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.
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…
We present a study of the acceleration of electrons at a perpendicular shock that propagates through a turbulent magnetic field. The energization process of electrons is investigated by utilizing a combination of hybrid (kinetic ions and fluid electron) simulations and test-particle electron simulations. In this method, the motions of the test-particle electrons are numerically integrated in the time-dependent electric and magnetic fields generated by two-dimensional hybrid simulations. We show that large-scale magnetic fluctuations effect electrons in a number of ways and lead to efficient an…
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 ar…
In some solar energetic particle (SEP) events, a counter-streaming particle beam with a deep depression of flux near 90 degrees pitch angle during the beginning phase is observed. Two different interpretations exist in the community to explain this interesting phenomenon. One explanation invokes the hypothesis of an outer reflecting boundary or a magnetic mirror beyond the observer. The other one considers the effect of the perpendicular diffusion on the transport process of SEPs in the interplanetary space. In this work, we revisit the problem of the counter-streaming particle beams observed …
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 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…
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…
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 …
The processes responsible for the effective longitudinal transport of solar energetic particles (SEPs) are still not completely understood. We address this issue by simulating SEP electron propagation using a spatially 2D transport model that includes perpendicular diffusion. By implementing, as far as possible, the most reasonable estimates of the transport (diffusion) coefficients, we compare our results, in a qualitative manner, to recent observations {at energies of 55 -- 105 keV}, focusing on the longitudinal distribution of the peak intensity, the maximum anisotropy and the onset time. B…
Drifts are known to play a role in galactic cosmic ray transport within the heliosphere and are a standard component of cosmic ray propagation models. However, the current paradigm of Solar Energetic Particle (SEP) propagation holds the effects of drifts to be negligible, and they are not accounted for in most current SEP modelling efforts. We present full-orbit test particle simulations of SEP propagation in a Parker spiral interplanetary magnetic field which demonstrate that high energy particle drifts cause significant asymmetric propagation perpendicular to the interplanetary magnetic fiel…
In this work, a gradual solar energetic particle (SEP) event observed by multispacecraft has been simulated. The time profiles of SEP fluxes accelerated by an interplanetary shock in the three-dimensional interplanetary space are obtained by solving numerically the Fokker-Planck focused transport equation. The interplanetary shock is modeled as a moving source of energetic particles. By fitting the 1979/03/01 SEP fluxes observed by Helios 1, Helios 2, and IMP 8 with our simulations, we obtain the best parameters for the shock acceleration efficiency model. And we also find that the particle pe…
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 …
Observations and modelling suggest that the fluctuations in magnetised plasmas exhibit scale-dependent anisotropy, with more energy in the fluctuations perpendicular to the mean magnetic field than in the parallel fluctuations and the anisotropy increasing at smaller scales. The scale-dependence of the anisotropy has not been studied in full-orbit simulations of particle transport in turbulent plasmas so far. In this paper, we construct a model of critically balanced turbulence, as suggested by \cite{GoSr1995}, and calculate energetic particle spatial diffusion coefficients using full-orbit si…
This paper investigates the conditions for producing rapid variations of solar ener- getic particle (SEP) intensity commonly known as dropouts. In particular, we use numerical model simulations based on solving the focused transport equation in the 3-dimensional Parker interplanetary magnetic field to put constraints on the proper- ties of particle transport coefficients both in the direction perpendicular and parallel to the magnetic field. To simulate the effect of field lines that may alternatively connect and disconnect an observer from a compact SEP source on the solar surface, we place s…
We investigate multi-spacecraft observations of the January 17, 2010 solar energetic particle event. Energetic electrons and protons have been observed over a remarkable large longitudinal range at the two STEREO spacecraft and SOHO suggesting a longitudinal spread of nearly 360 degrees at 1AU. The flaring active region, which was on the backside of the Sun as seen from Earth, was separated by more than 100 degrees in longitude from the magnetic footpoints of each of the three spacecraft. The event is characterized by strongly delayed energetic particle onsets with respect to the flare and onl…
