Collisionless damping of Alfvén waves in an inhomogeneous plasma: Solution of the initial value problem

The initial value problem of the linearized ideal MHD equations for a low-β plasma in an inhomogeneous magnetic field is solved for a broad class of initial conditions. The validity of the solutions breaks down after a time, which is determined by the magnitude of the initial conditions. The energy is transported to the inhomogeneous region. The mechanism described here could therefore possibly be used for shaping of the plasma temperature profile.