Boundary effects on M=0,±1 Alfvén waves in a cylindrical, collisionless plasma

The dispersion relations for Alfvén waves with exp(jmϑ) azimuthal dependency are calculated for a cylindrical, cold, collisionless plasma. If the electron inertia term is included in the dielectric tensor, then, in a bounded plasma, there are two transverse wavenumbers for each axial wavenumber. The phase velocities for m=0, ±1 fast and slow waves are calculated for different vacuum thicknesses between the uniform plasma and the metal walls. It is found that m=0 and −1 fast waves each experience a cutoff below a given frequency, but the m=+1 fast wave can propagate even at very low frequencies provided the vacuum layer is of sufficient thickness. The calculations are shown to agree with previously reported experimental results.