The influence of the magnetic field on the problem of stability in a crossed-field diode

Although in general an axial magnetic field is frequently used to stabilize an electron beam, its influence is highly deleterious in the case of a coaxial vircator. In our investigations of the above effect we have modelled the electron-beam generating element of the vircator using a plane crossed-field diode (magnetic gap). In the process of analyzing the effect of the strength of the magnetic field on the development of a ´virtual cathode´ we have assumed, following the case of zero magnetic field, that for certain ranges of the parameters the electron now is stable, whereas for other ranges it is unstable. Our assumption was largely based on some topological similarities of the two systems. In our present work we are investigating the problem more rigorously using analytical procedures. Following some earlier work which was however limited to the case of zero magnetic field, we investigated the roots of a complex variable function in order to determine the stability properties of the system. We were then able to show that the assumptions concerning the stability of solutions are in fact justified. Furthermore we were also able to show how the ranges of instability depend on the strength of the magnetic field.