In the full-orbit particle simulations of energetic particle transport in plasmas, the plasma turbulence is typically described as a homogeneous superposition of linear Fourier modes. The turbulence evolution is, however, typically a nonlinear process, and, particularly in the heliospheric context, the solar wind plasma is inhomogeneous due to the transient structures, as observed by remote and in-situ measurements. In this work, we study the effects of the inhomogeneities on energetic particle transport by using spatially distributed, superposed turbulence envelopes. We find that the cross-field transport is significantly reduced, when compared to the results obtained with homogeneous turbulence. The reduction can reach an order of magnitude when the enveloping breaks the wave phase coherence along the mean magnetic field direction.
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 perfo…
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…
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…
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…
The topic of this review paper is on the influence of solar wind turbulence on shock propagation and its consequence on the acceleration and transport of energetic particles at shocks. As the interplanetary shocks sweep through the turbulent solar wind, the shock surfaces fluctuate and ripple in a range of different scales. We discuss particle acceleration at rippled shocks in the presence of ambient solar-wind turbulence. This strongly affects particle acceleration and transport of energetic particles (both ions and electrons) at shock fronts. In particular, we point out that the effects of u…
Insights into the processes of Solar Energetic Particle (SEP) propagation are essential for understanding how solar eruptions affect the radiation environment of near-Earth space. SEP propagation is influenced by turbulent magnetic fields in the solar wind, resulting in stochastic transport of SEPs to Earth. Multi-spacecraft observations suggest that the cross-field propagation shapes the SEP fluxes at Earth strongly. However, modelling SEP cross-field transport as spatial diffusion has been shown to be insufficient without use of unrealistically large cross-field diffusion coefficients. Recen…
Energetic particles spectra at interplanetary shocks often exhibit a power law within a narrow momentum range softening at higher energy. We introduce a transport equation accounting for particle acceleration and escape with diffusion contributed by self-generated turbulence close to the shock and by pre-existing turbulence far upstream. The upstream particle intensity steepens within one diffusion length from the shock as compared with diffusive shock acceleration rollover. The momentum spectrum, controlled by macroscopic parameters such as shock compression, speed, far upstream diffusion coe…
Propagation of energetic particles across the mean field direction in turbulent magnetic fields is often described as spatial diffusion. Recently, it has been suggested that initially the particles propagate systematically along meandering field lines, and only later reach the time-asymptotic diffusive cross-field propagation. In this paper, we analyse cross-field propagation of 1--100 MeV protons in composite 2D-slab turbulence superposed on a constant background magnetic field, using full-orbit particle simulations, to study the non-diffusive phase of particle propagation with a wide range o…
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…
Acceleration of Energetic Particles through Reconnection of Weakly Stochastic Magnetic Field
天体物理介质是湍流的，因此重联应该在存在预先存在的湍流的情况下进行处理。我们考虑Lazarian & Vishniac（1999）的快速磁重联模型，该模型预言重联速率受湍流运动的强度和注入尺度的控制。我们提供了新的证据，成功的测试模型，并认为该模型提出了一个通用的设置为天体物理重联事件。我们研究粒子加速，发生在体积的驱动湍流以及湍流体积中存在的大规模重联。我们证明，在后一种情况下，加速度是一阶费米型，从而支持Gouveia dal Pino和Lazarian（2005）提出的加速度模型。
Effects of Turbulent Magnetic Fields on the Transport and Acceleration of Energetic Charged Particles: Numerical Simulations with Application to Heliospheric Physics
Planets in close proximity to their parent star, such as those in the habitable zones around M dwarfs, could be subject to particularly high doses of particle radiation. We have carried out test-particle simulations of ~GeV protons to investigate the propagation of energetic particles accelerated by flares or travelling shock waves within the stellar wind and magnetic field of a TRAPPIST-1-like system. Turbulence was simulated with small-scale magnetostatic perturbations with an isotropic power spectrum. We find that only a few percent of particles injected within half a stellar radius from th…
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…
Solar energetic particles acceleration by a shock wave accompanying a coronal mass ejection (CME) is studied. The description of the accelerated particle spectrum evolution is based on the numerical calculation of the diffusive transport equation with a set of realistic parameters. The relation between the CME and the shock speeds, which depend on the initial CME radius, is determined. Depending on the initial CME radius, its speed, and the magnetic energy of the scattering Alfven waves, the accelerated particle spectrum is established during 10-60 minutes from the beginning of CME motion. The…
