Spectrum and stability of a rigidly rotating compressible plasma

Abstract

We consider the spectrum and stability of a compressible, rigidly rotating plasma column with constant magnetic pitch. It is found that when the pressure on axis is zero, a continuous spectrum arises, which may become unstable. When the pressure on axis is finite or a conducting core is included, the spectrum is discrete, but may still be unstable. The instability is due to the poloidal magnetic field and/or the rotation of the cylinder in combination with the density profile. It is found numerically that the pressure stabilizes both types of instabilities.

Mode coupling in two-dimensional magnetohydrodynamic flows

“…The flow clearly has a stabilizing effect in the sense that the real part of the spectral value σ has diminished. This was also shown by Nijboer et al (1997a). Furthermore, the damped and unstable modes are shifted into the complex plane, so that the unstable modes now become overstable.…”

“…Also, the density is chosen to be constant. Instabilities driven by an unfavourable density profile are not considered here, but are considered by Fung (1984) and Nijboer et al (1997a). Thus the instabilities that we encounter are either driven by the magnetic field or by the plasma flow.…”

“…6, except that M = 1.15. It is known for circular incompressible plasmas that the plasma is completely stable in this case (Nijboer et al 1997a). In Fig.…”

Coupled flows and oscillations in asymmetric rotating plasmas

“…1,[3][4][5][6][7][8][9][10][11] Such exact solutions for highly nonlinear dynamic equilibrium states are useful in verifying new analytical and numerical schemes for solving nonlinear partial differential equations and as starting points for numerical investigations of more realistic problems. [12][13][14][15][16] In a recent paper, an exact model for cold plasma motion is used to investigate energy transfer among the different degrees of freedom in an expanding ͑or contracting͒ rotating plasma. In the model, the governing cold-plasma equations are solved nonperturbatively by first constructing a basis solution for the inertial ͑force free͒ motion of the electron ͑e͒ and ion ͑i͒ fluids.…”

Energy coupling among the degrees of freedom in an electron–positron plasma

“…On the other hand, there also exists a number of nonperturbative plasma wave solutions of relatively simple problems, (see, e.g., [3][4][5][6][7][8][9][10][11]). Besides useful for understanding quasi-steady dynamic states and fully nonlinear evolution of waves and instabilities, such exact solutions are also important for verifying new analytical and numerical methods for solving nonlinear partial differential equations, as well as in formulating more realistic problems [4,5]. Recently, an exact model for cold plasma motion is used to investigate the energy transfer among the different degrees of freedom in a rotating plasma [9][10][11].…”