arXiv subjects

Andreas Shalchi

Publications and source records attributed to Andreas Shalchi.

14 recordsLinked to original sources

arXiv2026

Boris and Exponential Integrators in the Theory of Particles Interacting with Magnetic Turbulence

The interaction of electrically charged particles with magnetic fields is a fundamental problem in several areas of physics. An example is the motion of energetic particles through a magnetized plasma. The most accurate and reliable way to explore theoretically the interactions between particles and fields is via test-particle simulations. In such simulations one creates the turbulent magnetic field and solves the Newton-Lorentz equation numerically by employing an integration scheme. In the current article we discuss exponential integrators and derive systematically from this the Rodrigues scheme as well as the famous Boris integrator. For an approach where one creates the magnetic field anew at each time step, both integrators are overall comparable. In theory the Rodrigues approach should be more accurate due to the fact that the occurring matrix exponential is evaluated without further approximations. Practically, both methods provide very similar results. It is argued in the current article that a Rodrigues based integrator is a very strong alternative because for the specific problem discussed here, it does not require longer computing times.

physics.plasm-ph↗

arXiv2025

Parallel and perpendicular diffusion of energetic particles in the near-Sun solar wind observed by Parker Solar Probe

We investigate energetic particle diffusion in the inner heliosphere (approximately 0.06-0.3 AU) explored by Parker Solar Probe (PSP). Parallel (kappa_parallel) and perpendicular (kappa_perp) diffusion coefficients are calculated using second-order quasi-linear theory (SOQLT) and unified nonlinear transport (UNLT) theory, respectively. PSP's in situ measurements of magnetic turbulence spectra, including sub-Alfvenic solar wind, are decomposed into parallel and perpendicular wavenumber spectra via a composite two-component turbulence model. These spectra are then used to compute kappa_parallel and kappa_perp across energies ranging from sub-GeV to GeV. Our results reveal a strong energy and radial distance dependence in kappa_parallel. While kappa_perp remains much smaller, it can increase in regions with relatively high turbulence levels delta B / B0. To validate our results, we estimate kappa_parallel using the upstream time-intensity profile of a solar energetic particle event observed by PSP and compare it with theoretical values from different diffusion models. Our results suggest that the SOQLT-calculated parallel diffusion generally shows better agreement with SEP intensity-derived estimates than the classic QLT model. This indicates that the SOQLT framework, which incorporates resonance broadening and nonlinear corrections and does not require an ad hoc pitch-angle cutoff, may provide a more physically motivated description of energetic particle diffusion near the Sun.

physics.space-ph↗

arXiv2025

Solar Coronal Heating: Role of Kinetic and Inertial Alfv\'en Waves in Heating and Charged Particle Acceleration

A comprehensive understanding of solar coronal heating and charged particle acceleration remains one of the most critical challenges in space and astrophysical plasma physics. In this study, we explore the contribution of Alfv\'en waves, both in their kinetic (KAWs) and inertial (IAWs) regimes, to particle acceleration processes that ultimately lead to coronal heating. Using a kinetic plasma framework based on the generalized Vlasov-Maxwell model, we analyze the dynamics of these waves with a focus on the perpendicular components of the Poynting flux vectors and the net resonance speed of the particles. Our results show that both the magnitude and dissipation rate of the Poynting flux for KAWs and IAWs decrease with increasing electron-to-ion temperature ratio (T_e/T_i) and normalized perpendicular electron inertial length (c k_x / omega_pe). We evaluate the associated electric potentials and find that KAWs are significantly influenced in the high wavenumber (k_x rho_i) regime. IAWs, on the other hand, show a decrease in electric potential along the magnetic field and an increase across it when the perpendicular electric field (E_x) is enhanced. We also determine the net resonant speeds of particles in the perpendicular direction and show that these wave-particle interactions can efficiently heat the solar corona over large distances (R_Sun). Finally, we quantify the power transported by KAWs and IAWs through solar flux loop tubes, finding that both wave types deliver greater energy with increasing T_e/T_i and c k_x / omega_pe. These findings offer deeper insights into wave-driven heating and are relevant to solar wind and magnetospheric physics.

