Magnetic Reconnection Challenge Research Articles

A GPU-enabled implicit Finite Volume solver for the ideal two-fluid plasma model on unstructured grids

This paper describes the main features of a pioneering unsteady solver for simulating ideal two-fluid plasmas on unstructured grids, taking profit of GPGPU (General-purpose computing on graphics processing units). The code, which has been implemented within the open source COOLFluiD platform, is implicit, second-order in time and space, relying upon a Finite Volume method for the spatial discretization and a three-point backward Euler for the time integration. In particular, the convective fluxes are computed by a multi-fluid version of the AUSM+up scheme for the plasma equations, in combination with a modified Rusanov scheme with tunable dissipation for the Maxwell equations. Source terms are integrated with a one-point rule, using the cell-centered value. Some critical aspects of the porting to GPU’s are discussed, as well as the performance of two open source linear system solvers (i.e. PETSc, PARALUTION). The code design allows for computing both flux and source terms on the GPU along with their Jacobian, giving a noticeable decrease in the computational time in comparison with the original CPU-based solver. The code has been tested in a wide range of mesh sizes and in three different systems, each one with a different GPU. The increased performance (up to 14x) is demonstrated in two representative 2D benchmarks: propagation of circularly polarized waves and the more challenging Geospace Environmental Modeling (GEM) magnetic reconnection challenge.

Two-dimensional full-electromagnetic Vlasov code with conservative scheme and its application to magnetic reconnection

A detailed procedure of full-electromagnetic Vlasov simulation technique is presented. Our new unsplitting conservative scheme exactly satisfies the continuity equation for charge. The implicit Finite Difference Time Domain method is also adopted for computation of electromagnetic fields, which is not restricted by the CFL condition for light. The Geospace Environment Modeling magnetic reconnection challenge problem is adopted as a benchmark test. The characteristics of the present Vlasov code are studied by varying the resolution in configuration space.

Extended MHD Modelling with the Ten-Moment Equations

High-order moment fluid equations for simulation of plasmas are presented. The ten-moment equations are a two-fluid model in which time dependent equations are used to advance the pressure tensor. With the inclusion of the full pressure tensor Finite Larmor Radius (FLR) effects are captured. Further, Hall-effects are captured correctly by including the full electron momentum equation. Hall and FLR effects are important to understand stability of compact toroids like Field Reversed Configurations (FRCs) and also to detailed understanding of small scale instabilities in current carrying plasmas. The effects of collisions are discussed. Solutions to a Riemann problem for the ten-moment equations are presented. The ten-moment equations show complex dispersive solutions which come about from the source terms. The model is validated with the GEM fast magnetic reconnection challenge problem.

Vlasov simulations of collisionless magnetic reconnection without background density

A standard starting point for the simulation of collisionless reconnection is the Harris equilibrium which is made up of a current sheet that separates two regions of opposing magnetic field. Magnetohydrodynamic simulations of collisionless reconnection usually include a homogeneous background density for reasons of numerical stability. While, in some cases, this is a realistic assumption, the background density may introduce new effects both due to the more involved structure of the distribution function or due to the fact that the Alfvèn speed remains finite far away from the current sheet. We present a fully kinetic Vlasov simulation of the perturbed Harris equilibrium using a Vlasov code. Parameters are chosen to match the Geospace Environment Modeling (GEM) Magnetic Reconnection Challenge but excluding the background density. This allows to compare with earlier simulations [Schmitz H, Grauer R. Kinetic Vlasov simulations of collisionless magnetic reconnection. Phys Plasmas 2006;13:092309] which include the background density. It is found that the absence of a background density causes the reconnection rate to be higher. On the other hand, the time until the onset of reconnection is hardly affected. Again the off diagonal elements of the pressure tensor are found to be important on the X-line but with modified importance for the individual terms.

Kinetic Vlasov simulations of collisionless magnetic reconnection

A fully kinetic Vlasov simulation of the Geospace Environment Modeling Magnetic Reconnection Challenge is presented. Good agreement is found with previous kinetic simulations using particle in cell (PIC) codes, confirming both the PIC and the Vlasov code. In the latter the complete distribution functions fk (k=i,e) are discretized on a numerical grid in phase space. In contrast to PIC simulations, the Vlasov code does not suffer from numerical noise and allows a more detailed investigation of the distribution functions. The role of the different contributions of Ohm’s law are compared by calculating each of the terms from the moments of the fk. The important role of the off-diagonal elements of the electron pressure tensor could be confirmed. The inductive electric field at the X line is found to be dominated by the nongyrotropic electron pressure, while the bulk electron inertia is of minor importance. Detailed analysis of the electron distribution function within the diffusion region reveals the kinetic origin of the nongyrotropic terms.

GEM reconnection challenge: Implicit kinetic simulations with the physical mass ratio

We extend kinetic simulations of the Geospace Environment Modeling (GEM) magnetic reconnection challenge [Birn et al., J. Geophys. Res., 106, 3715, 2001] to a physical mass ratio, using the implicit Particle‐in‐Cell (PIC) code CELESTE3D which allows the use of a coarser grid and a bigger time step. We compare results for three values of the mass ratio mi/me = 25 (GEM challenge standard mass ratio), mi/me = 180 and the physical mass ratio mi/me = 1836. The results of the three simulations are compared and the scaling laws based on reconnection via nongyrotropic electron pressure are verified.

