Detailed analytical investigation of magnetic field line random walk in turbulent plasmas: II. Isotropic turbulence

2009 ◽  
Vol 75 (2) ◽  
pp. 183-192 ◽  
Author(s):  
I. KOURAKIS ◽  
R. C. TAUTZ ◽  
A. SHALCHI
Keyword(s):  
Magnetic Field ◽  
Random Walk ◽  
Field Line ◽  
Isotropic Turbulence ◽  
Mean Square Displacement ◽  
Analytical Investigation ◽  
Turbulence Spectrum ◽  
Quasilinear Theory ◽  
Magnetic Turbulence ◽  
Field Lines

AbstractThe random walk of magnetic field lines in the presence of magnetic turbulence in plasmas is investigated from first principles. An isotropic model is employed for the magnetic turbulence spectrum. An analytical investigation of the asymptotic behavior of the field-line mean-square displacement 〈(Δx)2〉 is carried out, in terms of the position variable z. It is shown that 〈(Δx)2〉 varies as ~z ln z for large distance z. This result corresponds to a superdiffusive behavior of field line wandering. This investigation complements previous work, which relied on a two-component model for the turbulence spectrum. Contrary to that model, quasilinear theory appears to provide an adequate description of the field-line random walk for isotropic turbulence.

Detailed analytical investigation of magnetic field line random walk in turbulent plasmas: I. Two-component slab/two-dimensional turbulence

2008 ◽  
Vol 74 (5) ◽  
pp. 657-677 ◽  
Author(s):  
I. KOURAKIS ◽  
A. SHALCHI
Keyword(s):  
Magnetic Field ◽  
Field Line ◽  
Mean Square Displacement ◽  
Analytical Investigation ◽  
Asymptotic Result ◽  
Two Dimensional ◽  
Plasma Parameters ◽  
Diffusive Regime ◽  
Two Component ◽  
Field Lines

AbstractThe random displacement of magnetic field lines in the presence of magnetic turbulence in plasmas is investigated from first principles. A two-component (slab/two-dimensional composite) model for the turbulence spectrum is employed. An analytical investigation of the asymptotic behavior of the field-line mean square displacement (FL-MSD) is carried out. It is shown that the magnetic field lines behave superdiffusively for very large values of the position variable z, since the FL-MSD σ varies as σ ~ z4/3. An intermediate diffusive regime may also possibly exist for finite values of z under conditions which are explicitly determined in terms of the intrinsic turbulent plasma parameters. The superdiffusive asymptotic result is confirmed numerically via an iterative algorithm. The relevance to previous results is discussed.

scholarly journals Random Walk and Trapping of Interplanetary Magnetic Field Lines: Global Simulation, Magnetic Connectivity, and Implications for Solar Energetic Particles

2021 ◽  
Author(s):  
David Ruffolo ◽  
Rohit Chhiber ◽  
William H. Matthaeus ◽  
Arcadi V. Usmanov ◽  
Paisan Tooprakai ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Random Walk ◽  
Field Line ◽  
Large Scale ◽  
Transport Model ◽  
Source Region ◽  
Science Research ◽  
Energetic Particles ◽  
Solar Energetic Particles ◽  
Field Lines

<p>The random walk of magnetic field lines is an important ingredient in understanding how the connectivity of the magnetic field affects the spatial transport and diffusion of charged particles. As solar energetic particles (SEPs) propagate away from near-solar sources, they interact with the fluctuating magnetic field, which modifies their distributions. We develop a formalism in which the differential equation describing the field line random walk contains both effects due to localized magnetic displacements and a non-stochastic contribution from the large-scale expansion. We use this formalism together with a global magnetohydrodynamic simulation of the inner-heliospheric solar wind, which includes a turbulence transport model, to estimate the diffusive spreading of magnetic field lines that originate in different regions of the solar atmosphere. We first use this model to quantify field line spreading at 1 au, starting from a localized solar source region, and find rms angular spreads of about 20 – 60 degrees. In the second instance, we use the model to estimate the size of the source regions from which field lines observed at 1 au may have originated, thus quantifying the uncertainty in calculations of magnetic connectivity; the angular uncertainty is estimated to be about 20 degrees. Finally, we estimate the filamentation distance, i.e., the heliocentric distance up to which field lines originating in magnetic islands can remain strongly trapped in filamentary structures. We emphasize the key role of slab-like fluctuations in the transition from filamentary to more diffusive transport at greater heliocentric distances. This research has been supported in part by grant RTA6280002 from Thailand Science Research and Innovation and the Parker Solar Probe mission under the ISOIS project (contract NNN06AA01C) and a subcontract to University of Delaware from Princeton University (SUB0000165).  MLG acknowledges support from the Parker Solar Probe FIELDS MAG team.  Additional support is acknowledged from the  NASA LWS program  (NNX17AB79G) and the HSR program (80NSSC18K1210 & 80NSSC18K1648).</p>

