Long-Wavelength Phenomena in a Plasma

The long-wavelength modes of excitation of a two-component plasma in a steady magnetic field are examined. Two linearized Boltzmann equations are given with collision terms which are coupled through the difference in temperatures and difference in velocities of the two gases. A formal means of classification of phenomena is described in terms of the nature of the roots about k = 0. Two types of behavior are uncovered: magnetohydrodynamics, which includes finite phase-speed phenomena near k = 0; and plasma electromagnetics, which includes infinite-phase-speed phenomena near k = 0. The dissipative effects of collisions are included. In the limit of vanishing collision frequency, roots previously obtained are recaptured. The relevance of the pertinent domains are discussed and the complex interplay between the ``fast'' and ``Alfvén'' modes of magnetohydrodynamics and the plasma-magnetic modes of the plasma electromagnetic domain is demonstrated. Equations macroscopic in appearance are derived which include the effects of the initial configuration. In the limit of large collision frequency these equations reduce to standard forms. The dispersion of the Nth-order Larmor resonance is given which includes the effect of the mass ratio.