The concept of energetic particle reservoirs, essentially based on the assumption of the presence of outer reflecting boundaries/magnetic mirrors or diffusion barriers (deterministic) rather than on the effect of particle diffusive propagation (stochastic) in magnetic turbulence, has been used for decades to describe the space-extended decay phases of energetic particle events within the fields of space physics, solar physics, and plasma physics. Using five-dimensional time-dependent Fokker-Planck transport equation simulations, in this work we demonstrate that the so-called particle reservoir…
Current particle transport models describe the propagation of charged particles across the mean field direction in turbulent plasmas as diffusion. However, recent studies suggest that at short time-scales, such as soon after solar energetic particle (SEP) injection, particles remain on turbulently meandering field lines, which results in non-diffusive initial propagation across the mean magnetic field. In this work, we use a new technique to investigate how the particles are displaced from their original field lines, and quantify the parameters of the transition from field-aligned particle pro…
Enhancement of minor ions such as $^3$He and heavy ions in flare-associated solar energetic particle (SEP) events remains one of the major puzzles in heliophysics. In this work, we use 3D hybrid simulations (kinetic protons and fluid electrons) to investigate particle energization in a turbulent low-beta environment similar to solar flares. It is shown that in this regime the injected large-amplitude Alfvén waves develop into compressible and anisotropic turbulence, which efficiently heats thermal ions of different species. We find that temperature increase of heavy ions is inversely proportio…
Context. Current solar energetic particle (SEP) propagation models describe the effects of interplanetary plasma turbulence on SEPs as diffusion, using a Fokker-Planck (FP) equation. However, FP models cannot explain the observed fast access of SEPs across the average magnetic field to regions that are widely separated in longitude within the heliosphere without using unrealistically strong cross-field diffusion. Aims. We study whether the recently suggested early non-diffusive phase of SEP propagation can explain the wide SEP events with realistic particle transport parameters. Methods. We us…
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 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 …
We present the implementation of turbulence transport equations in addition to the Reynolds-averaged MHD equations within the Cronos framework. The model is validated by comparisons with earlier findings before it is extended to be applicable to regions in the solar wind that are not highly super-Alfvénic. We find that the respective additional terms result in absolute normalized cross-helicity to decline more slowly, while a proper implementation of the mixing terms can even lead to increased cross-helicities in the inner heliosphere. The model extension allows to place the inner boundary of …
Magnetic reconnection has been suggested to play an important role in the dynamics and energetics of plasma turbulence by spacecraft observations, simulations and theory over the past two decades, and recently, by magnetosheath observations of MMS. A new method based on magnetic flux transport (MFT) has been developed to identify reconnection activity in turbulent plasmas. This method is applied to a gyrokinetic simulation of two-dimensional (2D) plasma turbulence. Results on the identification of three active reconnection X-points are reported. The first two X-points have developed bi-directi…
Energetic particles accelerated via turbulent magnetic reconnection in protoplanetary discs -- I. Ionisation rates
INAF-Osservatorio Astrofisico di Arcetri（意大利国家天体物理研究所阿切特里天文台）；SETI Institute（SETI研究所）；IAPS, INAF（罗马国际天体物理学研究所，意大利国家天体物理研究所）；Laboratoire Univers et Particules de Montpellier, Université de Montpellier/CNRS（蒙彼利埃宇宙与粒子实验室，蒙彼利埃大学/法国国家科学研究中心）；University Observatory, Faculty of Physics, Ludwig-Maximilians-Universität München（慕尼黑大学物理学院大学天文台）；Max-Planck-Institut für extraterrestrische Physik（马克斯·普朗克地外物理学研究所）；Laboratoire d’étude de l’Univers et des phénomènes eXtrêmes, Observatoire de Paris, Université PSL, CNRS（极端宇宙现象研究实验室，巴黎天文台，巴黎文理研究大学/法国国家科学研究中心）
Plasma turbulence occurs ubiquitously in space and astrophysical plasmas, mediating the nonlinear transfer of energy from large-scale electromagnetic fields and plasma flows to small scales at which the energy may be ultimately converted to plasma heat. But plasma turbulence also generically leads to a tangling of the magnetic field that threads through the plasma. The resulting wander of the magnetic field lines may significantly impact a number of important physical processes, including the propagation of cosmic rays and energetic particles, confinement in magnetic fusion devices, and the fu…
