J. Neudorfer

Three-Dimensional Numerical Simulation of a 30-GHz Gyrotron Resonator With an Explicit High-Order Discontinuous-Galerkin-Based Parallel Particle-In-Cell Method

Fast design codes for the simulation of the particle-field interaction in the interior of gyrotron resonators are available. They procure their rapidity by making strong physical simplifications and approximations, which are not known to be valid for many variations of the geometry and the operating setup. For the first time, we apply a fully electromagnetic (EM) transient 3-D high-order discontinuous Galerkin particle-in-cell method solving the complete self-consistent nonlinear Vlasov-Maxwell equations to simulate a 30-GHz high-power millimeter-wave gyrotron resonator without physical reductions. This is a computational expensive endeavor, which requires todays high-performance computing capacity. However, this enables a detailed analysis of the EM field, the excited TE2,3 mode, the frequencies, and the azimuthal particle bunching in the beam. Therefrom, we present new insights into the complex particle-field interaction of the electron cyclotron maser instability transferring kinetic energy from the electron beam to the EM field.

Comparison of coupling techniques in a high-order discontinuous Galerkin-based particle-in-cell solver.

Highly rarefied plasma flows in technical devices are physically modelled by the Maxwell?Lorentz equations. They combine the solution of the Maxwell equations, where the electric field E and magnetic induction B are determined, with the Lorentz system, accounting for the movement of charged particles due to the electromagnetic forces. To solve these equations for complex-shaped domains, a fully electromagnetic particle-in-cell (PIC) code has been developed using high-order discontinuous Galerkin methods for the Maxwell equations on a computational mesh, coupled with a Lorentz solver on the basis of a second-order leapfrog scheme, acting on the particles at their current positions. Since the particles move freely in space, the mesh-based and the mesh-free values have to be coupled. This coupling includes the deposition of the charge and current densities from the current particle positions onto the mesh as well as the interpolation of the electromagnetic fields from the mesh to the actual particle positions. Both steps have to be computed with appropriate accuracy. Different approaches to particle-grid coupling within the PIC solver have been investigated. In this paper, these concepts are described and corresponding simulation results with respect to accuracy and computational demand are presented.

Efficient Parallelization of a Three-Dimensional High-Order Particle-in-Cell Method for the Simulation of a 170 GHz Gyrotron Resonator

We present the simulation of the transient excitation and evolution of a TE34, 19 mode in the resonant cavity of the 170 GHz gyrotron. This gyrotron is planned for electron cyclotron resonance heating in the ITER tokamak fusion reactor. The numerical computation of a state-of-the-art gyrotron resonant cavity with a transient 3-D full wave particle-in-cell (PIC) method is a computationally demanding task. It was enabled by a highly scalable PIC scheme. To allow the numerical simulation of the high-frequency electromagnetic waves, we use a high-order discontinuous Galerkin method.

Numerical Investigation of High-Order Gyrotron Mode Propagation in Launchers at 170 GHz

This paper presents for the first time the transient simulation of the 3-D mode converter with surface deformation. The simulation results were obtained by solving the Maxwell equations directly on a 3-D domain with a discontinuous Galerkin method. The presented full-wave simulation was possible only through the use of an advanced highly scalable numerical method operating on a large-scale high-performance computing system. Moreover, the properties of the Maxwell solver with respect to accuracy and computation time are discussed for the application to a smooth-wall waveguide where an analytical solution is available.

Three-Dimensional Gyrotron Simulation Using a High-Order Particle-in-Cell Method

A three-dimensional highly parallelized code for plasma simulation based on the Particle-In-Cell (PIC) approach using a discontinuous Galerkin method has been developed and validated within the instationary magneto-plasma dynamic (IMPD) thruster project (Associated with the DFG project “Numerical Modeling and Simulation of Highly Rarefied Plasma Flows”). With this code, it is for the first time possible to simulate the highly challenging gyrotron launcher and resonator, i.e. a high-energetic microwave source used for fusion-plasma heating, without using any physical approximations. We present the results of the gyrotron simulations with special focus on the parallelization capabilities of our code. For the gyrotron launcher, computations with up to 2048 processes have been performed. Parallel scaling of the PIC code with at most 1024 processes for simulating the gyrotron resonator is investigated in detail.

