It is very important to understand stochastic diffusion of energetic charged particles in non-uniform background magnetic field in plasmas of astrophysics and fusion devices. Using different methods considering along-field adiabatic focusing effect, various authors derived parallel diffusion coefficient $κ_\parallel$ and its correction $T$ to $κ_{\parallel 0}$, where $κ_{\parallel 0}$ is the parallel diffusion coefficient without adiabatic focusing effect. In this paper, using the improved perturbation method developed by He \& Schlickeiser and iteration process, we obtain a new correction $T'$ to $κ_{\parallel 0}$. Furthermore, by employing the isotropic pitch-angle scattering model $D_{μμ}=D(1-μ^2)$, we find that $T'$ has the different sign as that of $T$. In this paper the spatial perpendicular diffusion coefficient $κ_\bot$ with the adiabatic focusing effect is also obtained.
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.
The turbulence and spatial nonuniformity of the guide magnetic field cause two competitive effects, namely, the scattering effect and the adiabatic focusing effect, respectively. In this work, we numerically solve the five-dimensional Fokker-Planck transport equation to investigate the radial evolutions of these important effects undergone by the solar energetic particles (SEPs) propagating through interplanetary space. We analyze the interplay process between the scattering and adiabatic focusing effects in the context of three-dimensional propagation, with special attention to the scenario o…
The transport of energetic charged particles (e.g., cosmic rays) in turbulent magnetic fields is usually characterized in terms of the diffusion parallel and perpendicular to a large-scale (or mean) magnetic field. The nonlinear guiding center theory (NLGC) has been a prominent perpendicular diffusion theory. A recent version of this theory, based on random ballistic spreading of magnetic field lines and a backtracking correction (RBD/BC), has shown good agreement with test particle simulations for a two-component magnetic turbulence model. The aim of the present study is to test the generalit…
The multitude of recent multi-point spacecraft observations of solar energetic particle (SEP) events have made it possible to study the longitudinal distribution of SEPs in great detail. SEPs, even those accelerated during impulsive events, show a much wider than expected longitudinal extent, bringing into question the processes responsible for their transport perpendicular to the local magnetic field. In this paper we examine some aspects of perpendicular transport by including perpendicular diffusion into a numerical SEP transport model that simulates the propagation of impulsively accelerat…
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 Mark…
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 transpo…
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 efficiency of drift effects. The latter phenomenon is well known in cosmic ray studies, but not yet considered in SEP models. Additionally, SEP models which do not include drifts, especially for electrons, use turbulent drift reduction as a justificat…
The Diffusion Approximation vs. the Telegraph Equation for Modeling Solar Energetic Particle Transport with Adiabatic Focusing. I. Isotropic Pitch-angle Scattering
Based on Magnetospheric Multiscale (MMS) observations from the Earth's bow shock, we have identified two plasma heating processes that operate at quasi-perpendicular shocks. Ions are subject to stochastic heating in a process controlled by the heating function $χ_j = m_j q_j^{-1} B^{-2}\mathrm{div}(\mathbf{E}_\perp)$ for particles with mass $m_j$ and charge $q_j$ in the electric and magnetic fields $\mathbf{E}$ and $\mathbf{B}$. Test particle simulations are employed to identify the parameter ranges for bulk heating and stochastic acceleration of particles in the tail of the distribution funct…
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…
Recent modelling of solar energetic particles (SEPs) propagation through the heliospheric turbulence, also discussed in this workshop, has investigated the role of the pitch-angle scattering and the perpendicular transport in spreading particles in heliolongitude, as shown by multi-spacecraft measurements (STEREO A/B, ACE, SOHO, etc.) at 1 AU in various energy ranges. In some events the first-order pitch-angle anisotropy of the particles distribution is not-negligible. We calculate the average perpendicular displacement due to the gradient/curvature drift in an inhomogeneous turbulence account…
Interplanetary Coronal Mass Ejection (ICME) shocks are known to accelerate particles and contribute significantly to Solar Energetic Particle (SEP) events. We have performed Magnetohydrodynamic-Particle in Cell (MHD-PIC) simulations of ICME shocks to understand the acceleration mechanism. These shocks vary in Alfvénic Mach numbers as well as in magnetic field orientations (parallel \& quasi-perpendicular). We find that Diffusive Shock Acceleration (DSA) plays a significant role in accelerating particles in a parallel ICME shock. In contrast, Shock Drift Acceleration (SDA) plays a pivotal role …
A complete theory for the complex interaction between solar energetic particles and the turbulent interplanetary magnetic field remains elusive. In this work we aim to contribute towards such a theory by modelling the propagation of solar energetic particle electrons in plasma wave turbulence. We specify a background turbulence spectrum, as constrained through observations, calculate the transport coefficients from first principles, and simulate the propagation of these electrons in the inner heliosphere. We have also, for the first time, included dynamical effects into the perpendicular diffu…
Using the field-particle correlation technique, we examine the particle energization in a 1D-2V continuum Vlasov--Maxwell simulation of a perpendicular magnetized collisionless shock. The combination of the field-particle correlation technique with the high fidelity representation of the particle distribution function provided by a direct discretization of the Vlasov equation allows us to ascertain the details of the exchange of energy between the electromagnetic fields and the particles in phase space. We identify the velocity-space signatures of shock-drift acceleration of the ions and adiab…
Effects of Turbulent Magnetic Fields on the Transport and Acceleration of Energetic Charged Particles: Numerical Simulations with Application to Heliospheric Physics
Collisionless shocks play an important role in space and astrophysical plasmas by irreversibly converting the energy of the incoming supersonic plasma flows into other forms, including plasma heat, particle acceleration, and electromagnetic field energy. Here we present the application of the field-particle correlation technique to an idealized perpendicular magnetized collisionless shock to understand the transfer of energy from the incoming flow into ion and electron energy through the structure of the shock. The connection between a Lagrangian perspective following particle trajectories, an…
