Rayleigh-Taylor instabilities with sheared magnetic fields in partially ionised plasmas

Aims. In the present study we investigate the nature of the magnetic Rayleigh-Taylor instability appearing at a tangential discontinuity in a partially ionised plasma when the effect of magnetic shear is taken into account. Methods. The partially ionised character of the plasma is described by the ambipolar diffusion in the induction equation. The dynamics of the plasma is investigated in a single-fluid approximation. After matching the solutions on both sides of the interface we derive a dispersion equation and calculate the instability increment using analytical methods for particular cases of parameters, and numerical investigation for a wide range of parameters. Results. We calculated the dependence of the instability increment on the perturbation wavenumber. We also calculated the dependence of the maximum instability increment on the shear angle of the magnetic field for various values of the ionisation degree. Conclusions. Our results show that the Rayleigh-Taylor instability becomes sensitive to the degree of plasma ionisation only for plasmas with small values of plasma beta and in a very weakly ionised state. Perturbations are unstable only for those wavenumbers that are below a cut-off value.

Parametric instabilities of circularly polarized small-amplitude Alfvén waves in Hall plasmas

We study the stability of circularly polarized Alfvén waves (pump waves) in Hall plasmas. First we re-derive the dispersion equation governing the pump wave stability without making anad hocassumption about the dependences of perturbations on time and the spatial variable. Then we study the stability of pump waves with small non-dimensional amplitudea(a≪ 1) analytically, restricting our analysis tob< 1, wherebis the ratio of the sound and Alfvén speed. Our main results are the following. The stability properties of right-hand polarized waves are qualitatively the same as in ideal MHD. For any values ofband the dispersion parameter τ they are subject to decay instability that occurs for wave numbers from a band with width of ordera. The instability increment is also of ordera. The left-hand polarized waves can be subject, in general, to three different types of instabilities. The first type is the modulational instability. It only occurs whenbis smaller than a limiting value that depends on τ. Only perturbations with wave numbers smaller than a limiting value of orderaare unstable. The instability increment is proportional toa2. The second type is the decay instability. It has the same properties as in the case of right-hand polarized waves; however, it occurs only whenb< 1 τ. The third type is the beat instability. It occurs for any values ofband τ, and only perturbations with the wave numbers from a narrow band with the width of ordera2are unstable. The increment of this instability is proportional toa2, except for τ close to τcwhen it is proportional toa, where τcis a function ofb.

Instability of tangential discontinuities in pinching plasmas

A new mechanism for the formation of pinching plasma instability related to a tangential discontinuity is discussed. With this in mind we use a simple model of the Davydov–Zakharov class. It appears that there is a strong dependence of the instability increment on current density, resulting from the corresponding dispersion relation. Modulation of a current pulse is shown to be a possible way of stabilizing powerful discharges.