arXiv subjects

A. Shalchi

Publications and source records attributed to A. Shalchi.

12 recordsLinked to original sources

arXiv2025

Subspace Approximation to the Focused Transport Equation. II. The Modified Form

The transport of energetic particles in a spatially varying magnetic field is described by the focused transport equation. In the past two versions of this equation were investigated. The more commonly used standard form described a pitch-angle isotropization process but does not conserve the norm. In the current paper we consider the focused transport equation in conservative form also called modified focused transport equation. This equation conserves the norm but does not describe pitch-angle isotropization. We use the previously developed subspace method to solve the focused transport equation analytically and numerically. For a pure analytical treatment we employ the two-dimensional subspace approximation. Furthermore, we consider a higher dimensionality for which one needs to evaluate occurring matrix exponentials numerically. This type of semi-numerical approach is much faster than traditional solvers and, therefore, it is very useful.

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arXiv2025

Subspace Approximations to the Focused Transport Equation of Energetic Particles, I. The Standard Form

The Fokker-Planck equation describing the transport of energetic particles interacting with turbulence is difficult to solve analytically. Numerical solutions are of course possible but they are not always useful for applications. In the past a subspace approximation was proposed which allows to compute important quantities such as the characteristic function as well as certain expectation values. This previous approach was applied to solve the one-dimensional Fokker-Planck equation which contains only a pitch-angle scattering term. In the current paper we extend this approach in order to solve the Fokker-Planck equation with a focusing term. We employ two- and three-dimensional subspace approximations to achieve a pure analytical description of particle transport. Additionally, we show that with higher dimensions, the subspace method can be used as a hybrid analytical-numerical method which produces an accurate approximation. Although the latter approach does not lead to analytical results, it is much faster compared to pure numerical solutions of the considered transport equation.

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arXiv2019

Heuristic Description of Perpendicular Diffusion of Energetic Particles in Astrophysical Plasmas

A heuristic approach for collisionless perpendicular diffusion of energetic particles is presented. Analytic forms for the corresponding diffusion coefficient are derived. The heuristic approach presented here explains the parameter $a^2$ used in previous theories in order to achieve agreement with simulations and its relation to collisionless Rechester & Rosenbluth diffusion. The obtained results are highly relevant for applications because previously used formulas are altered significantly in certain situations.

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arXiv2015

Monte-Carlo simulations of intensity profiles for energetic particle propagation

Aims. Numerical test-particle simulations are a reliable and frequently used tool to test analytical transport theories and to predict mean-free paths. The comparison between solutions of the diffusion equation and the particle flux is used to critically judge the applicability of diffusion to the stochastic transport of energetic particles in magnetized turbulence. Methods. A Monte-Carlo simulation code is extended to allow for the generation of intensity profiles as well as anisotropy-time profiles. Due to the relatively low number density of computational particles, a kernel function has to be used to describe the spatial extent of each particle. Results. The obtained intensity profiles are interpreted as solutions of the diffusion equation by inserting the diffusion coefficients that have been directly determined from the mean-square displacements. The comparison shows that the time dependence of the diffusion coefficients needs to be considered, in particular the initial ballistic phase and the often sub-diffusive perpendicular coefficient. Conclusions. It is argued that the perpendicular component of the distribution function is essential if agreement between the diffusion solution and the simulated flux is to be obtained. In addition, time-dependent diffusion can provide a better description than the classic diffusion equation only after the initial ballistic phase.

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arXiv2014

Pitch-angle scattering of energetic particles with adiabatic focusing

Understanding turbulent transport of charged particles in magnetized plasmas often requires a model for the description of random variations in the particle's pitch angle. The Fokker-Planck coefficient of pitch-angle scattering, which is used to describe scattering parallel to the mean magnetic field, is therefore of central importance. Whereas quasi-linear theory assumes a homogeneous mean magnetic field, such a condition is often not fulfilled, especially for high-energy particles. Here, a new derivation of the quasi-linear approach is given that is based on the unperturbed orbit found for an adiabatically focused mean magnetic field. The results show that, depending on the ratio of the focusing length and the particle's Larmor radius, the Fokker-Planck coefficient is significantly modified but agrees with the classical expression in the limit of a homogeneous mean magnetic field.

