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 j(0) 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 m(e) and charge e, are injected with velocity v(0), it is found that for \j(0)\much greater thanm(e)v(0)(3)/18pi\e\L-2, fsimilar toroot\j(0)\which is in contrast to the relation fsimilar to\j(0)\ reported by earlier workers. (C) 2004 American Institute of Physics.