Energy-Casimir stability of hybrid Vlasov-MHD models

Abstract

Different variants of hybrid kinetic-fluid models are considered for describing the interaction of a bulk fluid plasma obeying MHD and an energetic component obeying a kinetic theory. Upon using the Vlasov kinetic theory for energetic particles, two planar Vlasov-MHD models are compared in terms of their stability properties. This is made possible by the Hamiltonian structures underlying the considered hybrid systems, whose infinite number of invariants makes the energy-Casimir method effective for determining stability. Equilibrium equations for the models are obtained from a variational principle and in particular a generalized hybrid Grad-Shafranov equation follows for one of the considered models. The stability conditions are then derived and discussed with particular emphasis on kinetic particle effects on classical MHD 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 (55)- (57) and it is lost in other models. As a final remark, we notice that cross-helicity can be exploited to perform Lyapunov stability studies [23] along the lines of those already carried out for the case of the Vlasov PCS model (13)-(15) [58,41].…”

“…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. In this context, standard viscous and resistive terms can be added a posteriori , after the ideal (energy-conserving) model has been formulated.…”

“…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;Tronci et al 2014;Tronci, Tassi & Morrison 2015;Burby & Tronci 2017) to which this paper belongs. In this context, standard viscous and resistive terms can be added a posteriori, after the ideal (energy-conserving) model has been formulated.…”

Hamiltonian kinetic-Hall magnetohydrodynamics with fluid and kinetic ions in the current and pressure coupling schemes

“…This approach resulted in Vlasov kinetic-MHD models in the CCS and the PCS. The Hamiltonian construction of these models opened up the possibility to employ the energy-Casimir Hamiltonian variational principle (Morrison 1998) to derive equilibrium and stability conditions for planar kinetic-MHD using CCS and PCS in the studies by Morrison et al (2014) and Tronci, Tassi & Morrison (2015). Tronci (2010) also provides the derivation of a noncanonical Poisson bracket that correctly describes the dynamics of a standard hybrid model that treats the electrons as a fluid with zero inertia while retaining a Vlasov description for the ions (see e.g.…”

Ισορροπία Και Ευστάθεια Μαγνητικά Περιορισμένου Πλάσματος Στα Πλαίσια Γενικευμένων Μαγνητοϋδροδυναμικών Μοντέλων, Μέσω Χαμιλτονιανών Παραλλακτικών Αρχών

“…More specifically, kinetic effects could be incorporated into the XMHD framework in future studies. For example hybrid fluid-kinetic Hamiltonian models have already been employed in the framework of MHD forming EC principles for planar plasmas [136] and deriving new stability criteria. The motivation is that the inclusion of kinetic effects is important for a multiscale description, especially when energetic particle populations exist within the plasma.…”