A Simplified Implicit Maxwell Solver

We apply the second-order formulation of Maxwell's equations proposed by Jiang et al. (1996, J. Comput. Phys. 125, 104) to the solution of the implicit formulation of the three-dimensional, time-dependent Vlasov–Maxwell's system. An implicit finite difference algorithm is developed to solve the Maxwell's equations in a bounded domain with physical boundary conditions comprising electrically conducting walls (perfect conductors) and constant magnetic flux walls. We formulate the boundary conditions for Maxwell's equations to satisfy Poisson's equation throughout the domain by solving it only on the boundary. This eliminates the need for a separate projection step. We compare numerical results with analytical solutions for electromagnetic waves in vacuo, and using the implicit particle-in-cell code CELESTE3D, we test the new solver on the geospace environment modeling magnetic reconnection challenge problem.

Geospace Environment Modeling (GEM) magnetic reconnection challenge: Resistive tearing, anisotropic pressure and Hall effects

The nonlinear evolution of resistive tearing is studied in various regimes, including one‐fluid isotropic MHD, anisotropic (gyrotropic) MHD with terms approximating the effects of anisotropy driven instabilities, and HaIl‐MHD. Both uniform resistivity and spatially localized resistivity are investigated. The initial state is a plane one‐dimensional current sheet with an initial perturbation representing a periodic structure with magnetic islands and x type neutral points, chosen for the “GEM magnetic reconnection challenge” [Birn et al., this issue]. In the absence of dissipation, within ideal MHD, the initially imposed x type configuration collapses into a thin current sheet of finite length, while the magnetic islands contract, conserving their magnetic flux. The current density in the thin sheet becomes significantly enhanced, so that microscopic dissipation mechanisms can be expected to be ignited, even if they were absent in the initial state. Finite resistivity enables reconnection, and the growth of magnetic islands as in particle simulations. A comparison of reconnection rates shows that for the chosen initial current sheet thickness, a localized resistivity, corresponding to a Lundquist number (magnetic Reynolds number) of order unity, is necessary to approximate the growth and the reconnection electric field in the particle simulations. Pressure anisotropy, governed by double adiabatic conservation laws (modified by Ohmic heating), leads to reduced growth rates. This reduction is drastic for uniform resistivity. Isotropizing terms, modeling the effects of anisotropy driven microinstabilities again destabilize. HaIl‐MHD simulations can reproduce the fast growth of the particle simulations. The various models show both similarities and dissimilarities in their spatial structure. For similar amounts of reconnected flux, the variation of the normal magnetic field and of the (ion) flow speed along the current sheet are similar, but electric field and current density show significant differences.

Collisionless magnetic reconnection: Electron processes and transport modeling

Particle‐in‐cell simulations are used to investigate collisionless magnetic reconnection in thin current sheets, based on the configuration chosen for the Geospace Environment Modeling (GEM) magnetic reconnection challenge [Birn et al., this issue]. The emphasis is on the overall evolution, as well as details of the particle dynamics in the diffusion region. Here electron distributions show clear signatures of nongyrotropy, whereas ion distributions are simpler in structure. The investigations are extended to current sheets of different widths. Here we derive a scaling law for the evolution dependence on current sheet width. Finally, we perform a detailed comparison between a kinetic and Hall‐magnetohydrodynamic model of the same system. The comparison shows that although electric fields appear to be quite similar, details of the evolution appear to be considerably different, indicative of the role of further anisotropies in the ion pressures.

Geospace Environment Modeling magnetic reconnection challenge: Simulations with a full particle electromagnetic code

The objective of the Geospace Environment Modeling (GEM) magnetic reconnection challenge is to understand the collisionless physics that controls the rate of magnetic reconnection in a two‐dimensional configuration. The challenge involves investigating a standard model problem based on a simple Harris sheet configuration by means of a variety of physical models in order to isolate the essential physics. In the present work the challenge problem is modeled using an electromagnetic particle‐in‐cell code in which full particle dynamics are retained for both electrons and ions and Maxwell's equations are solved without approximation. The timescale for reconnection is of the order of (where Ωi is the ion cyclotron frequency based on the asymptotic field B0), and the corresponding reconnection electric field is (c/vA)Ey/B0 ∼ 0.24. The diffusion region near the neutral line is observed to develop a multiscale structure based on the electron and ion inertial lengths c/ωpe and c/ωpi. The difference between the ion and electron dynamics in the diffusion region gives rise to in‐plane (Hall) currents which produce an out‐of‐plane By field with a quadrupolar structure. In the diffusion region the magnetic field is no longer frozen‐in to the electrons; the inductive Ey field is supported primarily by the off‐diagonal electron pressure terms in the generalized Ohm's law. The reconnection rate is found to be insensitive to electron inertia effects and to the presence of a moderate out‐of‐plane initial field component B0y ≲ B0. The results are consistent with the theory that the reconnection rate is independent of the mechanism which breaks the frozen‐in condition and is controlled by dynamics at length scales much greater than the electron dissipation region.

Geospace Environment Modeling (GEM) magnetic reconnection challenge: MHD and Hall MHD—constant and current dependent resistivity models

The work is part of several papers investigating two‐dimensional magnetic reconnection in the same initial configuration with different plasma approximations. The present work compares the results of magnetic reconnection in this configuration using constant and current dependent resistivity models in the framework of traditional MHD and Hall MHD. The results can be summarized as follows. For constant resistivity the effects of diffusion or the formation of a long thin current layer limit the reconnection rate. Current dependent resistivity models result in enhanced reconnection rates in all considered cases. In these cases, reconnection is faster by a factor of 2 in the Hall MHD approximation compared to the traditional MHD. The maximum reconnection rate for the Hall MHD for all current dependent resistivities is ∼0.2 and appears largely independent of the model specifics and the initial perturbation.