The goal of this paper is spectral analysis of an evolutionary semigroup generator describing the dynamics of a rarefied two-component plasma subjected to a self-consistent electromagnetic field. For ...the problem in question, the spectrum is given in terms of the dispersion relationship and an effective approach to the calculation of the instability index is developed.
A physics-based-adaptive plasma model and an appropriate computational algorithm are developed to numerically simulate plasma phenomena in high fidelity. The physics-based-adaptive plasma model can ...be dynamically refined based on the local plasma conditions to increase model fidelity uniformity throughout the domain at all times of the simulation. The adaptive plasma model uses continuum representations of the plasma, which include a kinetic Vlasov model for the highest fidelity, multi-fluid 5N-moment plasma model, and single-fluid MHD model for the lowest fidelity. The models include evolution equations for the electromagnetic fields, electron species, ion species, and neutral species. A nodal discontinuous Galerkin finite element method is implemented and is coupled with various implicit and explicit Runge-Kutta methods. Various model coupling techniques are investigated for a 5N-moment multi-fluid models with a Vlasov-Maxwell model, and a 5N-moment two-fluid model with an MHD model. Continuum plasma models using consistent normalizations and identical spatial representations provide straightforward and accurate coupling between the models. The solution approach offers high-order accuracy and computational efficiency. Target compute platforms are heterogeneous computer architectures using a compute model that minimizes data movement.
Using the self-consistent steady-state 2-D Kinetic Plasma Solver (KIPS-2D), thorough characterizations are performed of high-voltage cylindrical sheaths surrounding ion-attracting conductive ...cylinders immersed in stationary as well as flowing collisionless plasmas. Analytical fits are obtained that allow for the accurate prediction of stationary sheath sizes for round-cylinder radii anywhere from one thousandth of a Debye length to five Debye lengths and for any bias potential beyond a small lower bound. Plasma flow is shown to progressively compress the sheath on its ram and lateral sides, down to a limit that closely matches the stationary frozen-ion sheath radius. Conversely, plasma flow is shown to cause a significant wake-side elongation of the sheath. The quasi-elliptical sheath-edge contours observed under flowing conditions can be characterized by their along-flow and across-flow dimensions. By normalizing these dimensions against stationary-sheath diameters, contour plots of the corresponding flow-effect correction factors can be obtained that account for plasma-flow velocity effects in a wide range of speed regimes and bias potentials. In this paper, Mach numbers up to ten and bias potentials from -10T e to -500T e (where T e is the electron temperature in units of volts) are simulated and corresponding correction factors are computed, although KiPS is capable of simulating even higher speeds and bias potentials. These correction factors appear to stabilize at high voltages, suggesting that their values at the highest simulated potential bias possibly can be used with reasonable accuracy to predict performance at even higher (but nonrelativistic) bias-potential values using analytical equations derived from stationary simulations. For example, at a Mach number of 1.1, the along-flow and across-flow sheath dimensions at high voltages are expected to be around 115% and 85% of the stationary-sheath diameter, respectively. Flow-effect correction factors for current collection are also obtained for the ram-side, wake-side, and total collected current. For the same plasma-velocity example, at high voltages, total current collection is minimized to about half of the stationary value, which would translate into a 50% reduction in power to collect the current. This example is of significance for Earth-radiation-belt remediation-system concepts using high-voltage tethers
A self-consistent steady-state 2-D kinetic plasma solver has been applied to the problem of Langmuir triple-probe plasma diagnostic measurements in a flowing collisionless plasma. The triple-probe ...response is simulated for ion Mach numbers M = 0 - 5 and probe radii rp = 1 - 90 lambda D (Debye length). Results indicate that a high probe radius and high ion Mach numbers more closely approximate the ideal thin-sheath triple-probe response. Small probe radii on the order of the Debye length can result in temperature errors of the ideal model greater than 70% for a probe bias of 20 V. An analytical approximation is described, approximating triple-probe measurement offsets given arbitrary probe bias and probe radius and ion Mach numbers 0 < M < 5. The fitting error from this analytical approximation is estimated at 2%-6%.
This chapter describes a particular hybrid model that is a coupling between two‐dimensional (planar) magnetohydrodynamics (MHD) and Vlasov theory. It explains its Hamiltonian structure and applies ...the energy‐Casimir method to a class of equilibrium states. Some details regarding stability and the energy‐Casimir method are reviewed. This is followed by a discussion on the planar hybrid model, its noncanonical Hamiltonian structure and associated Casimir invariants. The chapter focuses on the application of the energy‐Casimir method giving rise to the sufficient conditions. The Casimir structure is divided into three independent contributions: two of these are inherited from reduced MHD and Vlasov equation. The third family of Casimirs, that originates from the coupling terms in the bracket is peculiar to this model and expresses the conservation of a generalized hybrid cross‐helicity, which, unlike the usual cross‐helicity of MHD, accounts also for the contribution of the fluid momentum of the hot particle species.
A numerical method is developed for coupling a multi-species kinetic plasma model with a 5N-moment multi-fluid plasma model. The simulation domain is decomposed such that the local conditions satisfy ...the corresponding plasma model's region of validity. The method allows for hybrid simulations by formulating each model as a set of conservation laws and using a continuum numerical method to solve each model's governing equations in the subdomains of the decomposed domain. The models are coupled through fluxes across subdomain interfaces. Two methods are explored for the formulation of the fluxes that can be self-consistently represented by both plasma models. One method allows for flux calculations consistent with the 5N-moment multi-fluid plasma model and assumes thermodynamic equilibrium within each species of the kinetic plasma model. The second method ensures conservation of the distribution function as well as mass, momentum, and energy by formulating the fluxes using a composite underlying distribution function at the subdomain interfaces. The methods are compared in 1D1V simulations of a double rarefaction wave and a plasma sheath using the WARPXM framework, which solves each model using the discontinuous Galerkin finite element method. Both methods for formulating the fluxes perform well as the subdomain interface distribution function approaches a Maxwellian, with the consistent method being more robust to larger deviations. A simulation of the magnetized Kelvin-Helmholtz instability in 2D2V is also performed using the consistent method, which demonstrates the potential of the domain-decomposed hybrid method in facilitating speedup and reduction in required computational resources for high-fidelity plasma simulations, allowing for the investigation of problems that are beyond current capabilities.
•A hybrid method coupling kinetic and fluid plasma models in simulation is presented.•Two approaches specifying discontinuous Galerkin numerical fluxes are shown.•Double rarefaction wave and plasma sheath tests are used to compare the approaches.•Magnetized Kelvin-Helmholtz instability simulations show the method's viability.
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