Collapse of Cycloidal flow in 2d Crossed Field Gaps

The start up of crossed-field amplifiers and magnetrons can result in noise detrimental to many applications. The transient of a 2d crossed field diode can be divided into three separate stages: cycloidal flow, collapse of cycloidal flow and non-uniform (E×B) sheared flow. Recent 1d results show cycloidal flows will collapse into near Brillouin flow(P. J. Christenson, et. al. Phys. Plasmas), 3(12):4455-4462, Dec 1996. In this study 2d electrostatic PIC simulations show that cycloidal flows also collapse into flow that is dominated by the E×B drift, but is not uniform or stable. This observed instability has nothing to do with the magnetron or diocotron fluid instability(O. Buneman, et. al. J of Applied Physics), 37(8):3203-22, July 1966. The growth of the mode produced from the collapse of cycloidal flow is faster than those of the above mentioned fluid instabilities. After the perturbation from the collapse of the cycloidal flow saturates, eventually the fastest growing fluid instability will dominate the system. Numerical simulations indicate that the initial instability does not occur for systems where the cathode length is less than about 2h and reaches a maximum growth rate at about 4h, where h is the ideal Brillouin hub height.