Particle-in-cell simulations of start-up dynamics in a grounded cathode magnetron

Simulations results of a relativistic magnetron using the MAGIC particle-In-cell (PIC) code are reported. The time evolution of the buildup process for different magnetron azimuthal modes is studied for a variety of initial voltages, with and without a second, oscillatory small voltage in addition to the drive. The self-field is seen to evolve so that the anode-cathode voltage nears the Buneman-Hartree voltage of a particular mode. Simulations show that the output power is larger in the case where the voltage dynamically approaches the Buneman-Hartree value from above than when it is approached from below. The time evolution of a pure mode (without mode competition) resembles the time evolution of some autoresonant systems. An oscillatory voltage, of relatively small amplitude, fixed or chirped in frequency is seen to modify mode competition. The frequency of the first occurring mode is shown to follow the external drive with small phase deviations. This appears to be the beginning of an autoresonance process driven by the external drive, which stops abruptly at the mode transition. Small changes in the azimuthal structure are seen to lead to different mode dynamics; when the pi-mode symmetry is enforced other competing modes are suppressed to some extent