The low-frequency limit of Maxwell equations is considered in the Maxwell-Vlasov system. This limit produces a neutral Vlasov system that captures essential features of plasma dynamics, while neglecting radiation effects. Euler-Poincare reduction the
ory is used to show that the neutral Vlasov kinetic theory possesses a variational formulation in both Lagrangian and Eulerian coordinates. By construction, the model recovers all collisionless neutral models employed in plasma simulations. Then, comparisons between the neutral Vlasov system and hybrid kinetic-fluid models are presented in the linear regime.
This paper investigates hybrid kinetic-MHD models, where a hot plasma (governed by a kinetic theory) interacts with a fluid bulk (governed by MHD). Different nonlinear coupling schemes are reviewed, including the pressure-coupling scheme (PCS) used i
n modern hybrid simulations. This latter scheme suffers from being non-Hamiltonian and to not exactly conserve total energy. Upon adopting the Vlasov description for the hot component, the non-Hamiltonian PCS and a Hamiltonian variant are compared. Special emphasis is given to the linear stability of Alfven waves, for which it is shown that a spurious instability appears at high frequency in the non-Hamiltonian version. This instability is removed in the Hamiltonian version.
The non-modal approach for a linearized system differs from a normal mode analysis by following the temporal evolution of some perturbed equilibria, and therefore includes transient effects. We employ a non-modal approach for studying the stability o
f a bi-Maxwellian magnetized plasma using the Landau fluid model, which we briefly describe. We show that bi-Maxwellian stable equilibria can support transient growth of some physical quantities, and we study how these transients behave when an equilibrium approaches its marginally stable condition. This is relevant to anisotropic plasma, that are often observed in the solar wind with a temperature anisotropy close to values that can trigger a kinetic instability. The results obtained with a non-modal approach are relevant to a re-examination of the concept of linear marginal stability. Moreover, we discuss the topic of the dissipation of turbulent fluctuations, suggesting that the non-modal approach should be included in future studies.
The first kinetic study of transient growth for a collisionless homogeneous Maxwellian plasma in a uniform magnetic field is presented. A system which is linearly stable may display transient growth if the linear operator describing its evolution is
non-normal, so that its eigenvectors are non-orthogonal. In order to include plasma kinetic effects a Landau fluid model is employed. The linear operator of the model is shown to be non-normal and the results suggest that the nonnormality of a collisionless plasma is intrinsically related to its kinetic nature, with the transient growth being more accentuated for smaller scales and higher plasma beta. The results based on linear spectral theory have been confirmed with nonlinear simulations.