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arXiv2013

Simulated Energetic Particle Transport in the Interplanetary Space: The Palmer Consensus Revisited

Reproducing measurements of the scattering mean free paths for energetic particles propagating through the solar system has been a major problem in space physics. The pioneering work of Bieber et al. [Astrophys. J. 420, 294 (1994)] provided a theoretical explanation of such observations, which, however, was based on assumptions such as the questionable hypothesis that quasi-linear theory is correct for parallel diffusion. By employing a hybrid plasma-wave/magnetostatic turbulence model, a test-particle code is used to investigate the scattering of energetic particles. The results show excellent agreement with solar wind observations.

astro-ph.HE↗

arXiv2010

Simulating Heliospheric and Solar Particle Diffusion using the Parker Spiral Geometry

Cosmic Ray transport in curved background magnetic fields is investigated using numerical Monte-Carlo simulation techniques. Special emphasis is laid on the Solar system, where the curvature of the magnetic field can be described in terms of the Parker spiral. Using such geometries, parallel and perpendicular diffusion coefficients have to be re-defined using the arc length of the field lines as the parallel displacement and the distance between field lines as the perpendicular displacement. Furthermore, the turbulent magnetic field is incorporated using a WKB approach for the field strength. Using a test-particle simulation, the diffusion coefficients are then calculated by averaging over a large number of particles starting at the same radial distance from the Sun and over a large number of turbulence realizations, thus enabling one to infer the effects due to the curvature of the magnetic fields and associated drift motions.

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arXiv2008

Forms of Eulerian correlation functions in the solar wind

Current spacecraft missions such as Wind and ACE can be used to determine magnetic correlation functions in the solar wind. Data sets from these missions can, in principle, also be used to compute so-called Eulerian correlation functions. These temporal correlations are essential for understanding the dynamics of solar wind turbulence. In the current article we calculate these dynamical correlations by using well-established methods. These results are very useful for a comparison with Eulerian correlations obtained from space craft missions.

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arXiv2007

Nonlinear damping of slab modes and cosmic ray transport

By applying recent results for the slab correlation time scale onto cosmic ray scattering theory, we compute cosmic ray parallel mean free paths within the quasilinear limit. By employing these results onto charged particle transport in the solar system, we demonstrate that much larger parallel mean free paths can be obtained in comparison to previous results. A comparison with solar wind observations is also presented to show that the new theoretical results are much closer to the observations than the previous results.

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arXiv2007

Analytical description of stochastic field-line wandering in magnetic turbulence

A non-perturbative nonlinear statistical approach is presented to describe turbulent magnetic systems embedded in a uniform mean magnetic field. A general formula in the form of an ordinary differential equation for magnetic field-line wandering (random walk) is derived. By considering the solution of this equation for different limits several new results are obtained. As an example, it is demonstrated that the stochastic wandering of magnetic field-lines in a two-component turbulence model leads to superdiffusive transport, contrary to an existing diffusive picture. The validity of quasilinear theory for field-line wandering is discussed, with respect to different turbulence geometry models, and previous diffusive results are shown to be deduced in appropriate limits.

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arXiv2007

Random walk of magnetic field lines for different values of the energy-range spectral index

An analytical nonlinear description of field-line wandering in partially statistically magnetic systems was proposed recently [A. Shalchi, I. Kourakis, Astronomy and Astrophysics, 470, 405 (2007)]. In this article we investigate the influence of the wave-spectrum in the energy-range onto field line random walk by applying this formulation. It is demonstrated that in all considered cases we clearly obtain a superdiffusive behaviour of the field-lines. If the energy-range spectral index exceeds unity a free-streaming behaviour of the field-lines can be found for all relevant length-scales of turbulence. Since the superdiffusive results obtained for the slab model are exact, it seems that superdiffusion is the normal behavior of field line wandering.

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arXiv2004

Spurious contribution to CR scattering calculations

The quasilinear theory for cosmic ray propagation is a well known and widely accepted theory. In this paper, we discuss the different contributions to the pitch-angle Fokker-Planck coefficient from large and small scales for slab geometry using the damping model of dynamical turbulence. These examinations will give us a hint on the limitation range where quasilinear approximation is a good approximation.

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