Numerical simulations of the nonlinear evolution of the magnetron instability for several geometric configurations

Summary form only given. We present the theory of the magnetron instability, which is developed using a fluid plasma description. A 1-D non-linear steady-state model is developed for relativistic and non-relativistic planar and cylindrical smooth-bore magnetron geometries. To this steady-state background, 1-D and 2-D linear perturbation analyses are applied to determine the modes and growth rates for the magnetron instability for these configurations. Analytic results are verified via numerical simulation. The mode and the growth rate are compared to particle-in-cell (PIC) code result using ICEPIC, XPDP1, and XPDC1. In addition, the modes resulting from the non-linear saturation of these instabilities are presented and compared to the theoretically obtained linear modes. The growth rate and saturation of the instability and resulting operating mode is examined as a function of magnetron geometry. Specifically, we focus on the transition from non-relativistic to relativistic-applied voltages and from planar to cylindrical geometries. We have also added a circuit model to represent the cavities and extraction of power from the cavities. With this combined model, we can optimize the magnetron geometry to obtain high power and fast growth rate. The parameters that we have used in the optimization are the magnetic field, voltage, number, length, and form of the vanes, as well as the external coupling to extract the power. The fluid model coupled to the circuit model is compared to 3-D PIC simulations performed with ICEPIC.