Spectral estimates, stability conditions, and the rotating screw-pinch

Abstract

This article presents two sufficient conditions for the linear stability of rotating ideal plasmas, the first based on conservation of circulation and the second based on circle theorems applicable to linear Hamiltonian systems. The circle theorems also provide bounds on eigenmodes in the complex plane. All results are applied to the rotating screw-pinch which can be described by a single second-order ordinary differential equation.

Spectrum and stability of a rigidly rotating compressible plasma

“…Owing to the symmetry of the equilibrium profiles we can consider perturbations that have an f (r) exp[i(mθ + kz − ωt)] dependence. Then the equations describing the MHD stability of this plasma are (Hameiri 1981;Bondeson et al 1987):…”

“…For example, Suydam modes were considered both by Hameiri (1981) and by Bondeson et al (1987). In astrophysics the stability of rotating jets was studied by, for example, Bodo et al (1989) and Appl and Camenzind (1992) and the effect of compressibility on these jets was studied by Corbelli and Torricelli-Ciamponi (1989).…”

“…Therefore, most papers deal with stability conditions, like Howard and Gupta (1962) for an incompressible plasma. With the use of circle theorems, stability conditions for general plasma configurations were found by, for example, Barston (1977) and Hameiri (1981). They were applied to cylindrical geometries by Lucas (1981Lucas ( , 1986.…”

Surface-wave instabilities in a plasma rotating with step-like frequency profile

“…[9,10] (see also Refs. [11][12][13][14]) and for arbitrary heat conductivity in Refs. 15 and 16. The main benchmarks of our technique are the pair of the canonical first-order differential equations for perturbations called the Hameiri-Bondeson-Iakono-Bhattacharjee (HBIB) type equations, first derived in [12,13].…”

“…[11][12][13][14]) and for arbitrary heat conductivity in Refs. 15 and 16. The main benchmarks of our technique are the pair of the canonical first-order differential equations for perturbations called the Hameiri-Bondeson-Iakono-Bhattacharjee (HBIB) type equations, first derived in [12,13]. The variables in these equations are the perturbed radial magnetic field B r , the socalled Friman-Rotenberg (FR) variable, p * = p + B z B 0 /(4π), (1.4) and…”