Effect of the radial boundary condition on Alfven wave dynamics in reduced magnetohydrodynamics

The effects of different boundary conditions on Alfven wave dynamics in reduced magnetohydrodynamics are described. If one assumes that the derivative or the second derivative of the electrostatic potential Φ is zero at one of the radial (across the magnetic field) boundaries, radially localized (guided) Alfven wave solutions are possible, but if Φ is set to zero (grounded) at both boundaries, the solutions consistent with the boundary condition exhibit radial propagation of energy. To confirm the ideas discussed, numerical tests were done in slab geometry with a density gradient across the magnetic field