A Monte Carlo simulation of magnetic field line tracing in the solar wind

International audienceIt is well known that the structure of magnetic field lines in solar wind can be influenced by the presence of the magnetohydrodynamic turbulence. We have developed a Monte Carlo simulation which traces the magnetic field lines in the heliosphere, including the effects of magnetic turbulence. These effects are modelled by random operators which are proportional to the square root of the magnetic field line diffusion coefficient. The modelling of the random terms is explained, in detail, in the case of numerical integration by discrete steps. Furthermore, a proper evaluation of the diffusion coefficient is obtained by a numerical simulation of transport in anisotropic magnetic turbulence. The scaling of the fluctuation level and of the correlation lengths with the distance from the Sun are also taken into account. As a consequence, plasma transport across the average magnetic field direction is obtained. An application to the propagation of energetic particles from corotating interacting regions to high heliographic latitudes is considered

Superdiffusive and Subdiffusive Transport of Energetic Particles in Solar Wind Anisotropic Magnetic Turbulence

The transport of energetic particles in a mean magnetic field and the presence of anisotropic magnetic turbulence are studied numerically, for parameter values relevant to the solar wind. A numerical realization of magnetic turbulence is set up in which we can vary the type of anisotropy by changing the correlation lengths lx, ly, lz. We find that for lx, ly lz, transport can be non-Gaussian, with superdiffusion along the average magnetic field and subdiffusion perpendicular to it. Decreasing the lx/lz ratio down to 0.3, Gaussian diffusion is obtained, showing that the transport regime depends on the turbulence anisotropy. Implications for energetic particle propagation in the solar wind and for diffusive shock acceleration are discussed

Diffusion and dispersion of passive tracers: Navier-Stokes versus MHD turbulence

A comparison of turbulent diffusion and pair-dispersion in homogeneous, macroscopically isotropic Navier-Stokes (NS) and nonhelical magnetohydrodynamic (MHD) turbulence based on high-resolution direct numerical simulations is presented. Significant differences between MHD and NS systems are observed in the pair-dispersion properties, in particular a strong reduction of the separation velocity in MHD turbulence as compared to the NS case. It is shown that in MHD turbulence the average pair-dispersion is slowed down for $\tau_\mathrm{d}\lesssim t\lesssim 10 \tau_\mathrm{d}$, $\tau_\mathrm{d}$ being the Kolmogorov time, due to the alignment of the relative Lagrangian tracer velocity with the local magnetic field. Significant differences in turbulent single-particle diffusion in NS and MHD turbulence are not detected. The fluid particle trajectories in the vicinity of the smallest dissipative structures are found to be characterisically different although these comparably rare events have a negligible influence on the statistics investigated in this work.Comment: Europhysics Letters, in prin

Subdiffusive transport in intergranular lanes on the Sun. The Leighton model revisited

In this paper we consider a random motion of magnetic bright points (MBP) associated with magnetic fields at the solar photosphere. The MBP transport in the short time range [0-20 minutes] has a subdiffusive character as the magnetic flux tends to accumulate at sinks of the flow field. Such a behavior can be rigorously described in the framework of a continuous time random walk leading to the fractional Fokker-Planck dynamics. This formalism, applied for the analysis of the solar subdiffusion of magnetic fields, generalizes the Leighton's model.Comment: 7 page

The role of oxygen ions in the formation of a bifurcated current sheet in the magnetotail

Cluster observations in the near-Earth magnetotail have shown that sometimes the current sheet is bifurcated, i.e. it is divided in two layers. The influence of magnetic turbulence on ion motion in this region is investigated by numerical simulation, taking into account the presence of both protons and oxygen ions. The magnetotail current sheet is modeled as a magnetic field reversal with a normal magnetic field component $B_n$, plus a three-dimensional spectrum of magnetic fluctuations $\delta {\bf B}$, which represents the observed magnetic turbulence. The dawn-dusk electric field E$_y$ is also included. A test particle simulation is performed using different values of $\delta {\bf B}$, E$_y$ and injecting two different species of particles, O$^+$ ions and protons. O$^+$ ions can support the formation of a double current layer both in the absence and for large values of magnetic fluctuations ($\delta B/B_0 = 0.0$ and $\delta B/B_0 \geq 0.4$, where B$_0$ is the constant magnetic field in the magnetospheric lobes).Comment: 8 pages, 8 figures. J. Geophys. Res., in pres