astro-ph.SR↗

arXiv2021

Perpendicular Diffusion of Energetic Particles: A Complete Analytical Theory

Over the past two decades scientists have achieved a significant improvement of our understanding of the transport of energetic particles across a mean magnetic field. Due to test-particle simulations as well as powerful non-linear analytical tools our understanding of this type of transport is almost complete. However, previously developed non-linear analytical theories do not always agree perfectly with simulations. Therefore, a correction factor $a^2$ was incorporated into such theories with the aim to balance out inaccuracies. In this paper a new analytical theory for perpendicular transport is presented. This theory contains the previously developed unified non-linear transport theory, the most advanced theory to date, in the limit of small Kubo number turbulence. For two-dimensional turbulence new results are obtained. In this case the new theory describes perpendicular diffusion as a process which is sub-diffusive while particles follow magnetic field lines. Diffusion is restored as soon as the turbulence transverse complexity becomes important. For long parallel mean free paths one finds that the perpendicular diffusion coefficient is a reduced field line random walk limit. For short parallel mean free paths, on the other hand, one gets a hybrid diffusion coefficient which is a mixture of collisionless Rechester & Rosenbluth and fluid limits. Overall the new analytical theory developed in the current paper is in agreement with heuristic arguments. Furthermore, the new theory agrees almost perfectly with previously performed test-particle simulations without the need of the aforementioned correction factor $a^2$ or any other free parameter.

physics.plasm-ph↗

arXiv2017

Time-Dependent Perpendicular Transport of Energetic Particles for Different Turbulence Configurations and Parallel Transport Models

Recently a new theory for the transport of energetic particles across a mean magnetic field was presented. Compared to other non-linear theories the new approach has the advantage that it provides a full time-dependent description of the transport. Furthermore, a diffusion approximation is no longer part of that theory. It is the purpose of the current paper to combine this new approach with a time-dependent model for parallel transport and different turbulence configurations in order to explore the parameter regimes for which we get ballistic transport, compound sub-diffusion, and normal Markovian diffusion.

physics.plasm-ph↗

arXiv2017

Time-Dependent Perpendicular Transport of Energetic Particles in Magnetic Turbulence with Transverse Complexity

The motion of energetic particles in magnetic turbulence across a mean magnetic field is explored analytically. The approach presented here allows for a full time-dependent description of the transport, including compound sub-diffusion. The first time it is shown systematically that as soon as there is transverse structure of the turbulence, diffusion is restored even if no Coulomb collisions are invoked. Criteria for sub-diffusion and normal Markovian diffusion are found as well.

physics.plasm-ph↗

arXiv2016

The implicit contribution of slab modes to the perpendicular diffusion coefficient of particles interacting with two-component turbulence

We explore the transport of energetic particles in two-component turbulence in which the stochastic magnetic field is assumed to be a superposition of slab and two-dimensional modes. It is known that in magnetostatic slab turbulence, the motion of particles across the mean magnetic field is subdiffusive. If a two-dimensional component is added, diffusion is recovered. It was also shown before that in two-component turbulence, the slab modes do not explicitly contribute to the perpendicular diffusion coefficient. In the current paper the implicit contribution of slab modes is explored and it is shown that this contribution leads to a reduction of the perpendicular diffusion coefficient. This effect improves the agreement between simulations and analytical theory. Furthermore, the obtained results are relevant for investigations of diffusive shock acceleration.

physics.space-ph↗

arXiv2016

Simulations of Energetic Particles Interacting with Nonlinear Anisotropic Dynamical Turbulence

We investigate test-particle diffusion in dynamical turbulence based on a numerical approach presented before. For the turbulence we employ the nonlinear anisotropic dynamical turbulence model which takes into account wave propagation effects as well as damping effects. We compute numerically diffusion coefficients of energetic particles along and across the mean magnetic field. We focus on turbulence and particle parameters which should be relevant for the solar system and compare our findings with different interplanetary observations. We vary different parameters such as the dissipation range spectral index, the ratio of the turbulence bendover scales, and the magnetic field strength in order to explore the relevance of the different parameters. We show that the bendover scales as well as the magnetic field ratio have a strong influence on diffusion coefficients whereas the influence of the dissipation range spectral index is weak. The best agreement with solar wind observations can be found for equal bendover scales and a magnetic field ratio of $δ$B/B0 = 0.75.

astro-ph.HE↗

arXiv2015

Finite Gyroradius Corrections in the Theory of Perpendicular Diffusion, 1. Suppressed Velocity Diffusion

A fundamental problem in plasma physics, space science, and astrophysics is the transport of energetic particles interacting with stochastic magnetic fields. In particular the motion of particles across a large scale magnetic field is difficult to describe analytically. However, progress has been achieved in the recent years due to the development of the unified non-linear transport theory which can be used to describe magnetic field line diffusion as well as perpendicular diffusion of energetic particles. The latter theory agrees very well with different independently performed test-particle simulations. However, the theory is still based on different approximations and assumptions. In the current article we extend the theory by taking into account the finite gyroradius of the particle motion and calculate corrections in different asymptotic limits. We consider different turbulence models as examples such as the slab model, noisy slab turbulence, and the two-dimensional model. Whereas there are no finite gyroradius corrections for slab turbulence, the perpendicular diffusion coefficient is reduced in the other two cases. The matter investigated in this article is also related to the parameter a^2 occurring in non-linear diffusion theories.

