Vlasov simulation of kinetic shear Alfven waves

The treatment of kinetic shear Alfven waves in homogeneous magnetized plasmas by means of Vlasov simulation is examined. To this end, the driftkinetic version of the Vlasov-Maxwell equations is solved via various numerical schemes, all employing a grid in (1 + 1)D phase space. Since kinetic shear Alfven waves are Landau damped, the use of an equidistant grid in velocity space leads to a recurrence problem. The latter can be circumvented, however, by damping the finest velocity space scales through higher-order collision operators. Of particular interest is the question if and under which circumstances the magnetohydrodynamic limit (small perpendicular wavenumber) can be recovered.