Regimes of cosmic-ray diffusion in Galactic turbulence

Cosmic-ray transport in astrophysical environments is often dominated by the diffusion of particles in a magnetic field composed of both a turbulent and a mean component. This process, which is two-fold turbulent mixing in that the particle motion is stochastic with respect to the field lines, needs to be understood in order to properly model cosmic-ray signatures. One of the most important aspects in the modeling of cosmic-ray diffusion is that fully resonant scattering, the most effective such process, is only possible if the wave spectrum covers the entire range of propagation angles. By taking the wave spectrum boundaries into account, we quantify cosmic-ray diffusion parallel and perpendicular to the guide field direction at turbulence levels above 5% of the total magnetic field. We apply our results of the parallel and perpendicular diffusion coefficient to the Milky Way. We show that simple purely diffusive transport is in conflict with observations of the inner Galaxy, but that just by taking a Galactic wind into account, data can be matched in the central 5 kpc zone. Further comparison shows that the outer Galaxy at $$>5$$ > 5 kpc, on the other hand, should be dominated by perpendicular diffusion, likely changing to parallel diffusion at the outermost radii of the Milky Way.

Perpendicular Diffusion of Energetic Particles: A Complete Analytical Theory

Over the past two decades scientists have significantly improved our understanding of the transport of energetic particles across a mean magnetic field. Due to test-particle simulations, as well as powerful nonlinear analytical tools, our understanding of this type of transport is almost complete. However, previously developed nonlinear 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 nonlinear transport theory, the most advanced theory to date, in the limit of small Kubo number turbulence. New results have been obtained for two-dimensional turbulence. In this case, the new theory describes perpendicular diffusion as a process that 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 that 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.

On the Turbulent Reduction of Drifts for Solar Energetic Particles

Particle drifts perpendicular to the background magnetic field have been proposed by some authors as an explanation for the very efficient perpendicular transport of solar energetic particles (SEPs). This process, however, competes with perpendicular diffusion caused by magnetic turbulence, which can also disrupt the drift patterns and reduce the magnitude of drift effects. The latter phenomenon is well known in cosmic-ray studies, but not yet considered in SEP models. Additionally, SEP models that do not include drifts, especially for electrons, use turbulent drift reduction as a justification of this omission, without critically evaluating or testing this assumption. This article presents the first theoretical step for a theory of drift suppression in SEP transport. This is done by deriving the turbulence-dependent drift reduction function with a pitch-angle dependence, as is applicable for anisotropic particle distributions, and by investigating to what extent drifts will be reduced in the inner heliosphere for realistic turbulence conditions and different pitch-angle dependencies of the perpendicular diffusion coefficient. The influence of the derived turbulent drift reduction factors on the transport of SEPs are tested, using a state-of-the-art SEP transport code, for several expressions of theoretically derived perpendicular diffusion coefficients. It is found, for realistic turbulence conditions in the inner heliosphere, that cross-field diffusion will have the largest influence on the perpendicular transport of SEPs, as opposed to particle drifts.

Effect of Light Irradiation on the Diffusion Rate of the Charge Carrier Hopping Mechanism in P3HT–ZnO Nanoparticles Studied by μ+SR

Blended regio-regular P3HT–ZnO nanoparticles are a hybrid material developed as an active layer for hybrid solar cells. The study of the hopping mechanisms and diffusion rates of regio-regular P3HT–ZnO nanoparticles is significant for obtaining intrinsic charge transport properties that provide helpful information for preparing high-performance solar cells. The temperature dependences of the parallel and perpendicular diffusion rates in regio-regular P3HT–ZnO nanoparticles determined from muon spin relaxation measurements were investigated by applying various longitudinal fields. We investigated the effect of light irradiation on the diffusion rates in regio-regular P3HT–ZnO nanoparticles. We found that with increasing temperature, the parallel diffusion rate decreased, while the perpendicular diffusion rate increased. The ratio of the parallel to perpendicular diffusion rate (D‖/D⊥) can be used to indicate the dominant charge carrier hopping mechanism. Without light irradiation, perpendicular diffusion dominates the charge carrier hopping, starting at 25 K, with a ratio of 1.70×104, whereas with light irradiation, the perpendicular diffusion of the charge carrier starts to dominate at the temperature of 10 K, with a ratio of 2.40×104. It is indicated that the additional energy from light irradiation affects the diffusion, especially the charge diffusion in the perpendicular direction.

