A Discontinuous Galerkin Method for Ideal Two-Fluid Plasma Equations

A discontinuous Galerkin method for the ideal 5 moment two-fluid plasma system is presented. The method uses a second or third order discontinuous Galerkin spatial discretization and a third order TVD Runge-Kutta time stepping scheme. The method is benchmarked against an analytic solution of a dispersive electron acoustic square pulse as well as the two-fluid electromagnetic shock and existing numerical solutions to the GEM challenge magnetic reconnection problem. The algorithm can be generalized to arbitrary geometries and three dimensions. An approach to maintaining small gauge errors based on error propagation is suggested.Comment: 40 pages, 18 figures

Whole Device Modeling of the FuZE Sheared-Flow-Stabilized Z Pinch

The FuZE sheared-flow-stabilized Z pinch at Zap Energy is simulated using whole-device modeling employing an axisymmetric resistive magnetohydrodynamic formulation implemented within the discontinuous Galerkin WARPXM framework. Simulations show formation of Z pinches with densities of approximately 10^22 m^-3 and total DD fusion neutron rate of 10^7 per {\mu}s for approximately 2 {\mu}s. Simulation-derived synthetic diagnostics show peak currents and voltages within 10% and total yield within approximately 30% of experiment for similar plasma mass. The simulations provide insight into the plasma dynamics in the experiment and enable a predictive capability for exploring design changes on devices built at Zap Energy.Comment: 8 pages, 9 figures, IAEA FEC 202

A high resolution wave propagation scheme for ideal two-fluid plasma equations

Abstract Algorithms for the solution of the five-moment ideal Two-Fluid equations are presented. The ideal Two-Fluid model is more general than the often used magnetohydrodynamic (MHD) model. The model takes into account electron inertia effects, charge separation and the full electromagnetic field equations and allows for separate electron and ion motion. The algorithm presented is the high resolution wave propagation method. The wave propagation method is based on solutions to the Riemann problem at cell interfaces. Operator splitting is used to incorporate the Lorentz and electromagnetic source terms. To preserve the divergence constraints on the electric and magnetic fields two different approaches are used. In the first approach Maxwell equations are rewritten in their mixed-potential form. In the second approach the so-called perfectly hyperbolic form of Maxwell equations are used which explicitly incorporate the divergence equations into the time stepping scheme. The algorithm is applied to a one-dimensional Riemann problem, ion-acoustic soliton propagation and magnetic reconnection. In each case Two-Fluid physics described by the ideal Two-Fluid model is highlighted

Sheared Flow As A Stabilizing Mechanism In Astrophysical Jets

It has been hypothesized that the sustained narrowness observed in the asymptotic cylindrical region of bipolar outflows from Young Stellar Objects (YSO) indicates that these jets are magnetically collimated. The j cross B force observed in z-pinch plasmas is a possible explanation for these observations. However, z-pinch plasmas are subject to current driven instabilities (CDI). The interest in using z-pinches for controlled nuclear fusion has lead to an extensive theory of the stability of magnetically confined plasmas. Analytical, numerical, and experimental evidence from this field suggest that sheared flow in magnetized plasmas can reduce the growth rates of the sausage and kink instabilities. Here we propose the hypothesis that sheared helical flow can exert a similar stabilizing influence on CDI in YSO jets.Comment: 13 pages, 2 figure

Numerical approximation of the Euler-Poisson-Boltzmann model in the quasineutral limit

This paper analyzes various schemes for the Euler-Poisson-Boltzmann (EPB) model of plasma physics. This model consists of the pressureless gas dynamics equations coupled with the Poisson equation and where the Boltzmann relation relates the potential to the electron density. If the quasi-neutral assumption is made, the Poisson equation is replaced by the constraint of zero local charge and the model reduces to the Isothermal Compressible Euler (ICE) model. We compare a numerical strategy based on the EPB model to a strategy using a reformulation (called REPB formulation). The REPB scheme captures the quasi-neutral limit more accurately

