GEMPIC: geometric electromagnetic particle-in-cell methods

Kraus, Michael; Kormann, Katharina; Morrison, Philip J.; Sonnendrücker, Eric

doi:10.1017/s002237781700040x

Title: GEMPIC: geometric electromagnetic particle-in-cell methods

Journal Article · Mon Jul 03 00:00:00 EDT 2017 · Journal of Plasma Physics

DOI:https://doi.org/10.1017/s002237781700040x· OSTI ID:1534399

; Kormann, Katharina; Morrison, Philip J.; Sonnendrücker, Eric

We present a novel framework for finite element particle-in-cell methods based on the discretization of the underlying Hamiltonian structure of the Vlasov–Maxwell system. We derive a semi-discrete Poisson bracket, which retains the defining properties of a bracket, anti-symmetry and the Jacobi identity, as well as conservation of its Casimir invariants, implying that the semi-discrete system is still a Hamiltonian system. In order to obtain a fully discrete Poisson integrator, the semi-discrete bracket is used in conjunction with Hamiltonian splitting methods for integration in time. Techniques from finite element exterior calculus ensure conservation of the divergence of the magnetic field and Gauss’ law as well as stability of the field solver. The resulting methods are gauge invariant, feature exact charge conservation and show excellent long-time energy and momentum behaviour. Due to the generality of our framework, these conservation properties are guaranteed independently of a particular choice of the finite element basis, as long as the corresponding finite element spaces satisfy certain compatibility conditions.

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Research Organization:: Univ. of Texas, Austin, TX (United States)

Sponsoring Organization:: USDOE

DOE Contract Number:: FG05-80ET53088

OSTI ID:: 1534399

Journal Information:: Journal of Plasma Physics, Vol. 83, Issue 4; ISSN 0022-3778

Publisher:: Cambridge University Press

Country of Publication:: United States

Language:: English

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