Diffusion of High-Temperature and High-Pressure CH4 Gas in SiO2 Nanochannels

Fundamental understandings of nanoconfined methane (CH4) are crucial to improving the exploitation of tight gas. In this study, diffusivity, one of the key transport properties of high-temperature and high-pressure methane gas, is examined under confinement in the silica nanochannels by using molecular dynamics simulations by employing Einstein diffusion equation. It was found that the diffusivity of nanoconfined methane is obviously anisotropic, namely, the perpendicular diffusion coefficient is lower than that in the longitudinal direction. The anisotropic diffusivity of nanoconfined methane is attributed to the restricted effect of potential interactions from the atoms of walls, which is verified by analyzing the diffusivity of methane molecules in the potential wells with Lagrangian dynamics. The diffusion coefficients of nanoconfined methane decrease with the increase of atomic potentials in the wall, which can be explained by the density distributions of methane in the nanochannels. Furthermore, we reveal the dependence of the diffusivity of nanoconfined methane on the channel height and confining effect of the wall on the diffusivity of methane molecules. The obtained results can provide a molecular insight into the transport properties of methane confined in nanospace and a theoretical guidance for the efficient extraction of tight gas.

Study on the Diffusion Rate of the Charge Carrier Transport in Regio-Random and Regio-Regular P3HT

Muon spin relaxation experiment has been conducted to probe the hopping mechanism in the poly(3-hexylthiophene-2,5-diyl) (P3HT) for both types of regio-random (Rdm) and regio-regular (RR). In this study we have performed calculations over the collected data to obtain the parallel and perpendicular diffusion rates, at temperatures of 10 K and 300 K. The calculation is based on the fitting method to the empirical function that relates the relaxation rate with the diffusion rates. For Rdm-P3HT, we have obtained the parallel diffusion rate to be 5.43 x 1013 rad/s at 300 K and 4.90 x 1014 rad/s at 10 K. While the perpendicular diffusion rates are 5.29 x 108 rad/s at 300 K and 1.88 x 106 rad/s at 10 K. For RR-P3HT, we have obtained the parallel diffusion rate to be 1.04 x 1014 rad/s at 300 K and 1.28 x 1015 rad/s at 10 K. While the perpendicular diffusion rates are 6.10 x 108 rad/s at 300 K and 5.35 x 105 at 10 K. The diffusion rates of RR-P3HT are higher than that of Rdm-P3HT, especially in the parallel direction. In both types of material, the parallel diffusion rate decreased with temperature, while the perpendicular diffusion rate increased with temperature, showing a change of behavior from 1D to 3D direction of charge transport.

Numerical simulation and data analysis of the 23 July 2012 SEP event observed by ACE, STEREO-A, and STEREO-B

An extremely powerful, superfast interplanetary coronal mass ejection (ICME) from the Sun on 23 July 2012 was detected by widely separated multiple spacecraft, namely STEREO-A, STEREO-B, and ACE, together with the ICME-driven shock and associated solar energetic particles (SEPs). We use the Parker spiral magnetic field model to analyze the relationship between the propagation of the shock and the SEP flux. Furthermore, we simulate the SEP event by numerically solving the three-dimensional focused transport equation of SEPs considering the shock as the moving source of energetic particles. To deal with the fact that protons and electrons behave completely differently for both parallel and perpendicular diffusion, for simplicity, we use the same diffusion model format for the simulations of protons and electrons but with different parameters. We find that the analysis can qualitatively explain the important features of the SEP flux observed by the multiple spacecraft simultaneously. In addition, the numerical results for both energetic protons and electrons approximately agree with multi-spacecraft observations.