Evolution of Plasma Flow Shear and Stability in the ZaP Flow Z-Pinch

Abstract. The stabilizing effect of an axial flow on the m = 1 kink instability in Z-pinches has been studied numerically with a linearized ideal MHD model to reveal that a sheared axial flow stabilizes the kink mode when the shear exceeds a threshold. The sheared flow stabilizing effect is investigated with the ZaP Flow Zpinch experiment. An azimuthal array of surface mounted magnetic probes measures the fluctuation levels of the azimuthal modes m = 1, 2, and 3. After pinch assembly a quiescent period is found where the mode activity is significantly reduced. The quiescent period lasts for over 2000 times the expected instability growth time in a static Z-pinch. Optical images from a fast framing camera, a two-chord HeNe interferometer, and a ruby holographic interferometer indicate a stable, discrete pinch plasma during this time. Multichord Doppler shift measurements of impurity lines show a large, sheared flow during the quiescent period and low, uniform flow profiles during periods of high mode activity. The value of the velocity shear satisfies the theoretical threshold for stability during the quiescent period and does not satisfy the threshold during the high mode activity. Experiments are conducted with varying amounts of injected neutral gas to gain an understanding of the Z-pinch formation and lifetime

Entropy Stable Numerical Schemes for Two-Fluid Plasma Equations

Two-fluid ideal plasma equations are a generalized form of the ideal MHD equations in which electrons and ions are considered as separate species. The design of efficient numerical schemes for the these equations is complicated on account of their non-linear nature and the presence of stiff source terms, especially for high charge to mass ratios and for low Larmor radii. In this article, we design entropy stable finite difference schemes for the two-fluid equations by combining entropy conservative fluxes and suitable numerical diffusion operators. Furthermore, to overcome the time step restrictions imposed by the stiff source terms, we devise time-stepping routines based on implicit-explicit (IMEX)-Runge Kutta (RK) schemes. The special structure of the two-fluid plasma equations is exploited by us to design IMEX schemes in which only local (in each cell) linear equations need to be solved at each time step. Benchmark numerical experiments are presented to illustrate the robustness and accuracy of these schemes.Comment: Accepted in Journal of Scientific Computin

2-D Magnetohydrodynamic Simulations of Induced Plasma Dynamics in the Near-Core Region of a Galaxy Cluster

We present results from numerical simulations of the cooling-core cluster A2199 produced by the two-dimensional (2-D) resistive magnetohydrodynamics (MHD) code MACH2. In our simulations we explore the effect of anisotropic thermal conduction on the energy balance of the system. The results from idealized cases in 2-D axisymmetric geometry underscore the importance of the initial plasma density in ICM simulations, especially the near-core values since the radiation cooling rate is proportional to ${n_e}^2$. Heat conduction is found to be non-effective in preventing catastrophic cooling in this cluster. In addition we performed 2-D planar MHD simulations starting from initial conditions deliberately violating both thermal balance and hydrostatic equilibrium in the ICM, to assess contributions of the convective terms in the energy balance of the system against anisotropic thermal conduction. We find that in this case work done by the pressure on the plasma can dominate the early evolution of the internal energy over anisotropic thermal conduction in the presence of subsonic flows, thereby reducing the impact of the magnetic field. Deviations from hydrostatic equilibrium near the cluster core may be associated with transient activity of a central active galactic nucleus and/or remnant dynamical activity in the ICM and warrant further study in three dimensions.Comment: 16 pages, 13 figures, accepted for publication in MNRA

Pressure-driven instabilities in astrophysical jets

Astrophysical jets are widely believed to be self-collimated by the hoop-stress due to the azimuthal component of their magnetic field. However this implies that the magnetic field is largely dominated by its azimuthal component in the outer jet region. In the fusion context, it is well-known that such configurations are highly unstable in static columns, leading to plasma disruption. It has long been pointed out that a similar outcome may follow for MHD jets, and the reasons preventing disruption are still not elucidated, although some progress has been accomplished in the recent years. In these notes, I review the present status of this open problem for pressure-driven instabilities, one of the two major sources of ideal MHD instability in static columns (the other one being current-driven instabilities). I first discuss in a heuristic way the origin of these instabilities. Magnetic resonances and magnetic shear are introduced, and their role in pressure-driven instabilities discussed in relation to Suydam's criterion. A dispersion relation is derived for pressure-driven modes in the limit of large azimuthal magnetic fields, which gives back the two criteria derived by Kadomtsev for this instability. The growth rates of these instabilities are expected to be short in comparison with the jet propagation time. What is known about the potential stabilizing role of the axial velocity of jets is then reviewed. In particular, a nonlinear stabilization mechanism recently identified in the fusion literature is discussed. Key words: Ideal MHD: stability, pressure-driven modes; Jets: stabilityComment: 20 pages, 3 figures. Lecture given at the JETSET European school "Numerical MHD and Instabilities". To be published by Springer in the "Lectures notes in physics" serie