Lagrangian approach in the analysis of plasma-filled diodes

Summary form only given. So far our detailed analysis of a plasma-filled diode was largely based on the work of Brendan Godfrey published in a seminal paper of 1987. Having extended Godfrey´s analysis from /spl alpha/=1 to /spl alpha//spl ne/1, where /spl alpha/=n/sub i0//n/sub e0/ is the ion/electron number densities ratio at the entrance electrode, we have been able to show that the diode can operate in four distinct regimes: stable, oscillatory, chaotic and unstable (Chen and Lindsay, 1996). The oscillatory regime, which is of importance in such microwave devices as vircators, was so far limited to a hydrodynamic model (Chen and Lindsay, 1997). However we know that in the case of a vircator in particular, oscillations may occur by reversal in the direction of the electron flow, a new regime of operation which lies outside the hydrodynamic model. This regime can be handled only either by using a large number of electron sheets in place of an electron beam of by employing a powerful PIC code, in our case MAGIC2D/3D. In our contribution we propose to present the analysis of our enlarged system together with the results of some early computations, in particular the range of system parameters for which virtual-cathode type of oscillations are likely to occur.