T. Passot

Transverse dynamics of dispersive Alfvén waves. I. Direct numerical evidence of filamentation

The three-dimensional dynamics of a small-amplitude monochromatic Alfven wave propagating along an ambient magnetic field is simulated by direct numerical integration of the Hall-magnetohydrodynamics equations. As predicted by the two-dimensional nonlinear Schrodinger equation or by more general amplitude equations retaining the coupling to low-frequency magnetosonic waves, the transverse instability of the pump leads to wave collapse and formation of intense magnetic filaments, in spite of the presence of competing, possibly linearly dominant, instabilities that in some instances distort the above structures. In computational boxes, including a large number of pump wavelengths, an early arrest of the collapse is possible under the effect of quasi-transverse instabilities that drive magnetosonic waves and also prescribe the directions of the filaments.

Extending Magnetohydrodynamics to the Slow Dynamics of Collisionless Plasmas

A fluid approach aimed to provide a consistent description of the slow dynamics of a collisionless plasma, is presented. In this regime, both Landau damping and finite Larmor radius effects cannot be ignored. Two models are discussed; one retains the dynamics at sub-ionic scales, while the other is restricted to scales larger than the ion gyroscale. Special attention is paid to the capability of these approaches to accurately reproduce the properties of linear waves that are known to play an important role, for example, in the small-scale dynamics of solar wind turbulence.

POLARIZATION AND COMPRESSIBILITY OF OBLIQUE KINETIC ALFVÉN WAVES

It is well known that a complete description of the solar wind requires a kinetic description and that, particularly at sub-proton scales, kinetic effects cannot be ignored. It is nevertheless usually assumed that at scales significantly larger than the proton gyroscale r{sub L} , magnetohydrodynamics or its extensions, such as Hall-MHD and two-fluid models with isotropic pressures, provide a satisfactory description of the solar wind. Here we calculate the polarization and magnetic compressibility of oblique kinetic Alfven waves and show that, compared with linear kinetic theory, the isotropic two-fluid description is very compressible, with the largest discrepancy occurring at scales larger than the proton gyroscale. In contrast, introducing anisotropic pressure fluctuations with the usual double-adiabatic (or CGL) equations of state yields compressibility values which are unrealistically low. We also show that both of these classes of fluid models incorrectly describe the electric field polarization. To incorporate linear kinetic effects, we use two versions of the Landau fluid model that include linear Landau damping and finite Larmor radius (FLR) corrections. We show that Landau damping is crucial for correct modeling of magnetic compressibility, and that the anisotropy of pressure fluctuations should not be introduced without taking into account the Landau dampingmorexa0» through appropriate heat flux equations. We also show that FLR corrections to all the retained fluid moments appear to be necessary to yield the correct polarization. We conclude that kinetic effects cannot be ignored even for kr{sub L} << 1.«xa0less

IMPLICATIONS OF A NON-MODAL LINEAR THEORY FOR THE MARGINAL STABILITY STATE AND THE DISSIPATION OF FLUCTUATIONS IN THE SOLAR WIND

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 of 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.A magnetized plasma with anisotropic particle distributions may be unstable to a number of different kinetic instabilities. The solar wind is often observed in a state which is close to that implying instability, i.e., in a marginal stability state. Normal-mode linear theory predicts that fluctuations in a stable plasma damp exponentially. 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 of 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. The results obtained with a non-modal approach are relevant to a re-examination of the concept of linear marginal stability. Moreover, we highlight some aspects of the dissipation of turbulent fluctuations, which suggest that the non-modal approach should be included in future studies.

REDUCTION OF COMPRESSIBILITY AND PARALLEL TRANSFER BY LANDAU DAMPING IN TURBULENT MAGNETIZED PLASMAS

Three-dimensional numerical simulations of decaying turbulence in a magnetized plasma are performed using a so-called finite Larmor radius (FLR)-Landau fluid model which incorporates linear Landau damping and FLR corrections. It is shown that compared to simulations of compressible Hall-MHD, linear Landau damping is responsible for significant damping of magnetosonic waves, which is consistent with the linear kinetic theory. Compressibility of the fluid and parallel energy cascade along the ambient magnetic field are also significantly inhibited when the beta parameter is not too small. In contrast with Hall-MHD, the FLR-Landau fluid model can therefore correctly describe turbulence in collisionless plasmas such as solar wind, providing an interpretation for its nearly incompressible behavior.

INFLUENCE OF THE NONLINEARITY PARAMETER ON THE SOLAR WIND SUB-ION MAGNETIC ENERGY SPECTRUM: FLR–LANDAU FLUID SIMULATIONS

The cascade of kinetic Alfven waves (KAWs) at sub-ion scales in the solar wind is simulated numerically using a fluid approach that retains ion and electron Landau damping, together with ion finite Larmor radius (FLR) 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 wavenumber k0 such that (where di is the proton inertial length), 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 Alfven 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 and the homogenization of ion temperature 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.

Fluid simulations of mirror constraints on proton temperature anisotropy in solar wind turbulence

[1]xa0Non-resonant ion perpendicular heating by low-frequency kinetic Alfven wave turbulence, together with the constraining effect of the mirror instability on the developing temperature anisotropy observed in the solar wind, are simulated for the first time in a self-consistent way using a fluid model retaining low-frequency kinetic effects. This model which does not include solar wind expansion, concentrates on the influence of small-scale turbulence. It provides a sufficiently refined description of Landau damping and finite Larmor corrections to accurately capture the transverse dynamics at sub-ionic scales, including the self-regulating influence of the developing mirror modes. A fit of the simulation results with the usual mirror-instability threshold is obtained, reproducing the frontier of the slow solar wind WIND/SWE data in the (T⊥i/T∥i, β∥i) diagram. The quality of the fit is improved in the presence of a small amount of collisions, which suggests that the deviations from bi-Maxwellianity in the slow solar wind are weak enough not to significantly affect the mirror threshold.

Transverse dynamics of dispersive Alfvén waves. II. Driving of a reduced magnetohydrodynamic flow

The nonlinear dynamics resulting from transverse and quasi-transverse instabilities of a finite-amplitude dispersive Alfven wave propagating along an ambient magnetic field is studied by direct numerical simulations of the three-dimensional Hall-magnetohydrodynamic (Hall-MHD) equations. When the pump wave has a moderate amplitude and a long enough wavelength, one observes the generation of nonlinear structures in the form of helical filaments for the transverse magnetic field intensity and the density fluctuations. An interesting feature is the development of a quasi-incompressible turbulent flow, with a longitudinal characteristic scale large compared to the Alfven wavelength, that remains spectrally well separated from the wave throughout the evolution. The coexistence of this “reduced MHD” flow with nonlinear Alfven waves was predicted on the basis of an asymptotic analysis [A. Gazol, T. Passot, and P. L. Sulem, Phys. Plasmas 6, 3114 (1999)] carried out in the long-wavelength limit. Whereas in this reg...

Transient growth in stable collisionless plasma

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 nonorthogonal. 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 non-normality 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.

On the mirror instability in the presence of electron temperature anisotropy

Computation of the mirror instability growth rate in an ion-electron bi-Maxwellian plasma is revisited, starting from the low-frequency kinetic theory. The role of the electron finite Larmor radius (FLR) effects on the instability quenching is shown to possibly be dominant, even near threshold where the smallest unstable scales significantly exceed the electron gyroscale. Validation of the results by comparison with predictions of the fully kinetic whamp software is also presented. The influence of the electron temperatures on the ion FLR effects very near threshold, where the electron kinetic effects are negligible, is also pointed out.