Energy Stability Analysis for a Hybrid Fluid‐Kinetic Plasma Model

Abstract

In plasma physics, a hybrid fluid-kinetic model is composed of a magnetohydrodynamics (MHD) part that describes a bulk fluid component and a Vlasov kinetic theory part that describes an energetic plasma component. While most hybrid models in the plasma literature are non-Hamiltonian, this paper investigates a recent Hamiltonian variant in its two-dimensional configuration. The corresponding Hamiltonian structure is described along with its Casimir invariants. Then, the energy-Casimir method is used to derive explicit sufficient stability conditions, which imply a stable spectrum and suggest nonlinear stability.

A low-frequency variational model for energetic particle effects in the pressure-coupling scheme

“…We remark that, while the latter is also preserved by the non-conservative models appearing in the literature, cross-helicity conservation is a specific feature of the new PCS model (3.32)-(3.34) and it is lost in other models. As a final remark, we notice that cross-helicity can be exploited to perform Lyapunov stability studies (Holm et al 1985) along the lines of those already carried out for the case of the Vlasov PCS model (2.14)-(2.16) (Morrison et al 2014;.…”

“…An alternative direction is to identify the physical force terms that need to be added to the continuum equations in order to restore energy balance. This second strategy is precisely the program recently followed in the work stream (Tronci 2010; Holm & Tronci 2012; Morrison, Tassi & Tronci 2014; Tronci et al. 2014; Tronci, Tassi & Morrison 2015; Burby & Tronci 2017) to which this paper belongs.…”

“…Besides energy conservation, it is important to notice that these equations preserve a hybrid expression of the cross-helicity as follows (Holm & Tronci 2012): This conservation law has enabled a thorough Lyapunov stability study (Morrison et al. 2014; Tronci et al. 2015).…”

“…This conservation law has enabled a thorough Lyapunov stability study (Morrison et al 2014;.' It is the purpose of this paper to extend this construction to the case of energetic particles undergoing guiding center motion.…”

A Hamiltonian fluid-kinetic model for a two-species non-neutral plasma

“…We remark that further examples of Hamiltonian hybrid fluid-kinetic models, accounting for coupling via the current density, or via the pressure, have been discussed in Refs. [12][13][14].…”