Eder Sousa

Advanced physics calculations using a multi-fluid plasma model

Abstract The multi-fluid plasma model is derived from moments of the Boltzmann equation and typically has two fluids representing electron and ion species. Large mass differences between electrons and ions introduce disparate temporal and spatial scales and require a numerical algorithm with sufficient accuracy to capture the multiple scales. Source terms of the multi-fluid plasma model couple the fluids to themselves (interspecies interactions) and to the electromagnetic fields. The numerical algorithm must treat the inherent stiffness introduced by the multiple physical effects of the model and tightly couple the source terms of the governing equations. A discontinuous Galerkin method is implemented for the spatial representation. Time integration is investigated using explicit, implicit, semi-implicit methods. Semi-implicit treatment is accomplished using a physics-based splitting. The algorithm is applied to study drift turbulence in field reversed configuration plasmas to illustrate the physical accuracy of the model. The algorithm is also applied to plasma sheath formation which demonstrates Langmuir wave propagation.

A blended continuous–discontinuous finite element method for solving the multi-fluid plasma model

Abstract The multi-fluid plasma model represents electrons, multiple ion species, and multiple neutral species as separate fluids that interact through short-range collisions and long-range electromagnetic fields. The model spans a large range of temporal and spatial scales, which renders the model stiff and presents numerical challenges. To address the large range of timescales, a blended continuous and discontinuous Galerkin method is proposed, where the massive ion and neutral species are modeled using an explicit discontinuous Galerkin method while the electrons and electromagnetic fields are modeled using an implicit continuous Galerkin method. This approach is able to capture large-gradient ion and neutral physics like shock formation, while resolving high-frequency electron dynamics in a computationally efficient manner. The details of the Blended Finite Element Method (BFEM) are presented. The numerical method is benchmarked for accuracy and tested using two-fluid one-dimensional soliton problem and electromagnetic shock problem. The results are compared to conventional finite volume and finite element methods, and demonstrate that the BFEM is particularly effective in resolving physics in stiff problems involving realistic physical parameters, including realistic electron mass and speed of light. The benefit is illustrated by computing a three-fluid plasma application that demonstrates species separation in multi-component plasmas.

High-order finite element method for plasma modeling

High-order accurate finite element methods provide unique benefits for problems that have strong anisotropies and complicated geometries and for stiff equation systems that are coupled through large source terms, e.g. Lorentz force, collisions, or atomic reactions. Magnetized plasma simulations of realistic devices using the kinetic or the multi-fluid plasma models are examples that benefit from highorder accuracy. The multi-fluid plasma model only assumes local thermodynamic equilibrium within each fluid, e.g. ion and electron fluids for the two-fluid plasma model. The algorithm1 implements a discontinuous Galerkin method with an approximate Riemann solver to compute the fluxes of the fluids and electromagnetic fields at the computational cell interfaces. The multi-fluid plasma model has time scales on the order of the electron and ion cyclotron frequencies, the electron and ion plasma frequencies, the electron and ion sound speeds, and the speed of light. A general model for atomic reactions has been developed2 and is incorporated in the multi-fluid plasma model. The multi-fluid plasma algorithm is implemented in a flexible code framework (WARPX) that allows easy extension of the physical model to include multiple fluids and additional physics. The code runs on multi-processor machines and is being adapted with OpenCL to many-core systems, characteristic of the next generation of high performance computers. The algorithm is applicable to study advanced physics calculations of plasma dynamics including magnetic plasma confinement and astrophysical plasmas. The discontinuous Galerkin method has also been applied to solve the Vlasov-Poisson kinetic model. Recently, a mixed finite element algorithm has been developed and implemented which exploits the expected physical behavior to apply either a discontinuous or continuous finite element representation, which improves computational efficiency without sacrificing accuracy.

High-order computational method applied to the multi-fluid plasma model

High-order accurate finite element methods are important for problems that have strong anisotropies and complicated geometries and for stiff equation systems that are coupled through large source terms. Magnetized plasma simulations of realistic devices using the multi-fluid plasma model are examples that benefit from high-order accuracy. The multi-fluid plasma model only assumes local thermodynamic equilibrium within each fluid, e.g. ion and electron fluids for the two-fluid plasma model. Physical parameters indicate the importance of the two-fluid effects: electron to ion mass ratio, ion skin depth, and ion Larmor radius. The algorithm1 implements a discontinuous Galerkin method with an approximate Riemann solver to compute the fluxes of the fluids and electromagnetic fields at the computational cell interfaces. The multi-fluid plasma model has time scales on the order of the electron and ion cyclotron frequencies, the electron and ion plasma frequencies, the electron and ion sound speeds, and the speed of light. The multi-fluid plasma algorithm is implemented in a flexible code framework (WARPX) that allows easy extension of the physical model to include multiple fluids and additional physics. The code runs on multi-processor machines and is being adapted with OpenCL to many-core systems, characteristic of the next generation of high performance computers. WARPX has demonstrated a three-fluid (electrons, ions, and neutrals) simulation of a plasma sheath formation. Atomic reactions are incorporated that describe the effects of collisions between the species explicitly, allowing for the identification of regions of ionization/recombination, and interspecies momentum and energy transfer. The algorithm is validated with several test problems including the GEM challenge magnetic reconnection problem and the generation of dispersive plasma waves which are compared to analytical dispersion diagrams. The algorithm is applicable to study advanced physics calculations of plasma dynamics including magnetic plasma confinement and astrophysical plasmas. Three-dimensional solutions of the Z-pinch and the field reversed configuration (FRC) magnetic plasma confinement configurations are presented.