An implicit method for electromagnetic plasma simulation in two dimensions

Brackbill, J. U.; Forslund, D. W.

doi:10.1016/0021-9991(82)90016-x

Cited by 222 publications

(171 citation statements)

References 31 publications

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“…The implicit moment method is extended to electromagnetic plasma dynamics in two dimensions in Refs. [9,11] and in three dimensions in Ref. [56].…”

Section: The Numerical Algorithmmentioning

confidence: 99%

“…While the explicit methods are constrained to follow the fastest time scale of the physical system, so that the time step limit in an explicit plasma simulation is fixed by ω pe t < 2 (where ω pe is the electron plasma frequency), the time step constraints that have been discussed for the implicit methods are a Courant limit imposed by the propagation of acoustic waves [9,41] and an accuracy limit arising from the derivation of the fluid moment equations [9,11]. This limit restricts the mean particle motion to one grid cell per time step, effectively…”

Section: The Numerical Algorithmmentioning

confidence: 99%

“…[9,11,59]. Here we show how this formulation is changed when we solve the second-order Maxwell system (8) for the electric field E, in the form given by Eqs.…”

Section: The Numerical Algorithmmentioning

confidence: 99%

“…In Ref. [9], a Picard iteration is used in which the operator on the LHS is inverted using Fourier transforms, and the RHS is lagged. In Ref.…”

Section: Temporal Discretizationmentioning

confidence: 99%

“…These boundary conditions take an especially simple form for perfectly conducting and magnetic flux surfaces. Next, we describe the numerical implementation of consistent boundary conditions in CELESTE3D, a particle-in-cell (PIC) code based on the implicitmoment plasma simulation method [9,59]. Finally, we present the results of calculations for electromagnetic wave propagation in vacuo and for the geospace environment modeling (GEM) magnetic reconnection challenge [7].…”

Section: Introductionmentioning

confidence: 99%

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A Simplified Implicit Maxwell Solver

Ricci

Lapenta

Brackbill

2002

Journal of Computational Physics

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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. c 2002 Elsevier Science (USA)

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“…The implicit moment method is extended to electromagnetic plasma dynamics in two dimensions in Refs. [9,11] and in three dimensions in Ref. [56].…”

Section: The Numerical Algorithmmentioning

confidence: 99%

Section: The Numerical Algorithmmentioning

confidence: 99%

“…[9,11,59]. Here we show how this formulation is changed when we solve the second-order Maxwell system (8) for the electric field E, in the form given by Eqs.…”

Section: The Numerical Algorithmmentioning

confidence: 99%

“…In Ref. [9], a Picard iteration is used in which the operator on the LHS is inverted using Fourier transforms, and the RHS is lagged. In Ref.…”

Section: Temporal Discretizationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A Simplified Implicit Maxwell Solver

Ricci

Lapenta

Brackbill

2002

Journal of Computational Physics

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Evolution of the lower hybrid drift instability at reconnection jet front

et al. 2015

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We investigate current‐driven modes developing at jet fronts during collisionless reconnection. Initial evolution of the reconnection is simulated using conventional 2‐D setup starting from the Harris equilibrium. Three‐dimensional PIC calculations are implemented at later stages, when fronts are fully formed. Intense currents and enhanced wave activity are generated at the fronts because of the interaction of the fast flow plasma and denser ambient current sheet plasma. The study reveals that the lower hybrid drift instability develops quickly in the 3‐D simulation. The instability produces strong localized perpendicular electric fields, which are several times larger than the convective electric field at the front, in agreement with Time History of Events and Macroscale Interactions during Substorms observations. The instability generates waves, which escape the front edge and propagate into the undisturbed plasma ahead of the front. The parallel electron pressure is substantially larger in the 3‐D simulation compared to that of the 2‐D. In a time ∼normalΩci−1, the instability forms a layer, which contains a mixture of the jet plasma and current sheet plasma. The results confirm that the lower hybrid drift instability is important for the front evolution and electron energization.

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General mechanism and dynamics of the solar wind interaction with lunar magnetic anomalies from 3‐D particle‐in‐cell simulations

et al. 2015

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We present a general model of the solar wind interaction with a dipolar lunar crustal magnetic anomaly (LMA) using three‐dimensional full‐kinetic and electromagnetic simulations. We confirm that LMAs may indeed be strong enough to stand off the solar wind from directly impacting the lunar surface, forming a so‐called “minimagnetosphere,” as suggested by spacecraft observations and theory. We show that the LMA configuration is driven by electron motion because its scale size is small with respect to the gyroradius of the solar wind ions. We identify a population of back‐streaming ions, the deflection of magnetized electrons via the E × B drift motion, and the subsequent formation of a halo region of elevated density around the dipole source. Finally, it is shown that the presence and efficiency of the processes are heavily impacted by the upstream plasma conditions and, on their turn, influence the overall structure and evolution of the LMA system. Understanding the detailed physics of the solar wind interaction with LMAs, including magnetic shielding, particle dynamics and surface charging is vital to evaluate its implications for lunar exploration.

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An implicit method for electromagnetic plasma simulation in two dimensions

Cited by 222 publications

References 31 publications

A Simplified Implicit Maxwell Solver

A Simplified Implicit Maxwell Solver

Evolution of the lower hybrid drift instability at reconnection jet front

General mechanism and dynamics of the solar wind interaction with lunar magnetic anomalies from 3‐D particle‐in‐cell simulations

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