Investigating the power flow in a relativistic magnetron with radial output

Abstract

While impedance matching with a pulsed generator is well noted in the relativistic magnetron literature as a pre-requisite for avoiding pulse shortening and radiated power loss1, its effect has not been investigated. The impedance of a 3D radiating structure, such as a magnetron, is complex, dynamically non-linear and in most cases too difficult to predict analytically. It depends on spatial distribution of drifting electrons interacting with e/m waves in magnetron. This time-depending spatial distribution of electrons is determined by the external magnetic field, applied voltage, and the magnetron geometry. We have investigated by 3D PIC simulations a 6-vane magnetron with a single radial output iris and found that power flow efficiency, frequency stability, and pulse shortening are indeed a function of the relative dimensions of the magnetron cathode, anode radii, and radiator depth which determine the impedance of the structure. In particular, we find that when the magnetron impedance is under-matched relative to the power generator, it cannot support the high current supplied by the input voltage. Then, first the axial current is re-trapped, causing the voltage to decrease and the radial current to increase. The increased radial current cannot be supported by the magnetron unless the radiated power drops, resulting in pulse shortening. This unstable situation is also accompanied by mode competition. The impedance of the magnetron can be increased by reducing the cathode radius or the electron emission region thus reducing the emitted current. By doing this, pulse shortening and mode competition no longer occur and the radiated power can be optimized varying the magnetic field within the Hull cutoff and the Buneman-Hartree limit.