Dissipative instability in a partially ionised prominence plasma slab

Abstract

Aims. We aim to investigate the nature of dissipative instability appearing in a prominence planar thread filled with partially ionised plasma in the incompressible limit. The importance of partial ionisation is investigated in terms of the ionisation factor and the wavelength of sausage and kink waves propagating in the slab. Methods. In order to highlight the role of partial ionisation, we have constructed models describing various situations we can meet in solar prominence fine structure. Matching the solutions for the transversal component of the velocity and total pressure at the interfaces between the prominence slab and surrounding plasmas, we derived a dispersion relation whose imaginary part describes the evolution of the instability. Results were obtained in the limit of weak dissipation. We have investigated the appearance of instabilities in prominence dark plumes using single and two-fluid approximations .Results. Using simple analytical methods, we show that dissipative instabilities appear for flow speeds that are less than the Kelvin-Helmholtz instability threshold. The onset of instability is determined by the equilibrium flow strength, the ionisation factor of the plasma, the wavelength of waves and the ion-neutral collisional rate. For a given wavelength and for ionisation degrees closer to a neutral gas, the propagating waves become unstable for a narrow band of flow speeds, meaning that neutrals have a stabilising effect. Our results show that the partially ionised plasma describing prominence dark plumes becomes unstable only in a two-fluid (charged particles-neutrals) model, that is for periods that are smaller than the ion-neutral collision time.Conclusions. The present study improves our understanding of the complexity of dynamical processes and stability of solar prominences and the role partial ionisation in destabilising the plasma. We showed the necessity of two-fluid approximation when discussing the nature of instabilities: waves in a single fluid approximation show a great deal of stability. Our results clearly show that the problem of partial ionisation introduces new aspects of plasma stability with consequences on the evolution of partially ionised plasmas and solar prominences, in particular.

Dissipative instabilities in a partially ionised prominence plasma slab

“…and, therefore, modes might become unstable for super-Alfvénic flows. Previous studies, for example, by Ballai et al (2017), pointed out that in the case of sausage modes (see their Fig. 3), the necessary flow to have a dissipative instability was in the region of 30 km s −1 .…”

“…Due to the high temperatures of the corona (> 10 6 K), the plasma is fully ionised. Following on from the work by Ballai et al (2017), we consider that the dominant dissipative mechanism that modifies the amplitude of waves is the viscosity. Given that the dynamics in the solar corona are driven mainly by magnetic forces, the viscosity is anisotropic and its value is given by the Braginskii's tensor present in the momentum equation.…”

“…Ballai et al (2015) considered the dissipative instability in the case of an interface between a viscous and incompressible coronal plasma and a resistive (Cowling resistivity), incompressible and partially ionised prominence plasma. Ballai et al (2017) investigated a similar problem but now modelling the plasma as a slab, introducing dispersion. Both investigations found that, with the increase in the fraction of neutrals present, the value of the threshold velocity for the dissipative instability to occur increased.…”

“…Both investigations found that, with the increase in the fraction of neutrals present, the value of the threshold velocity for the dissipative instability to occur increased. The present study is a natural extension to Ballai et al (2017) and generalisation to this problem by including compressibility with the aim to investigate how this affects the threshold of the dissipative instability. With this addition, we can study these instabilities in a more realistic solar context.…”

Dispersive shock waves in partially ionised plasmas

“…Their determined that the RTI develops only for wavenumbers that are below a cut-off value. The possibility of developing of the dissipative instability (connected to negative energy waves) was studied by Ballai et al (2015) in incompressible limit and Mather et al (2018) for compressible plasma. They considered the interface between a partially ionised prominence plasmas and a fully ionised and viscous corona.…”