A Hamiltonian gyrofluid model based on a quasi-static closure

Abstract

A Hamiltonian six-field gyrofluid model is constructed, based on closure relations derived from the so-called ‘quasi-static’ gyrokinetic linear theory where the fields are assumed to propagate with a parallel phase velocity much smaller than the parallel particle thermal velocities. The main properties captured by this model, primarily aimed at exploring fundamental problems of interest for space plasmas such as the solar wind, are its ability to provide a reasonable agreement with kinetic theory for linear low-frequency modes, and at the same time to ensure a Hamiltonian structure in the absence of explicit dissipation. The model accounts for equilibrium temperature anisotropy, ion and electron finite Larmor radius corrections, electron inertia, magnetic fluctuations along the direction of a strong guide field and parallel Landau damping, introduced through a Landau-fluid modelling of the parallel heat transfers for both gyrocentre species. Remarkably, the quasi-static closure leads to exact and simple expressions for the nonlinear terms involving gyroaveraged electromagnetic fields and potentials. One of the consequences is that a rather natural identification of the Hamiltonian structure of the model becomes possible when Landau damping is neglected. A slight variant of the model consists of a four-field Hamiltonian reduction of the original six-field model, which is also used for the subsequent linear analysis. In the latter, the dispersion relations of kinetic Alfvén waves and the firehose instability are shown to be correctly reproduced, relatively far in the sub-ion range (depending on the plasma parameters), while the spectral range where the slow-wave dispersion relation and the field-swelling instabilities are precisely described is less extended. This loss of accuracy originates from the breaking of the condition of small phase velocity, relative to the parallel thermal velocity of the electrons (for kinetic Alfvén waves and firehose instability) or of the ions (in the case of the field-swelling instabilities).

Gyrofluid analysis of electron β e effects on collisionless reconnection

“…The system (2.1)-(2.7), although written with a different normalization, constitutes the Hamiltonian four-field model derived by Tassi et al (2020), taken in the 2-D limit (assuming that all the independent variables do not vary along the direction of the guide field).…”

“…where L U e and L U i are also operators, the explicit expression of which can be given in Fourier space. The model (2.1)-(2.7) can be formulated as an infinite-dimensional Hamiltonian system, adopting the four fields N i , N e , A i and A e as dynamical variables (Tassi et al 2020).…”

“…In this work, we make use of a gyrofluid model to study the linear and nonlinear evolution of the tearing instability in a collisionless plasma with strong guide field. This study is based on a two-field gyrofluid model that has been derived from gyrokinetic equations in Tassi, Passot & Sulem (2020), assuming a quasistatic closure. With respect to the above-mentioned reduced fluid models, such a gyrofluid model accounts for both finite electron Larmor radius effects and perturbations parallel to the direction of the guide field.…”

Inverse cascade and magnetic vortices in kinetic Alfvén-wave turbulence

“…The present study can be extended to include the coupling to slow magnetosonic waves, using a four-field gyrofluid model (Tassi, Passot & Sulem 2020). This description appears especially relevant in the regions near the Sun, explored by Parker Solar Probe and Solar Orbiter, where large-scale compressibility effects are important.…”

Impact of electron temperature anisotropy on the collisionless tearing mode instability in the presence of a strong guide field

“…Therefore, we present here also the derivation of a new reduced gyrofluid model, which takes into account equilibrium temperature anisotropy, and which will be the basis for our derivation and analysis of the dispersion relation for the linear growth rate. The gyrofluid model we present here, in particular, differs from similar gyrofluid models recently derived [34,36], as it assumes an isothermal closure referred to parallel and perpendicular particle temperatures.…”