Magnetron with virtual cathode

The lifetime limitation of high power magnetrons is failure of their cathodes due to intense electron bombardment [1]. In the present work we study the operation of a compact relativistic magnetron [2] with a virtual cathode (VC) in the interaction space of the device instead of a physical cathode. A VC whose potential is equal to that of a real cathode appears in an electron beam when it is injected into a vacuum channel with a current that exceeds the space-charge-limiting current I_lim [3]. As follows from the stationary theory [4], a VC appears at a distance about channel radius from the injection plane and the axial position of the VC is closer to the plane as the injected current increases above I_lim. Evidently, for stable magnetron operation the injected current must exceed I_lim at least by the anode current. Nevertheless, the stationary theory cannot answer many uncertainties that are necessary for using such a VC in a magnetron as, for example, the time for VC formation; change in VC position when electrons deposit onto the anode; the VC position when the plane of injection is absent, but a source of electrons is outside the magnetron; and others. We study these problems using the particle-in-cell (PIC) code MAGIC.