Statistics of passive tracers in three-dimensional magnetohydrodynamic turbulence

Magnetohydrodynamic (MHD) turbulence is studied from the Lagrangian viewpoint by following fluid particle tracers in high resolution direct numerical simulations. Results regarding turbulent diffusion and dispersion as well as Lagrangian structure functions are presented. Whereas turbulent single-particle diffusion exhibits essentially the same behavior in Navier-Stokes and MHD turbulence, two-particle relative dispersion in the MHD case differs significantly from the Navier-Stokes behavior. This observation is linked to the local anisotropy of MHD turbulence which is clearly reflected by quantities measured in a Lagrangian frame of reference. In the MHD case the Lagrangian structure functions display a lower level of intermittency as compared to the Navier-Stokes case contrasting Eulerian results. This is not only true for short time increments [ H. Homann, R. Grauer, A. Busse, and W.-C. Müller, J. Plasma Phys. 73, 821 (2007) ] but also holds for increments up to the order of the integral time scale. The apparent discrepancy can be explained by the difference in the characteristic shapes of fluid particle trajectories in the vicinity of most singular dissipative structure

Magnetic connection from the Earth to the solar corona, flare positions and solar energetic particle observations

Solar energetic particle (SEP) events are often associated with solar flares. Such particles propagate through the interplanetary medium, where significant levels of magnetic turbulence are found. We study the magnetic connection from the Earth to the solar corona in three dimensional magnetic turbulence. In the numerical simulation, different turbulence levels and solar wind velocities can be used. Input to the simulation is from web-based data sets, and comparison is made with the solar flare observations contained in the Goes catalogue for the years 1996, 1997, 1998, following solar minimum. For this data set, we find that SEPs can reach the Earth when the difference in the heliographic longitudes of the flare and of the magnetic foot point of the Earth is 25°–30° at most. On the other hand the longitudinal angular semi-width of the magnetic field line random walk in the solar wind, when mapped to the solar corona, is found to be typically $6^\circ$–10°. The discrepancy between the two values can be explained either by the presence of a flare – associated coronal mass ejection shock, with a longitudinal semi-size of ~$20^\circ$, or by particle propagation, which could be enhanced over the field line random walk by, e.g., gyroresonant effects, or by the presence of magnetic shear between the fast and the slow streams which enhances the longitudinal spread of field lines

High energy particle transport in stochastic magnetic fields in the solar corona

Aims.We study energetic particle transport in the solar corona in the presence of magnetic fluctuations by analyzing the motion of protons injected at the center of a model coronal loop. Methods.We set up a numerical realization of magnetic turbulence, in which the magnetic fluctuations are represented by a Fourier expansion with random phases. We perform test particle simulations by varying the turbulence correlation length λ, the turbulence level, and the proton energy. Coulomb collisions are neglected. Results.For large λ, the ratio $\rho/\lambda$ (with ρ the Larmor radius) is small, and the magnetic moment is conserved. In this case, a fraction of the injected protons, which grow with the fluctuation level, are trapped at the top of the magnetic loop, near the injection region, by magnetic mirroring due to the magnetic fluctuations. The rest of the protons propagate freely along $\vec B$, corresponding to nearly ballistic transport. Decreasing λ, that is, increasing the ratio $\rho/\lambda$, the magnetic moment is no longer well conserved, and pitch angle diffusion progressively sets in. Pitch angle diffusion leads to a decrease in the trapped population and progressively changes proton transport from ballistic to superdiffusive, and finally, for small λ, to diffusive. Conclusions.Particle mirroring by magnetic turbulence makes for compact trapping regions. The particle dynamics inside the magnetic loop is non-Gaussian and the statistical description of transport properties requires the use of such ideas as the Lévy random walk

Kolmogorov entropy of magnetic field lines in the percolating regime

Plasma Physics and Controlled Fusion, 51, p. 015005 (2009)International audienc