Divergence preservation in the ADI algorithms for electromagnetics

The recent advances in alternating direct implicit (ADI) methods promise important new capability for time domain plasma simulations, namely the elimination of numerical stability limits on the time step. But the utility of these methods in simulations with charge and current sources, such as in electromagnetic particle-in-cell (EMPIC) computations, has been uncertain, as the methods introduced so far do not have the property of divergence preservation. This property is related to charge conservation and self-consistency, and is critical for accurate and robust EMPIC simulation. This paper contains a complete study of these ADI methods in the presence of charge and current sources. It is shown that there are four significantly distinct cases, with four more related by duality. Of those, only one preserves divergence and, thus, is guaranteed to be stable in the presence of moving charged particles. Computational verification of this property is accomplished by implementation in existing 3D-EMPIC simulation software. Of the other three cases, two are verified unstable, as expected, and one remains stable, despite the lack of divergence preservation. This other stable algorithm is shown to be related to the divergence preserving case by a similarity transformation, effectively providing the complement of the divergence preserving field in the finite-difference energy quantity.     

MHD-to-PIC transition for modeling of conduction and opening in aplasma opening switch

The plasma opening switch (POS) is a critical element of some inductive-energy-storage pulsed-power generators. Detailed understanding of plasma redistribution and thinning during the POS conduction phase can be gained through magnetohydrodynamic fluid (MHD) simulations. As space-charge separation and kinetic effects become important late in the conduction phase (beginning of the opening phase), MHD methods become invalid and particle-in-cell (PIC) methods should be used. In this paper, the applicability of MHD techniques is extended into PIC-like regimes by including nonideal MHD phenomena such as the Hall effect and resistivity. The feasibility of the PIC technique is, likewise, extended into high-density, low-temperature-MHD-like regimes by using a novel numerical cooling algorithm. At an appropriate time, an MHD-to-PIC transition must be accomplished in order to accurately simulate the POS opening phase. The mechanics for converting MHD output into PIC input are introduced, as are the transition criteria determining when to perform this conversion. To establish these transition criteria, side-by-side MHD and PIC simulations are presented and compared. These separate simulations are then complemented by a proof-of-principle MHD-to-PIC transition, thereby demonstrating this MHD-to-PIC technique as a potentially viable tool for the simulation of POS plasmas. Practical limitations of the MHD-to-PIC transition method and applicability of the transition criteria to hybrid fluid-kinetic simulations are discussed     

Application of Dey–Mittra conformal boundary algorithm to 3D electromagnetic modeling

The Dey–Mittra conformal boundary conditions have been implemented for the finite-difference time-domain (FDTD) electromagnetic solver of the VORPAL plasma simulation framework and studied in the context of three-dimensional, large-scale computations. The maximum stable time step when using these boundary conditions can be arbitrarily small, due to the presence of small fractional cells inside the vacuum region. Use of the Gershgorin Circle theorem allows the determination of a rigorous criterion for exclusion of small cells in order to have numerical stability for particular values of the ratio f_DM≡Δt/Δt_CFL of the time step to the Courant–Friedrichs–Lewy value for the infinite system. Application to a spherical cavity shows that these boundary conditions allow computation of frequencies with second-order error for sufficiently small f_DM. However, for sufficiently fine resolution, dependent on f_DM, the error becomes first order, just like the error for stair-step boundary conditions. Nevertheless, provided one does use a sufficiently small value of f_DM, one can obtain third-order accuracy through Richardson extrapolation. Computations for the TESLA superconducting RF cavity design compare favorably with experimental measurements.     

Sheared poloidal flow driven by mode conversion in tokamak plasmas

A two-dimensional integral full-wave model is used to calculate poloidal forces driven by mode conversion in tokamak plasmas. In the presence of a poloidal magnetic field, mode conversion near the ion-ion hybrid resonance is dominated by a transition from the fast magnetosonic wave to the slow ion cyclotron wave. The poloidal field generates strong variations in the parallel wave spectrum that cause wave damping in a narrow layer near the mode conversion surface. The resulting poloidal forces in this layer drive sheared poloidal flows comparable to those in direct launch ion Bernstein wave experiments.