Collisionless Damping of Hydromagnetic Waves

Numerical solutions have been obtained for the dispersion relation for hydromagnetic waves in an infinite, uniform, collisionless plasma. Except for the Alfvén (shear) mode, all hydromagnetic waves are strongly damped in plasmas of moderate or high β (fluid pressure/magnetic pressure). For β greater than about ½, the damping factor $\mathcal{W}\mathrm{=-}\mathrm{Im}\mathrm{\hspace{0.17em}(\omega )/|}\mathrm{Re}\mathrm{\hspace{0.17em}(\omega )|}$ is a few percent greater for the fast mode (except for special directions of propagation) and of order ½ for the slow mode. The least damped (fast) magnetosonic mode exhibits two maxima in a plot of $\mathcal{W}$ versus the angle θ between the wave vector k and the static magnetic field: the first maximum occurs for θ between 20° and 40° and is associated with ion heating; the second occurs between 85° and 89° and is associated with electron heating. In addition, the modes associated with the ``hose'' and ``mirror'' plasma instabilities are considered in some detail.