# Frederic Effenberger

## Contact Details

NameFrederic Effenberger |
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## Pubs By Year |
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## Pub CategoriesSolar and Stellar Astrophysics (9) Physics - Space Physics (8) High Energy Astrophysical Phenomena (4) Physics - Plasma Physics (2) Mathematics - Numerical Analysis (1) Physics - Statistical Mechanics (1) |

## Publications Authored By Frederic Effenberger

In this review, an overview of the recent history of stochastic differential equations (SDEs) in application to particle transport problems in space physics and astrophysics is given. The aim is to present a helpful working guide to the literature and at the same time introduce key principles of the SDE approach via "toy models". Using these examples, we hope to provide an easy way for newcomers to the field to use such methods in their own research. Read More

Flares close to the solar limb, where the footpoints are occulted, can reveal the spectrum and structure of the coronal loop-top source in X-rays. We aim at studying the properties of the corresponding energetic electrons near their acceleration site, without footpoint contamination. To this end, a statistical study of partially occulted flares observed with RHESSI is presented here, covering a large part of solar cycles 23 and 24. Read More

At hard X-ray energies, the bright footpoint emission from solar flare loops often prevents a detailed analysis of the weaker loop-top source morphology due to the limited dynamic range available for X-ray imaging. Here, we study the X1.3 April 25, 2014 flare with the Reuven Ramaty High-Energy Solar Spectroscopic Imager (RHESSI). Read More

Starting from an exact, steady-state, force-free solution of the magnetohydrodynamic (MHD) equations, we investigate how resistive current layers are induced by perturbing line-tied three-dimensional magnetic equilibria. This is achieved by the superposition of a weak perturbation field in the domain, in contrast to studies where the boundary is driven by slow motions, like those present in photospheric active regions. Our aim is to quantify how the current structures are altered by the contribution of so called quasi-separatrix layers (QSLs) as the null point is shifted outside the computational domain. Read More

In-situ spacecraft observations recently suggested that the transport of energetic particles accelerated at heliospheric shocks can be anomalous, i.e. the mean square displacement can grow non-linearly in time. Read More

Diffusive cosmic-ray transport in nonuniform large-scale magnetic fields in the presence of boundaries is considered. Reflecting and absorbing boundary conditions are derived for a modified telegraph equation with a convective term. Analytical and numerical solutions of illustrative boundary problems are presented. Read More

The open problem of how singular current structures form in line-tied, three-dimensional magnetic fields is addressed. A Lagrangian magneto-frictional relaxation method is employed to model the field evolution towards the final near-singular state. Our starting point is an exact force-free solution of the governing magnetohydrodynamic (MHD) equations which is sufficiently general to allow for topological features like magnetic nulls to be inside or outside the computational domain, depending on a simple set of parameters. Read More

Motivated by recent applications of superdiffusive transport models to shock-accelerated particle distributions in the heliosphere, we solve analytically a one-dimensional fractional diffusion-advection equation for the particle density. We derive an exact Fourier transform solution, simplify it in a weak diffusion approximation, and compare the new solution with previously available analytical results and with a semi-numerical solution based on a Fourier series expansion. We apply the results to the problem of describing the transport of energetic particles, accelerated at a traveling heliospheric shock. Read More

The diffusion approximation to the Fokker-Planck equation is commonly used to model the transport of solar energetic particles in interplanetary space. In this study, we present exact analytical predictions of a higher order telegraph approximation for particle transport and compare them with the corresponding predictions of the diffusion approximation and numerical solutions of the full Fokker-Planck equation. We specifically investigate the role of the adiabatic focusing effect of a spatially varying magnetic field on an evolving particle distribution. Read More

The present work provides a critical assessment of numerical solutions of the space-fractional diffusion-advection equation, which is of high significance for applications in various natural sciences. In view of the fact that, in contrast to the case of normal (Gaussian) diffusion, no standard methods and corresponding numerical codes for anomalous diffusion problems have been established yet, it is of importance to critically assess the accuracy and performance of existing approaches. Three numerical methods, namely a finite-difference method, the so-called matrix transfer technique, and a Monte-Carlo method based on the solution of stochastic differential equations, are analyzed and compared by applying them to three selected test problems for which analytical or semi-analytical solutions were known or are newly derived. Read More

Galactic transport models for cosmic rays involve the diffusive motion of these particles in the interstellar medium. Due to the large-scale structured galactic magnetic field this diffusion is anisotropic with respect to the local field direction. We included this transport effect along with continuous loss processes in a quantitative model of galactic propagation for cosmic ray protons which is based on stochastic differential equations. Read More

The spatial diffusion of cosmic rays in turbulent magnetic fields can, in the most general case, be fully anisotropic, i.e. one has to distinguish three diffusion axes in a local, field-aligned frame. Read More

The formation of a thin current sheet in a magnetic quasi-separatrix layer (QSL) is investigated by means of numerical simulation using a simplified ideal, low-$\beta$, MHD model. The initial configuration and driving boundary conditions are relevant to phenomena observed in the solar corona and were studied earlier by Aulanier et al., A&A 444, 961 (2005). Read More