Rapid kinematic bunching and parametric instability in a crossed-field gap with a periodic magnetic field

Single particle orbit considerations show that the cycloidal orbits of electrons in a gap with crossed electric and magnetic fields lead to rapid spoke formation if the external magnetic field has a periodic variation. This spoke formation is primarily a result of kinematic bunching, which is independent of the radio frequency electric field and of the space charge field. A parametric instability in the orbits, which brings a fraction of the electrons from the cathode to the anode region, is discovered. These results are examined in light of the recent rapid startup, low noise magnetron experiments and simulations that employed periodic, azimuthal perturbations in the axial magnetic field.