Simulation of Magnetrons Using A Fast MOLT Based Implicit A-stable Scheme

We present a novel approach for computer simulation of magnetrons using a fast, high-order, A-stable implicit scheme. Since the simulator can model various structures of magnetron, it increases the physical intuition of how changes on the model effects electromagnetic behavior. The scheme works based on a MOLT formulation combined with an ADI splitting. A PDE is first discretized in time, and then the resulting boundary-value problems are solved using a Green's function. The integration is successively convolved using an O(N) fast algorithm. The high-order scheme is achieved by utilizing a Lax-Wendroff approach to exchange time derivatives with spatial derivatives. We solve magnetic vector potential A using Maxwell's equations under the Lorenz gauge, and apply PEC boundary condition using embedded boundary method.  We use emitters to mimic transparent cathode and a circular source is used for solid cathode. This simulator is successfully evaluated for 2D A6 magnetron and rising-suns using ping-test and frequency analysis. Further, A6 magnetron with diffraction output (MDO) is simulated by imposing a high-order outflow boundary condition along the horn boundary and obtained Q is verified. Extension to 3D magnetrons and parallel implementation will be considered in our next work.