MATHEMATICAL-MODELS OF MAGNETIC INSULATION

The problem of magnetic insulation in a plane diode is discussed. Star ting from the Child-Langmuir asymptotics of the stationary Vlasov-Maxw ell system, various limit problems are exhibited and solved. Explicit formulas for the magnetic field at the cathode and for the electron sh eath width are provided. The analysis allows one to recover and to com plete the various known results related to magnetic insulation. In add ition, an ensemble of intermediate models ranging from the quasilamina r to the laminar model, and involving the formation of virtual cathode s, is exhibited. A stability analysis is then performed to determine w hich of these models are stable. The virtual cathode models are shown to be unstable under dissipation effects, and most of them are shown t o be unstable under geometry effects (i.e., when replacing the planar geometry by the cylindrical one). The stability argument shows that in some situations, the laminar model is unstable while in other situati ons the quasilaminar one is unstable. This gives some indication for t he choice of the appropriate magnetic insulation model. (C) 1998 Ameri can Institute of Physics.