Hamiltonian reduction of Vlasov–Maxwell to a dark slow manifold

Miloshevich, George; Burby, Joshua W.

doi:10.1017/s0022377821000556

Hamiltonian reduction of Vlasov–Maxwell to a dark slow manifold

Journal Article · Tue Jun 08 00:00:00 EDT 2021 · Journal of Plasma Physics

DOI:https://doi.org/10.1017/s0022377821000556· OSTI ID:1874176

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École Normale Supérieure de Lyon (France)
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

In this work, we show that non-relativistic scaling of the collisionless Vlasov–Maxwell system implies the existence of a formal invariant slow manifold in the infinite-dimensional Vlasov–Maxwell phase space. Vlasov–Maxwell dynamics restricted to the slow manifold recovers the Vlasov–Poisson and Vlasov–Darwin models as low-order approximations, and provides higher-order corrections to the Vlasov–Darwin model more generally. The slow manifold may be interpreted to all orders in perturbation theory as a collection of formal Vlasov–Maxwell solutions that do not excite light waves, and are therefore ‘dark’. We provide a heuristic lower bound for the time interval over which Vlasov–Maxwell solutions initialized optimally near the slow manifold remain dark. We also show how the dynamics on the slow manifold naturally inherits a Hamiltonian structure from the underlying system. After expressing this structure in a simple form, we use it to identify a manifestly Hamiltonian correction to the Vlasov–Darwin model. The derivation of higher-order terms is reduced to computing the corrections of the system Hamiltonian restricted to the slow manifold.

View Accepted Manuscript (DOE)

Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE Laboratory Directed Research and Development (LDRD) Program

Grant/Contract Number:: 89233218CNA000001

OSTI ID:: 1874176

Report Number(s):: LA-UR-21-20381

Journal Information:: Journal of Plasma Physics, Journal Name: Journal of Plasma Physics Journal Issue: 3 Vol. 87; ISSN 0022-3778

Publisher:: Cambridge University PressCopyright Statement

Country of Publication:: United States

Language:: English

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