Efficient Parallelization of a Three-Dimensional High-Order Particle-in-Cell Method Applied to Gyrotron Resonator Simulations

Growing computational capabilities and simulation tools based on high-order methods allow the simulation of complex shaped plasma devices including the entire nonlinear dynamics of the Maxwell-Vlasov system. Such simulations model the particle-field-interactions of a non-neutral plasma without significant simplifications. Thereby, new insights into physics on a level of detail that has never been available before provide new design implications and a better understanding of the overall physics. We present a high-order discontinuous Galerkin method based Particle-In-Cell code for unstructured grids in a parallelization framework allowing for large scale applications on HPC clusters. We simulate the geometrically complex resonant cavity of the 170 GHz gyrotron aimed for plasma resonance heating of the fusion reactor ITER and we demonstrate that a highly efficient parallelization is a crucial requirement to simulate such a complex large-scale device.

Parallelization of a 3D high-order particle-in-cell method and numerical simulations of a 170 GHz resonator and launcher

Summary form only given. The transient 3D electromagnetic Particle-In-Cell [1,2] code HALO3D operates on unstructured meshes. It uses a high order discontinuous Galerkin approach to discretize the full set of the Maxwell equations in time domain. HALO3D is designed to be highly scalable, being able to simulate even high frequency particle-wave interactions and field propagation in state-of-the-art gyrotrons. Very recently, this solver was used to simulate the resonant cavity and the large-scale mode converter of a TE 34,19 gyrotron. To enable such computations, the coupled solver had to be optimized to run efficiently on more than 1000 CPU cores. The parallelization of the explicit scheme is base on a domain decomposition approach.

Numerical simulation of a 30 GHz gyrotron resonator with a 3D high-order discontinuous galerkin approach based particle-in-cell method

Summary form only given. Fast design codes for the simulation of the particle-field interaction in the interior of highly nonlinear gyrotron resonators are state of the art tools for gyrotron design [1,2]. While procuring their rapidity by making strong physical simplifications and approximations, the correctness of these assumptions is not known to be valid for all considered variations of the geometry and operation setup. Solving the self-consistent nonlinear Vlasov-Maxwell system without significant physical reductions, the transient 3D electromagnetic Particle-In-Cell (PIC) method [3] can provide better insights into these setups and beyond that can serve as validation tool for fast design codes.

High order PIC simulation of high power millimeter wave sources

Geometrically and physically complex plasma devices require the complete solution of the Maxwell-Vlasov equations without approximations that could restrict the results of the simulations to particular situations. Gyrotron oscillators provide an example of this category of radiation sources: they are successfully applied as high power microand millimetre wave sources for electron cyclotron current drive, electron cyclotron resonance heating, stability control and diagnostics of magnetically confined plasmas for generation of energy by controlled thermonuclear fusion. The Institute for Pulsed Power and Microwave Technology has been leading gyrotron designs for more than twenty years by means also of in-house codes like SELFT and ESRAY which provided excellent results but still included those geometrical and physical approximations, e.g. reduced, one-dimensional physical modelling as well as rotational symmetry, that prevented an exact description of the plasma. On the contrary, the HALO-PIC code is a novel, highly flexible, high-order tool developed at the IAG for the numerical solution of the Maxwell-Vlasov equations (MVE) in six-dimensional phase space [8, 5]. It is expected that this simulation code will serve for the assessment of a variety of engineering tools that rely on physical approximations. A co-operation between these two institutes has been established for the simulation of high energetic microwave source for fusion plasma heating, without the use of any physical approximations to the MVE.

Three-dimensional simulation of rarefied plasma flows using a high order particle in cell method.

A three-dimensional Particle In Cell scheme for unstructured grids is presented. Since simulations of this kind require large computational resources, the solver was parallelized. The scalability of two parallel simulations is shown and an engineering application as well as two validation test cases for the scheme are presented.