Mesh-Free Magnetoinductive Plasma Model

Mašek, M.; Gibbon, Paul

doi:10.1109/tps.2010.2052071

Cited by 6 publications

(6 citation statements)

References 21 publications

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“…The present mesh-free formulation of the Darwin model avoids the usual Lagrangian formulation of the Lorentz equation. As already mentioned in other articles, 1,7 this approach normally leads to numerical instabilities. As already explained, due to the Darwin approximation, we cannot use E sol ¼ -@A/@t in the Lorentz equation, because we would implicitly re-introduce retardations that we have neglected in Ampère law.…”

Section: Hamiltonian Formulationmentioning

confidence: 78%

“…In this section, we briefly recap on the formulation of Maxwell's equations according to the Darwin or magnetoinductive model, the description followed is the same as in previous works. [1][2][3]7,9 A key procedure is the use of Helmholtz's theorem, which states that any vector can be decomposed into irrotational and solenoidal parts. For instance, the electric field E ¼ E irr þ E sol .…”

Section: Maxwell's Equationsmentioning

confidence: 99%

“…Although the vector potential A satisfies a Poisson-like equation, the integration of its equation in two dimensions leads to diverging terms using the Green's function method. In fact, we can write the solenoidal current density 7 as…”

Section: D Darwin Model For Finite-sized Particlesmentioning

confidence: 99%

“…Recently, Masek & Gibbon 7 proposed a proof-of-principle mesh-free formulation of a three-dimensional Darwin model which behaved satisfactorily for simple test cases, but ran into difficulties for more general scenarios in which arbitrarily strong vector potentials were permitted. Nevertheless, the mesh-free approach does offer some significant advantages compared to traditional grid-based codes, which motivate the present quest for a more robust algorithm.…”

Section: Introductionmentioning

confidence: 99%

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Mesh-free Hamiltonian implementation of two dimensional Darwin model

2017

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A new approach to Darwin or magnetoinductive plasma simulation is presented, which combines a mesh-free field solver with a robust time-integration scheme avoiding numerical divergence errors in the solenoidal field components. The mesh-free formulation employs an efficient parallel Barnes-Hut tree algorithm to speed up the computation of fields summed directly from the particles, avoiding the necessity of divergence cleaning procedures typically required by particle-incell methods. The time-integration scheme employs a Hamiltonian formulation of the Lorentz force, circumventing the development of violent numerical instabilities associated with time differentiation of the vector potential. It is shown that a semi-implicit scheme converges rapidly and is robust to further numerical instabilities which can develop from a dominant contribution of the vector potential to the canonical momenta. The model is validated by various static and dynamic benchmark tests, including a simulation of the Weibel-like filamentation instability in beam-plasma interactions.

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Section: Hamiltonian Formulationmentioning

confidence: 78%

Section: Maxwell's Equationsmentioning

confidence: 99%

Section: D Darwin Model For Finite-sized Particlesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Mesh-free Hamiltonian implementation of two dimensional Darwin model

2017

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“…The first tests of this model have been made on charged-particle beam evolution in vacuum. The details are given in a separate publication [33].…”

Section: Magnetoinductive Plasma Simulationmentioning

confidence: 99%

Progress in Mesh-Free Plasma Simulation With Parallel Tree Codes

Gibbon

Speck

Karmakar

et al. 2010

IEEE Trans. Plasma Sci.

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The recent developments in mesh-free plasma modeling using parallel tree codes are described, covering the algorithmic and performance issues and how to apply this technique to multidimensional electrostatic plasma problems. Examples of the simulations of the ion acceleration by high-intensity lasers, heating, and the dynamics of the nanostructured targets, as well as more recent applications of this technique to the simulations of edge plasmas in tokamaks and mesh-free magnetoinductive models, are given.

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An Asymptotic Preserving Maxwell Solver Resulting in the Darwin Limit of Electrodynamics

et al. 2016

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In plasma simulations, where the speed of light divided by a characteristic length is at a much higher frequency than other relevant parameters in the underlying system, such as the plasma frequency, implicit methods begin to play an important role in generating efficient solutions in these multi-scale problems. Under conditions of scale separation, one can rescale Maxwell's equations in such a way as to give a magneto static limit known as the Darwin approximation of electromagnetics.In this work, we present a new approach to solve Maxwell's equations based on a Method of Lines Transpose (MOL T ) formulation, combined with a fast summation method with computational complexity O(N log N ), where N is the number of grid points (particles). Under appropriate scaling, we show that the proposed schemes result in asymptotic preserving methods that can recover the Darwin limit of electrodynamics.

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Mesh-Free Magnetoinductive Plasma Model

Cited by 6 publications

References 21 publications

Mesh-free Hamiltonian implementation of two dimensional Darwin model

Mesh-free Hamiltonian implementation of two dimensional Darwin model

Progress in Mesh-Free Plasma Simulation With Parallel Tree Codes

An Asymptotic Preserving Maxwell Solver Resulting in the Darwin Limit of Electrodynamics

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