D. Laveder

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.

Transverse collapse of low-frequency Alfvén waves

The dynamics of long-wavelength dispersive Alfven wave trains propagating parallel to an ambient field in a magnetized plasma is investigated by means of a three-dimensional extension of the derivative nonlinear Schrodinger equation that includes the mean effect of the longitudinal magneto-sonic waves. In the strongly dispersive regime, quasi-monochromatic right-hand polarized plane waves perturbed by a broad-spectrum noise develop a transverse collapse leading to the formation of strong magnetic filaments parallel to the ambient field, as asymptotically predicted by the nonlinear Schrodinger equation for the wave envelope. In contrast, for left-hand polarized waves filamentation only takes place when the noise is confined to Fourier modes with wavenumbers close enough to that of the pump. In the regime where dispersion and nonlinearity are comparable, the amplitude growth is strongly inhibited but intense gradients are still formed, associated with the creation of pancake-like magnetic structures. The transverse focusing of weakly nonlinear dispersive waves still takes place when the spectrum of the initial conditions is broadened, in spite of the fragmentation of the magnetic filaments into chains of magnetic bubbles and ultimately into randomly distributed three-dimensional structures.

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...

Wave collapse in dispersive magnetohydrodynamics: direct simulations and envelope modeling

An example of wave collapse arising in dispersive magnetohydrodynamics is analyzed by means of both direct numerical simulations and envelope formalism. It is shown that in spite of the presence of various types of waves and of purely hydrodynamic effects, the evolution of a longitudinally homogeneous Alfven-wave beam propagating along an ambient magnetic field is accurately described by a cubic nonlinear Schrodinger equation with an external potential proportional to the initial wave intensity. In this description, an axisymmetric beam can only collapse on its axis when its transverse extension significantly exceeds the typical scale of the modulational instability of the carrying wave. An axisymmetric configuration is however unstable with respect to azimuthal perturbations, leading to off-center collapse, even in situations that are smooth when axisymmetry is preserved. In the case of a wave packet with a finite longitudinal extension, a minimum size is required for blowup, associated with the formation of strongly anisotropic magnetic structures.

Formation and disruption of Alfvénic filaments in Hall magnetohydrodynamics

In magnetohydrodynamics with Hall effect (Hall-MHD), weakly nonlinear quasimonochromatic dispersive Alfven waves propagating along an ambient magnetic field can develop to transverse instabilities leading to the formation of intense magnetic filaments. This phenomenon, described as a transverse collapse within the asymptotic approach provided by the nonlinear Schrodinger equation for the pump envelope, was also reproduced by spectral direct numerical simulations of the Hall-MHD system. We address here the dynamics at longer times, using a finite difference scheme with adaptive mesh refinement to reproduce a strong filamentation regime, supplemented by a shock capturing scheme in the final phase of the simulations. We observe a strong distortion of the early time cylindrical filaments, associated with flattening and twisting of the structures and the transition from nonlinear waves to a hydrodynamic regime, characterized by intense current sheets and a strong acceleration of the plasma. A configuration whe...

Phase slips and dissipation of Alfvenic intermediate shocks and solitons

The time evolution of a rotational discontinuity, characterized by a change of the magnetic-field direction by an angle Δθ such that π 3π, which corresponds to a wave train limited on both sides by uniform fields, a sequence of such reconnection processes takes place. Differently, in the presence of a strong enough dispersion, the rotational discon...

Fluid simulations of plasma turbulence at ion scales: Comparison with Vlasov-Maxwell simulations

Comparisons are presented between a hybrid Vlasov-Maxwell (HVM) simulation of turbulence in a collisionless plasma and fluid reductions. These include Hall-magnetohydrodynamics (HMHD) and Landau fluid (LF) or FLR-Landau fluid (FLR-LF) models that retain pressure anisotropy and low-frequency kinetic effects such as Landau damping and, for the last model, finite Larmor radius (FLR) corrections. The problem is considered in two space dimensions, when initial conditions involve moderate-amplitude perturbations of a homogeneous equilibrium plasma subject to an out-of-plane magnetic field. LF turns out to provide an accurate description of the velocity field up to the ion Larmor radius scale, and even to smaller scales for the magnetic field. Compressibility nevertheless appears significantly larger at the sub-ion scales in the fluid models than in the HVM simulation. High frequency kinetic effects, such as cyclotron resonances, not retained by fluid descriptions, could be at the origin of this discrepancy. A significant temperature anisotropy is generated, with a bias towards the perpendicular component, the more intense fluctuations being rather spread out and located in a broad vicinity of current sheets. Non-gyrotropic pressure tensor components are measured and their fluctuations are shown to reach a significant fraction of the total pressure fluctuation, with intense regions closely correlated with current sheets.

Alfvén wave propagation through a moderate-amplitude transverse inhomogeneity in a magnetized plasma

Parallel propagation of a plane Alfven wave in a moderate-amplitude Gaussian-shaped transverse inhomogeneity is studied numerically using a fluid model retaining low-frequency kinetic effects. It is shown that in such a situation, common in the solar wind where elongated pressure-balanced structures are frequently observed, phase mixing competes with wave focusing, in contrast with coronal loops or auroral regions where sharp gradients present at the edges of the inhomogeneities make phase mixing dominant. Some understanding about this competition is provided by a model based on an envelope formalism. Depending on the magnitude of the Alfven wavelength and of the inhomogeneity transverse scale relative to the ion inertial length, various regimes can develop, ranging from the formation of localized gradients when phase mixing dominates to the development of an intense magnetic filament when focusing is stronger, with a different efficiency for the generation of magnetosonic and kinetic Alfven waves. Electr...