MAGNETIC FIELD LINE RANDOM WALK IN ISOTROPIC TURBULENCE WITH VARYING MEAN FIELD

2016 ◽  
Vol 225 (2) ◽  
pp. 20 ◽  
Author(s):  
W. Sonsrettee ◽  
P. Subedi ◽  
D. Ruffolo ◽  
W. H. Matthaeus ◽  
A. P. Snodin ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Random Walk ◽  
Field Line ◽  
Magnetic Field Line ◽  
Isotropic Turbulence ◽  
Mean Field

MAGNETIC FIELD LINE RANDOM WALK IN ISOTROPIC TURBULENCE WITH ZERO MEAN FIELD

2014 ◽  
Vol 798 (1) ◽  
pp. 59 ◽  
Author(s):  
W. Sonsrettee ◽  
P. Subedi ◽  
D. Ruffolo ◽  
W. H. Matthaeus ◽  
A. P. Snodin ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Random Walk ◽  
Field Line ◽  
Magnetic Field Line ◽  
Isotropic Turbulence ◽  
Mean Field

Diffusion coefficient and Kolmogorov entropy of magnetic field lines

1984 ◽  
Vol 32 (1) ◽  
pp. 141-158 ◽  
Author(s):  
Gaetano Zimbardo ◽  
Pierluigi Veltri ◽  
Francesco Malara
Keyword(s):  
Magnetic Field ◽  
Diffusion Coefficient ◽  
Random Walk ◽  
Diffusion Equation ◽  
Field Line ◽  
Statistical Techniques ◽  
Kolmogorov Entropy ◽  
Closed Set ◽  
Field Lines ◽  
Single Field

A diffusion equation for magnetic field lines of force in a turbulent magnetic field, which describes both the random walk of a single field line and how two nearby lines separate from each other, has been obtained using standard statistical techniques. Starting from such an equation, a closed set of equations for the moments may be obtained, in general, with suitable assumptions. From such a set of equations the Kolmogorov entropy may be explicitly calculated. The results have been applied to the most interesting examples of magnetic field geometries.

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

2001 ◽  
Vol 8 (3) ◽  
pp. 151-158 ◽  
Author(s):  
P. Pommois ◽  
G. Zimbardo ◽  
P. Veltri
Keyword(s):  
Magnetic Field ◽  
Monte Carlo Simulation ◽  
Solar Wind ◽  
Monte Carlo ◽  
Diffusion Coefficient ◽  
Field Line ◽  
Magnetic Field Line ◽  
Magnetic Turbulence ◽  
Field Lines ◽  
The Magnetic Field

Abstract. It 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.

scholarly journals The development of magnetic field line wander by plasma turbulence

2017 ◽  
Vol 83 (4) ◽  
Author(s):  
Gregory G. Howes ◽  
Sofiane Bourouaine
Keyword(s):  
Magnetic Field ◽  
Field Line ◽  
Magnetic Field Line ◽  
Large Scale ◽  
Magnetic Energy ◽  
Plasma Turbulence ◽  
Alfven Wave ◽  
Astrophysical Plasmas ◽  
Field Lines ◽  
The Magnetic Field

Plasma turbulence occurs ubiquitously in space and astrophysical plasmas, mediating the nonlinear transfer of energy from large-scale electromagnetic fields and plasma flows to small scales at which the energy may be ultimately converted to plasma heat. But plasma turbulence also generically leads to a tangling of the magnetic field that threads through the plasma. The resulting wander of the magnetic field lines may significantly impact a number of important physical processes, including the propagation of cosmic rays and energetic particles, confinement in magnetic fusion devices and the fundamental processes of turbulence, magnetic reconnection and particle acceleration. The various potential impacts of magnetic field line wander are reviewed in detail, and a number of important theoretical considerations are identified that may influence the development and saturation of magnetic field line wander in astrophysical plasma turbulence. The results of nonlinear gyrokinetic simulations of kinetic Alfvén wave turbulence of sub-ion length scales are evaluated to understand the development and saturation of the turbulent magnetic energy spectrum and of the magnetic field line wander. It is found that turbulent space and astrophysical plasmas are generally expected to contain a stochastic magnetic field due to the tangling of the field by strong plasma turbulence. Future work will explore how the saturated magnetic field line wander varies as a function of the amplitude of the plasma turbulence and the ratio of the thermal to magnetic pressure, known as the plasma beta.

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