Fully kinetic 3-D simulations of high-beta plasma in a mirror trap

Formation of a high-beta plasma in a mirror magnetic field is studied for the first time using three-dimensional semi-implicit particle-in-cell simulations providing a fully kinetic description of not only ions but also electrons. It is shown that, in addition to the longitudinal jump in electric potential between the centre of the trap and the wall, a radial electric field appears in the plasma. Due to this radial field, almost all of the azimuthal electric current required for equilibrium is created by electrons. It was also found that continuous model injection of plasma into the centre of the trap does not result in reaching the magnetohydrodynamic pressure limit ( $\beta =1$ ) due to the development of the flute instability with an azimuthal number $m=1$ . The instability growth rate in such a compact system is found to be comparable to the ion-cyclotron frequency. No stabilising effect is observed either from conducting ends or from the perfectly conducting sidewall. The probable reason for that is fast fluctuations of electric field localised inside the injection region that prevent electrons from being frozen into the field lines.