physics.space-ph↗

arXiv2015

The Influence of Different Turbulence Models on the Diffusion Coefficients of Energetic Particles

We explore the influence of turbulence on the transport of energetic particles by using test-particle simulations. We compute parallel and perpendicular diffusion coefficients for two-component turbulence, isotropic turbulence, a model based on Goldreich-Sridhar scaling, noisy reduced magnetohydrodynamic turbulence, and a noisy slab model. We show that diffusion coefficients have a similar rigidity dependence regardless which turbulence model is used and, thus, we conclude that the influence of turbulence on particle transport is not as strong as originally thought. Only fundamental quantities such as particle rigidity and the Kubo number are relevant. In the current paper we also confirm the unified nonlinear transport theory for noisy slab turbulence. To double-check the validity and accuracy of our numerical results, we use a second test-particle code. We show that both codes provide very similar results confirming the validity of our conclusions.

astro-ph.SR↗

arXiv2015

Perpendicular Diffusion of Energetic Particles in Collisionless Plasmas

A fundamental problem in plasma and astrophysics is the interaction between energetic particles and magnetized plasmas. In the current paper we focus on particle diffusion across the guide magnetic field. It is shown that the perpendicular diffusion coefficient depends only on the parallel diffusion coefficient and the Kubo number. Therefore, one can find four asymptotic limits depending on the values of these two parameters. These regimes are the quasilinear limit, the Kadomtsev & Pogutse limit, the scaling of Rechester & Rosenbluth, and the scaling found by Zybin & Istomin. In the current article we focus on the Rechester & Rosenbluth scenario because this was not discovered before in the context of collisionless plasmas. Examples and applications are discussed as well. We show that an energy independent ratio of perpendicular and parallel diffusion coefficients can be found and that this ratio can be very small but also close to unity. This is exactly what one observes in the solar wind.

astro-ph.SR↗

arXiv2014

Perpendicular diffusion of energetic particles in noisy reduced magnetohydrodynamic turbulence

Recently a model for noisy reduced magnetohydrodynamic turbulence was proposed. The latter model was already used to study the random walk of magnetic field lines. In the current article we use the same model to investigate the diffusion of energetic particles across the mean magnetic field. To compute the perpendicular diffusion coefficient two analytical theories are used, namely the Non- Linear Guiding Center (NLGC) theory and the Unified Non-Linear Transport (UNLT) theory. It is shown that the two theories provide different results for the perpendicular diffusion coefficient. We also perform test-particle simulations for the aforementioned turbulence model. We show that only the UNLT theory describes perpendicular transport accurately confirming that the latter theory is a powerful tool in diffusion theory.

astro-ph.SR↗

arXiv2014

Cosmic ray acceleration at perpendicular shocks in supernova remnants

Supernova remnants (SNRs) are believed to accelerate particles up to high energies through the mechanism of diffusive shock acceleration (DSA). Except for direct plasma simulations, all modeling efforts must rely on a given form of the diffusion coefficient, a key parameter that embodies the interactions of energetic charged particles with the magnetic turbulence. The so-called Bohm limit is commonly employed. In this paper we revisit the question of acceleration at perpendicular shocks, by employing a realistic model of perpendicular diffusion. Our coefficient reduces to a power-law in momentum for low momenta (of index $α$), but becomes independent of the particle momentum at high momenta (reaching a constant value $κ_{\infty}$ above some characteristic momentum $p_{\rm c}$). We first provide simple analytical expressions of the maximum momentum that can be reached at a given time with this coefficient. Then we perform time-dependent numerical simulations to investigate the shape of the particle distribution that can be obtained when the particle pressure back-reacts on the flow. We observe that, for a given index $α$ and injection level, the shock modifications are similar for different possible values of $p_{\rm c}$, whereas the particle spectra differ markedly. Of particular interest, low values of $p_{\rm c}$ tend to remove the concavity once thought to be typical of non-linear DSA, and result in steep spectra, as required by recent high-energy observations of Galactic SNRs.

astro-ph.HE↗

arXiv2012

Theoretical Explanation of the Cosmic Ray Perpendicular Diffusion Coefficient in the Nearby Starburst Galaxy NGC 253

Diffusion coefficients are usually used to describe the propagation of Cosmic Rays through the Universe. Whereas such transport parameters can be obtained from experiments in the Solar System, it is difficult to determine diffusion coefficients in the Milky Way or in external galaxies. Recently a value for the perpendicular diffusion coefficient in the nearby starburst halaxy NGC 253 has been proposed. In the present paper we reproduce this value theoretically by using an advanced analytical theory for perpendicular diffusion.

astro-ph.GA↗