High order PIC simulation of high power millimeter wave sources

Summary form only given. At present, gyrotron oscillators, as a source of high power millimeter waves, play a central role in fusion energy research. High power millimeter radiation in the frequency range of 100-200 GHz have shown to be a very efficient tool for electron cyclotron resonance heating, electron cyclotron current drive, stability control and diagnostics of magnetically confined fusion plasmas. Besides extensive experimental investigations in the frame of projects like ITER, numerical simulations are also a main pillar for these future developments. For this purpose, different kinds of simulation tools are available. Usually these codes introduce physical assumptions like rotational symmetry, constant magnetic field and one-dimensional modeling that reduce the quality of the solution. However, experimental investigations reveal that these assumptions are only justified under strong restrictions. In order to overcome these disadvantages, a novel high order Particle-In-Cell (PIC) code¹ has been developed for the numerical solution of the Maxwell-Vlasov equations in six-dimensional phase space. The Maxwell solver is based on a discontinuous Galerlin scheme which allows for polymorphic grid cell arragements and, in principle, arbitrary order of accuracy. In the spirit of the PIC approach, interpolation of grid-based data to the particles and, vice versa, assignment of particle-data to the grid is established by high order B-splines and polynomial shape functions. Furthermore, the simulation charges are advanced in phase space by solving the law of relativistic dynamics with a low-storage fourth-order Runge-Kutta method. In the conference presentation we show some details of the numerical methods used for the high order, 3D self-consistent PIC solver and, especially, introduce results obtained from comlex-shaped gyrotron launcher as well as gyrotron resonator simulations.