Axial eigenmodes for long −λ∥ waves in plasmas bounded by sheaths

Waves such as drift waves and lower hybrid oscillations in a plasma are sensitive to the degree to which charge neutrality can be maintained by electron flow along the magnetic field. When the plasma is bounded axially, the sheath conditions on the end plates determine the parallel wavelength. It is found that the nature of the bounded modes depends on whether the motion of electrons is resistive or inertial. If it is resistive, the sheath matching conditions can be satisfied by standing waves with the proper wavelength. If it is inertial, pure standing waves are not possible; there must also be a variation of phase along B. Application is made to two-ion hybrid waves in connection with isotope separation.