Dispersive shock waves in partially ionised plasmas

Abstract

Compressional waves propagating in the partially ionised solar lower atmospheric plasmas can easily steepen into nonlinear waves, including shocks. Here we investigate the effect of weak dispersion generated by Hall currents perpendicular to the ambient magnetic field on the characteristics of shock waves. Our study will also focus on the interplay between weak dispersion and partial ionisation of the plasma. Using a multiple scale technique we derive the governing equation in the form of a Korteweg-de Vries-Burgers equation. The effect of weak dispersion on shock waves is obtained using a perturbation technique. The secular behaviour of second order terms is addressed with the help of a renormalisation technique. Our results show that dispersion modifies the characteristics of shock waves and this change is dependent also on the ionisation degree of the plasma. Dispersion can create short lived oscillations in the shocked plasma. The shock fronts become wider with the increase in the number of neutrals in the plasma.

Interaction of convective plasma and small-scale magnetic fields in the lower solar atmosphere

“…From the viewpoint of theory [182], the focus is shifting more and more to understand partly ionized wave guides [e.g,. 183,184] as this will open new Fig. 9 Observational analysis of data obtained by the ROSA instrument situated at the Dunn Solar Telescope illustrating the idea of the phase-relationship interpretation for sausage mode waves detected in oscillations on 2008 August 22, as presented by [177].…”

Interaction of convective plasma and small-scale magnetic fields in the lower solar atmosphere

“…From the viewpoint of theory (Edwin and Roberts 1983), the focus is shifting more and more to understand partly ionized wave guides (e.g., Ballai et al 2019;Alharbi et al 2022) as this will open new avenues in better understanding and addressing waves in the chromosphere. In addition, there is still development going on to fully understand how waves get damped and energy absorbed (Van Doorsselaere et al 2020).…”

Chromospheric Heating by Magnetohydrodynamic Waves and Instabilities

“…These vortices, in the presence of non-ideal effects, may have a capability to heat the chromospheric plasma. Using simple analytical methods, Ballai et al (2019) have shown that the dissipative instabilities appear for the flow speeds that are lower than the KHI threshold at the fluid interfaces. While viscosity tends to destabilise the plasma, the effect of partial ionization through the Cowling resistivity will act towards stabilising the interface.…”

“…It requires higher amounts of energy input (10 6 –10 7 erg cm −2 s −1 ) to balance its radiative losses compared to the solar corona (10 4 –10 6 erg cm −2 s −1 ). Realistic models of the chromospheric plasma involve a multi‐fluid approach with a finite plasma‐beta and accommodate the additional physical effects of partial ionisation and radiative transfer in non‐local thermodynamic equilibrium (e.g., Ballai et al., 2019; Hansteen et al., 2007; Martínez‐Sykora et al., 2015; Soler et al., 2012; Soler et al., 2019). Although the single continuum fluid consideration at MHD length and time scales will suffice in dealing with the various wave modes or instabilities in the solar chromosphere, we do not invoke some additional frequency dependent physics of the region, for example., wave damping by ion‐neutral collisions, etc., there (Ballester et al., 2018).…”