On the relation between the frequency of oscillation of a virtual cathode and injected current in one-dimensional grounded drift space

The relationship between the injected current density j0 and the dominant fundamental oscillation frequency f of a virtual cathode in a one-dimensional grounded infinite planar drift space of length L is determined numerically. If the electrons, each of mass me and charge e, are injected with velocity v0, it is found that for vertical bar j0 vertical bar >>mev03/18π vertical bar e vertical bar L2, f∼√(vertical bar j0 vertical bar) which is in contrast to the relation f∼vertical bar j0 vertical bar reported by earlier workers