Ideal and resistive magnetohydrodynamic instabilities in cylindrical geometry with a sheared flow along the axis

Abstract

The problem of the linear stability of internal magnetohydrodynamic modes in a cylindrical plasma with a sheared longitudinal flow is addressed. A Newcomb-like equation describing the perturbation is derived and exactly solved for a class of analytic profiles for rotational transform, equilibrium flow and pressure. A dispersion relation for ideal modes is then derived and analysed for different limits of the poloidal mode number (viz. m = 1, > m 1 and  m 1). In the resistive case, a simple and exact expression for the tearing stability index D¢ is derived using the same class of equilibrium profiles. It is found that a small flow shear has a destabilising effect, while if the flow shear is dominant over the magnetic shear the tearing mode is stabilised. Implications on the stability of the m=1 resistive mode are also discussed.

Physics conditions for robust control of tearing modes in a rotating tokamak plasma

“…where n is the toroidal mode number, r s is the resonant point, s denotes the magnetic shear at r s and the parameter λ labels the profiles determining their steepness [18]. Note that we chose a reference frame which is moving along the longitudinal direction in a such way that the rotation frequency vanishes at r s (this is allowed within the cylindrical approximation).…”

“…. It is found that the key parameter is the ratio y = Ω /ω A q /q of toroidal rotation shear and magnetic shear [18,19] The main task of a theoretical study of rf control of tearing instabilities, in the observable Rutherford phase, is the estimate of the necessary driven current, e.g. the rf power necessary to reduce the state variable w(t) and to design real-time strategies for the rf launching for an effective power deposition and possible tracking of the moving island.…”

“…Recently the physics understanding has been enriched by new findings on nonuniformity effects on finite magnetic islands, of pressure and temperature associated with energy input [ECRH] and loss (e.g. by radiation) [9][10][11][12][13][14][15], rotation and [16][17][18][19][20][21], as well as by findings on small scale topological effects of the reconnection [22,23].…”

Analytic study on low- external ideal infernal modes in tokamaks with large edge pressure gradients

“…https://doi.org/10.1017/S002237781800020X is approached. We expand (3.4) and (3.5) about r s giving (we use the same notation as in Mikhailovskii (1998), Brunetti, Lazzaro & Nowak (2017)):…”

Energy-Casimir, dynamically accessible, and Lagrangian stability of extended magnetohydrodynamic equilibria

“…Also there are many studies proposing that plasma sheared rotation variously affects the stability properties of Tokamak equilibria in several cases, either inducing stabilization or destabilization (e.g. [5][6][7][8][9]), with the main destabilizing mechanism being the Kelvin-Helmholtz instability [10]. * dkaltsas@cc.uoi.gr † gthroum@uoi.gr ‡ morrison@physics.utexas.edu Furthermore, many astrophysical phenomena, such as the development of turbulence in various stages of the solar wind and in magnetized accretion disks, are consequences of flow-driven instabilities such as the Kelvin-Helmholtz instability (e.g.…”