a numerical standpoint [11][12][13][14][15][16][17][18], and the attempt to understand their role in ITG stability has resulted in a patchy collection of numerical findings rather than in a coherent physical picture. Moreover, most studies have neglected magnetic compressibility and have thus neglected the magnetic perturbations parallel to the equilibrium magnetic field, δ ∥ B , that are generated by the instability to maintain perpendicular pressure balance.…”

The effect of background flow shear on gyrokinetic turbulence in the cold ion limit

“…Perpendicular flow shear in tokamaks is particularly important as it may enable the improved confinement regime H-mode [3]. H-mode is a robust plasma phenomenon that improves the energy confinement time of the device by roughly a factor of two and is currently viewed as essential for the success of the ITER experiment [13] as well as arXiv:1812.08566v2 [physics.plasm-ph] 26 Mar 2019 a future power plant [14,15]. Thus, a full understanding of perpendicular flow shear is desirable to ensure that a prospective design can properly exploit H-mode.…”

“…A more recent analytic calculation [24] took the cold ion limit and calculated how PVG can be stabilized by perpendicular shear flow. References [25,26,27] have used fluid equations, rigorously derived from electromagnetic gyrokinetic theory, to understand the interplay between the density gradient, temperature gradient, parallel flow shear, perpendicular flow shear, and magnetic shear. Lastly, several works [28,29] study how perpendicular flow shear enables gyrokinetic simulations to exhibit "subcritical" turbulence, which is a nonlinear instability that is sustained despite the fact that the modes are linearly stable.…”