Plasma Diffusion in a Magnetic Field

The two‐dimensional diffusion of a partially ionized plasma in a magnetic field is studied using the macroscopic plasma equations. For a stable steady‐state plasma with uniform electron temperature and ionization frequency, it is shown that the density distribution can exist only in the lowest mode by virtue of the internal constraint that the space charge potential is conservative. While the electron and ion diffusion currents in an insulating cavity are everywhere equal, similar to Schottky's ambipolar diffusion theory for one dimension, the plasma in a conducting cavity exhibits an increase in the net particle current to the walls and an unbalance of ion and electron currents in the plasma. Thus an amperian current flows through the plasma and returns through the walls. With adjustable dc potentials applied to the walls of a split cavity, these currents may be continuously varied and even decreased below those given by the ambipolar condition. An experiment with a microwave cavity discharge demonstrates the existence of these unbalanced currents.