## Shock waves in partially ionised prominence plasmas

##### Emese Forgács-Dajka*, István Balla** (2021.05.01-2021.12.31)

* Eötvös University, Dept. of Astronomy

** Solar Physics and Space Plasma Research Centre (SP2RC), Department of Applied Mathematics, The University of Sheffield

**Abstract:** We investigate the nature and properties of shock waves propagating in an oblique direction to the ambient magnetic field in a partially ionised plasma modelling the plasma of solar prominences. In particular, we aim to analyse the observational signature of these shocks and investigate how our results can explain the recent observations of propagating bright blobs in solar prominences by Lin et al. (2012).

The equations of compressional single-fluid magnetohydrodynamic (MHD) equations are reduced with the help of a multiple scaling method to a well-known Burgers equation whose coefficients depend on the propagation angle of shock waves, plasma-β and the ionisation degree of the plasma. Our model is well-adapted for the separate discussion of shock waves arising from the nonlinear steepening of slow or fast magnetoacoustic waves. Using the standard jump conditions across the shock front (assuming a weak dissipation) we determine the jump in thermodynamic quantities that will be useful for comparison with observations.

Using the Cole-Hopf transform we solve the governing equation as an initial value problem of a diffusion-like equation and investigate the time necessary for a Gaussian initial wave profile to evolve into a shock, whose thickness is of the order of a few ion mean free path.