Theory of transverse charging of electrons into a magnetic mirror

Inductive charging is a method to inject electrons perpendicular to a magnetic field and trap them by means of this fast rising field. The method has been studied experimentally in recent years and densities higher than 1011 cm-3 were reached. It has been suggested to use it for the collective focusing ion accelerator and for high current betatrons. We present here a theory of the trapping mechanism. This theory explains most of the experimental results. We also give the various limits on the charge which can be trapped and held in a single mirror and in a multiple-mirrored torus