Microwave Gain Mechanisms in the Relativistic Magnetron

Recent simulations of the relativistic magnetron operating in the Π mode demonstrate that if the RF electric field becomes comparable to the applied electric field the microwave gain mechanism no longer involves synchronous azimuthal motion of the electrons with the RF fields. Instead, a negative resistance mechanism is responsible for microwave gain. Here electrons within a spoke move obliquely from the cathode to the anode with a time-of-flight much shorter than the RF period. The electrons gain energy from the RF electric field at the base of the spoke as they are drawn out from the cathode. However the applied magnetic field bends their orbits toward an adjacent resonator opening where they lose energy to the RF electric field. Since the RF fields are stronger near a resonator than near the cathode, a net RF gain results. In the work reported here, we investigate, via PIC simulations, the boundary in the operating space (V
_appl
B
_appl
) of the relativistic magnetron which separates the synchronous from the negative resistance gain mechanism. The effect of aspect ratio (A = r
_c
+ r
_a
on this boundary will also be examined. Finally, the validity of the negative resistance gain mechanism to modes other than the π mode (e.g. the 2Π and 7Π/3 modes) will be investigated.