Hamiltonian Quasineutrality

The ubiquitous and highly desirable quasineutrality (QN) approximation, which enforces local charge neutrality, is believed to be valid on scales larger than the Debeye length (LD). Two questions arise: Is the resulting system Hamiltonian and what forces are needed to exactly enforce QN. The first question is addressed using slow manifold reduction and the theory of Poisson-Dirac submanifolds [1], which lead to a Hamiltonian formulation. Explicitly, the Hamiltonian formulation in the QN limit of a magnetized, planar Vlasov-Poisson system for electrons moving through a frozen neutralizing ion background is obtained. Alternatively, the Hamiltonian structure can be obtained by using Dirac constraint theory [2], which also leads to a Hamiltonian formulation. This approach yields the forces required to enforce QN, providing the ability to assess the validity of QN. We investigate the constrained equations numerically with a semi-Lagrangian method applied to the 1-dimensional electron-ion two-stream instability. We verify that fast time scales are systematically removed and QN is well satisfied for lengths >> electron LD; deviations occur on smaller scales.

[1] J. Burby, D. Kaltsas, P. Morrison, E. Tassi, and G. Throumoulopoulos, "Hamiltonian formulation of the quasineutral Vlasov-Poisson system," on the arXiv (2025).

[2] D. Kaltsas J. Burby, P. Morrison, E. Tassi, and G. Throumoulopoulos, "Imposing quasineutrality on electrostatic plasmas via the Dirac theory of constraints," on the arXiv (2025).