Electron-scale reduced fluid models with gyroviscous effects

Reduced fluid models for collisionless plasmas including electron inertia and finite Larmor radius corrections are derived for scales ranging from the ion to the electron gyroradii. Based either on pressure balance or on the incompressibility of the electron fluid, they respectively capture kinetic Alfv\'en waves (KAWs) or whistler waves (WWs), and can provide suitable tools for reconnection and turbulence studies. Both isothermal regimes and Landau fluid closures permitting anisotropic pressure fluctuations are considered. For small values of the electron beta parameter $\beta_e$, a perturbative computation of the gyroviscous force valid at scales comparable to the electron inertial length is performed at order $O(\beta_e)$, which requires second-order contributions in a scale expansion. Comparisons with kinetic theory are performed in the linear regime. The spectrum of transverse magnetic fluctuations for strong and weak turbulence energy cascades is also phenomenologically predicted for both types of waves. In the case of moderate ion to electron temperature ratio, a new regime of KAW turbulence at scales smaller than the electron inertial length is obtained, where the magnetic energy spectrum decays like $k_\perp^{-13/3}$, thus faster than the $k_\perp^{-11/3}$ spectrum of WW turbulence.Comment: 29 pages, 4 figure

Hamiltonian fluid reductions of electromagnetic drift-kinetic equations for an arbitrary number of moments

International audienceWe present an infinite family of Hamiltonian electromagnetic fluid models for plasmas, derived from drift-kinetic equations. An infinite hierarchy of fluid equations is obtained from a Hamiltonian drift-kinetic systems by taking moments of a generalized distribution function and using Hermite polynomials as weight functions of the velocity coordinate along the magnetic guide field. Each fluid model is then obtained by truncating the hierarchy to a finite number N + 1 of equations by means of a closure relation. We show that, for any positive N , a linear closure relation between the moment of order N + 1 and the moment of order N guarantees that the resulting fluid model possesses a Hamiltonian structure, thus respecting the Hamiltonian character of the parent drift-kinetic model. An orthogonal transformation is identified which maps the fluid moments to a new set of dynamical variables in terms of which the Poisson brackets of the fluid models become a direct sum and which unveils remarkable dynamical properties of the models in the tw

Gyrofluid simulations of collisionless reconnection in the presence of diamagnetic effects

The effects of the ion Larmor radius on magnetic reconnection are investigated by means of numerical simulations, with a Hamiltonian gyrofluid model. In the linear regime, it is found that ion diamagnetic effects decrease the growth rate of the dominant mode. Increasing ion temperature tends to make the magnetic islands propagate in the ion diamagnetic drift direction. In the nonlinear regime, diamagnetic effects reduce the final width of the island. Unlike the electron density, the guiding center density does not tend to distribute along separatrices and at high ion temperature, the electrostatic potential exhibits the superposition of a small scale structure, related to the electron density, and a large scale structure, related to the ion guiding-center density

Gyrofluid simulations of collisionless reconnection in the presence of diamagnetic effects

The effects of the ion Larmor radius on magnetic reconnection are investigated by means of numerical simulations, with a Hamiltonian gyrofluid model. In the linear regime, it is found that ion diamagnetic effects decrease the growth rate of the dominant mode. Increasing ion temperature tends to make the magnetic islands propagate in the ion diamagnetic drift direction. In the nonlinear regime, diamagnetic effects reduce the final width of the island. Unlike the electron density, the guiding center density does not tend to distribute along separatrices and at high ion temperature, the electrostatic potential exhibits the superposition of a small scale structure, related to the electron density, and a large scale structure, related to the ion guiding-center density

Gyrofluid simulations of collisionless reconnection in the presence of diamagnetic effects

The effects of the ion Larmor radius on magnetic reconnection are investigated by means of numerical simulations, with a Hamiltonian gyrofluid model. In the linear regime, it is found that ion diamagnetic effects decrease the growth rate of the dominant mode. Increasing ion temperature tends to make the magnetic islands propagate in the ion diamagnetic drift direction. In the nonlinear regime, diamagnetic effects reduce the final width of the island. Unlike the electron density, the guiding center density does not tend to distribute along separatrices and at high ion temperature, the electrostatic potential exhibits the superposition of a small scale structure, related to the electron density, and a large scale structure, related to the ion guiding-center density

Hamiltonian closures for fluid models with four moments by dimensional analysis

Fluid reductions of the Vlasov-Amp{\`e}re equations that preserve the Hamiltonian structure of the parent kinetic model are investigated. Hamiltonian closures using the first four moments of the Vlasov distribution are obtained, and all closures provided by a dimensional analysis procedure for satisfying the Jacobi identity are identified. Two Hamiltonian models emerge, for which the explicit closures are given, along with their Poisson brackets and Casimir invariants

Derivation of reduced two-dimensional fluid models via Dirac's theory of constrained Hamiltonian systems

We present a Hamiltonian derivation of a class of reduced plasma two-dimensional fluid models, an example being the Charney-Hasegawa-Mima equation. These models are obtained from the same parent Hamiltonian model, which consists of the ion momentum equation coupled to the continuity equation, by imposing dynamical constraints. It is shown that the Poisson bracket associated with these reduced models is the Dirac bracket obtained from the Poisson bracket of the parent model

Hamiltonian magnetic reconnection with parallel electron heat flux dynamics

International audienceWe analyze, both analytically and numerically, a two-dimensional six-field fluid model for collisionless magnetic reconnection, accounting for temperature and heat flux fluctuations along the direction of the magnetic guide field. We show that the model possesses a Hamiltonian structure with a noncanonical Poisson bracket. This bracket is characterized by the presence of six infinite families of Casimirs, associated with Lagrangian invariants. This reveals that the model can be reformulated as a system of advection equations, thus generalizing previous results obtained for Hamiltonian isothermal fluid models for reconnection. Numerical simulations indicate that the presence of heat flux and temperature fluctuations yields slightly larger growth rates and similar saturated island amplitudes, with respect to the isothermal models. For values of the sonic Lar-mor radius much smaller than the electron skin depth, heat flux fluctuations tend to be suppressed and temperature fluctuations follow density fluctuations. Increasing the sonic Larmor radius results in an increasing fraction of magnetic energy converted into heat flux, at the expense of temperature fluctuations. In particular, heat flux fluctuations tend to become relevant along the magnetic island separatrices. The qualitative structures associated with the electron field variables are also reinterpreted in terms of the rotation of the Lagrangian invariants of the system

On the use of projectors for Hamiltonian systems and their relationship with Dirac brackets

The role of projectors associated with Poisson brackets of constrained Hamiltonian systems is analyzed. Projectors act in two instances in a bracket: in the explicit dependence on the variables and in the computation of the functional derivatives. The role of these projectors is investigated by using Dirac's theory of constrained Hamiltonian systems. Results are illustrated by three examples taken from plasma physics: magnetohydrodynamics, the Vlasov-Maxwell system, and the linear two-species Vlasov system with quasineutrality