Dissipative instability in partially ionised prominence plasmas

Abstract

Aims. We investigate the nature of dissipative instability at the boundary (seen here as tangential discontinuity) between the viscous corona and the partially ionised prominence plasma in the incompressible limit. The importance of the partial ionisation is investigated in terms of the ionisation fraction. Methods. Matching the solutions for the transversal component of the velocity and total pressure at the interface between the prominence and coronal plasmas, we derive a dispersion relation whose imaginary part describes the evolution of the instability. Results are obtained in the limit of weak dissipation. Results. Using simple analytical methods, we show that dissipative instabilities appear for flow speeds that are lower than the Kelvin-Helmholtz instability threshold. While viscosity tends to destabilise the plasma, the effect of partial ionisation (through the Cowling resistivity) will act towards stabilising the interface. For ionisation degrees closer to a neutral gas the interface will be unstable for larger values of equilibrium flow. The same principle is assumed when studying the appearance of instability at the interface between prominences and dark plumes. The unstable mode appearing in this case has a very small growth rate and dissipative instability cannot explain the appearance of flows in plumes.Conclusions. The present study improves our understanding of the complexity of dynamical processes at the interface of solar prominences and solar corona, and the role partial ionisation can have on the stability of the plasma. Our results clearly show that the problem of partial ionisation introduces new aspects of plasma stability with consequences on the evolution of solar prominences.

Dissipative instability in a partially ionised prominence plasma slab

“…The imaginary part of the frequency describes the damping or the growth of waves. The results on the role of viscosity and magnetic field are identical with the findings by Ballai et al (2015). Here we focussed on the role of dispersion and the ionisation degree on the stability threshold of waves.…”

“…For large values of kz 0 (wide slab or long wavelength approximation) the value of the Kelvin-Helmholtz speeds reaches the value obtained for a single interface (see, e.g. Ballai et al 2015). It is also clear that the threshold were waves become KH unstable increases with the density contrast between the prominence and the solar corona.…”

“…A discussion on the nature of transport processes that can act under these conditions is presented in an earlier paper by Ballai et al (2015). Here we are going to employ the same considerations and assume that the viscosity is the dominant transport mechanism in the solar corona and it is described by the first term in Braginskii's viscosity tensor, while the transport mechanisms in the prominence appear in the induction equation (single fluid description), or due to the friction of different species of particles evidenced in the momentum equation (two fluid description).…”

“…Let us assume harmonic oscillations, meaning that perturbations are chosen to be proportional to exp[i(kx − ωt)]. It was shown earlier by Ballai et al (2015) that, inside the slab, the total pressure, P 1 , and z component of the velocity vector, v z , are connected by…”

“…They found that due to the collision between ions and neutrals the KHI can appear even for sub-Alfvénic flow speeds and these collisions are able to reduce the growth rate of unstable perturbations but they cannot stop the instability completely. In an earlier paper, Ballai et al (2015) studied the appearance of dissipative instability at the interface of prominence and corona plasmas assuming that the prominence is partially ionised (they assumed the Cowling resistivity to be important) and the coronal plasma is viscous.…”