Quasicontinuous model for electron flow in magnetically insulated multigap inductive accelerator

This paper contains an analytical solution of the problem of electron flow in an inductive voltage adder operated in the positive polarity mode for the case when the number of stages is large, and the voltage distribution along the potential electrode (cathode) can be approximated as a smooth function. The stationary electron flow under such conditions has a laminar character. We present a simple analytic expression for the critical current in the anode conductor below which magnetic insulation collapses. We predict that, even if the anode current exceeds this critical value, there exists always some leakage to the anode. We present an analytic expression for the leakage current and for the energy of the electrons hitting the anode. A brief discussion of the possible role of instabilities and of an axial magnetic field is presented.