Fast magnetic field penetration into a plasma beam

In this preliminary theoretical treatment, the magnetic field penetration into a bean of plasma is investigated. Maxwell's equations and the generalized Ohm's law, including the Hall term, are combined in a fluid model to produce a nonlinear diffusion equation for the magnetic field. The equation is linearized, and analytically solved in slab and cylindrical geometries. In the cylindrical case, the vector potential is introduced to obtain a lowest order solution of the diffusion equations which are coupled by the Hall term. In both cases, the solution contains whistler wave oscillations and classical diffusion. The whistler waves, which vanish without the Hall term, carry-in the field and determine the penetration time. There is no fast penetration without a component of magnetic field normal to the beam surface. The Hall term also produces a field component parallel to the beam velocity. (C) 1996 American Institute of Physics.