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

Nonlinear mirror modes in the presence of hot electrons

A non-perturbative calculation of the gyrotropic pressures associated with large-scale mirror modes is performed, taking into account a finite, possibly anisotropic electron temperature. In the small-amplitude limit, this leads to an extension of an asymptotic model previously derived for cold electrons. A model equation for the profile of subcritical finite-amplitude large-scale structures is also presented

Influence of the nonlinearity parameter on the solar-wind sub-ion magnetic energy spectrum: FLR-Landau fluid simulations

The cascade of kinetic Alfv\'en waves (KAWs) at the sub-ion scales in the solar wind is numerically simulated using a fluid approach that retains ion and electron Landau damping, together with ion finite Larmor radius corrections. Assuming initially equal and isotropic ion and electron temperatures, and an ion beta equal to unity, different simulations are performed by varying the propagation direction and the amplitude of KAWs that are randomly driven at a transverse scale of about one fifth of the proton gyroradius in order to maintain a prescribed level of turbulent fluctuations. The resulting turbulent regimes are characterized by the nonlinearity parameter, defined as the ratio of the characteristic times of Alfv\'en wave propagation and of the transverse nonlinear dynamics. The corresponding transverse magnetic energy spectra display power laws with exponents spanning a range of values consistent with spacecraft observations. The meandering of the magnetic field lines together with the ion temperature homogenization along these lines are shown to be related to the strength of the turbulence, measured by the nonlinearity parameter. The results are interpreted in terms of a recently proposed phenomenological model where the homogenization process along field lines induced by Landau damping plays a central role

Nonlinear Mirror Modes in Space Plasmas

Since the first observations by Kaufmann et al.\ (1970), special attention has been paid to static pressure-balanced structures in the form of magnetic holes or humps observed in regions of the solar wind and of planetary magnetosheaths where the $\beta$ parameter is relatively large and the ion perpendicular temperature exceeds the parallel one. Although alternative interpretations have been proposed, these structures are usually viewed as associated with the mirror instability discovered in 1957 by Vedenov and Sagdeev. After reviewing observational results provided by satellite missions, high-resolution numerical simulations of the Vlasov--Maxwell equations together with asymptotic and phenomenological models of the nonlinear dynamics near the instability threshold are discussed. The constraining effect of the mirror instability on the temperature anisotropy associated with a dominant perpendicular ion heating observed in the solar wind is reported, and recent simulations of this phenomenon based on an elaborated fluid model including low-frequency kinetic effects are briefly mentioned.Comment: 3rd School and Workshop on Space Plasma Physics, (1-12 September 2010,Kiten, Bulgaria),I. Zhelyazkov and T. Mishonov eds., AIP Conference Proceedings 356, 159-176, ISBN 978-0-7354-0914-9 (American Institute of Physics, 2011

Computing the ground state solution of Bose-Einstein condensates by a normalized gradient flow

In this paper, we prove the energy diminishing of a normalized gradient flow which provides a mathematical justification of the imaginary time method used in physical literatures to compute the ground state solution of Bose-Einstein condensates (BEC). We also investigate the energy diminishing property for the discretization of the normalized gradient flow. Two numerical methods are proposed for such discretizations: one is the backward Euler centered finite difference (BEFD), the other one is an explicit time-splitting sine-spectral (TSSP) method. Energy diminishing for BEFD and TSSP for linear case, and monotonicity for BEFD for both linear and nonlinear cases are proven. Comparison between the two methods and existing methods, e.g. Crank-Nicolson finite difference (CNFD) or forward Euler finite difference (FEFD), shows that BEFD and TSSP are much better in terms of preserving energy diminishing property of the normalized gradient flow. Numerical results in 1d, 2d and 3d with magnetic trap confinement potential, as well as a potential of a stirrer corresponding to a far-blue detuned Gaussian laser beam are reported to demonstrate the effectiveness of BEFD and TSSP methods. Furthermore we observe that the normalized gradient flow can also be applied directly to compute the first excited state solution in BEC when the initial data is chosen as an odd function.Comment: 28 pages, 6 figure

A Landau fluid model for warm collisionless plasmas

A Landau fluid model for a collisionless electron-proton magnetized plasma, that accurately reproduces the dispersion relation and the Landau damping rate of all the magnetohydrodynamic waves, is presented. It is obtained by an accurate closure of the hydrodynamic hierarchy at the level of the fourth order moments, based on linear kinetic theory. It retains non-gyrotropic corrections to the pressure and heat flux tensors up to the second order in the ratio between the considered frequencies and the ion cyclotron frequency.Comment: to appear in Phys. Plasma

Phase Space Models for Stochastic Nonlinear Parabolic Waves: Wave Spread and Singularity

We derive several kinetic equations to model the large scale, low Fresnel number behavior of the nonlinear Schrodinger (NLS) equation with a rapidly fluctuating random potential. There are three types of kinetic equations the longitudinal, the transverse and the longitudinal with friction. For these nonlinear kinetic equations we address two problems: the rate of dispersion and the singularity formation. For the problem of dispersion, we show that the kinetic equations of the longitudinal type produce the cubic-in-time law, that the transverse type produce the quadratic-in-time law and that the one with friction produces the linear-in-time law for the variance prior to any singularity. For the problem of singularity, we show that the singularity and blow-up conditions in the transverse case remain the same as those for the homogeneous NLS equation with critical or supercritical self-focusing nonlinearity, but they have changed in the longitudinal case and in the frictional case due to the evolution of the Hamiltonian