We study the physics of electron acceleration at collisionless shocks that move through a plasma containing large-scale magnetic fluctuations. We numerically integrate the trajectories of a large number of electrons, which are treated as test particles moving in the time dependent electric and magnetic fields determined from 2-D hybrid simulations (kinetic ions, fluid electron). The large-scale magnetic fluctuations effect the electrons in a number of ways and lead to efficient and rapid energization at the shock front. Since the electrons mainly follow along magnetic lines of force, the large…
We analyzed properties of waves excited by mildly relativistic electron beams propagating along magnetic field with a ring-shape perpendicular momentum distribution in neutral and current-free solar coronal plasmas. These plasmas are subject to both the beam and the electron cyclotron maser (ECM) instabilities driven by the positive momentum gradient of the ring-beam electron distribution in the directions parallel and perpendicular to the ambient magnetic field, respectively. To explore the related kinetic processes self-consistently, 2.5-dimensional fully kinetic particle-in-cell (PIC) simul…
This paper investigates the onset time of Solar Energetic Particle (SEP) events with numerical simulations, and analyses the accuracy of the Velocity Dispersion Analysis (VDA) method. Using a 3-dimensional focused transport model, we calculate the fluxes of protons observed in the ecliptic at 1 AU in the energy range between 10 MeV and 80 MeV. In particular, three models are used to describe different SEP sources produced by flare or coronal shock, and the effects of particle perpendicular diffusion in the interplanetary space are also studied. We have the following findings: When the observer…
The trajectories of Solar Energetic Particles (SEPs) in an Interplanetary Magnetic Field (IMF) exhibiting large-scale fluctuations due to footpoint motions originating in the photosphere, are simulated using a full-orbit test-particle code. The cross-field transport experienced by the particles in three propagation conditions (scatter-free, with scattering mean free path lambda=0.3 AU and lambda=2 AU) is characterized in the Parker spiral geometry. The role of expansion of the magnetic field with radial distance from the Sun is taken into consideration in the calculation of particle displaceme…
It has been suggested that the Z-mode instability driven by energetic electrons with a loss-cone type velocity distribution is one candidate process behind the continuum and zebra pattern of solar type-IV radio bursts. Both the temperature of background plasma ($T_0$) and the energy of energetic electrons ($v_e$) are considered to be important to the variation of the maximum growth rate ($γ_{max}$). Here we present a detailed parameter study on the effect of $T_0$ and $v_e$, within a regime of the frequency ratio ($10 \leq \frac{ω_{pe}}{Ω_{ce}} \leq 30$). In addition to $γ_{max}$, we also anal…
Astrophysical reconnection takes place in a turbulent medium. The turbulence in most cases is pre-existing, not caused by the reconnection itself. The model of magnetic reconnection in Lazarian & Vishniac (1999) predicts that in the presence of turbulence the reconnection becomes fast, i.e. it is independent of resistivity, but dependent on the level of turbulence. Magnetic reconnection injects energy into plasmas through a turbulent outflow from the reconnection region and this outflow can enhance the level of turbulence creating bursts of reconnection. Magnetic reconnection in the presence o…
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…
Astrophysical media are turbulent and therefore reconnection should be treated in the presence of pre-existing turbulence. We consider the model of fast magnetic reconnection in Lazarian & Vishniac (1999) which predicts that the rate of reconnection is controlled by the intensity and the injection scale of turbulent motions. We provide new evidence of successful testing of the model and argue that the model presents a generic set up for astrophysical reconnection events. We study particle acceleration that takes place in volumes of driven turbulence as well turbulent volumes in the presence of…
Power-law distributions are a near universal feature of energetic particle spectra in the heliosphere. Anomalous Cosmic Rays (ACRs), super-Alfvénic ions in the solar wind and the hardest energetic electron spectra in flares all have energy fluxes with power-laws that depend on energy $E$ approximately as $E^{-1.5}$. We present a new model of particle acceleration in systems with a bath of merging magnetic islands that self-consistently describes the development of velocity-space anisotropy parallel and perpendicular to the local magnetic field and includes the self-consistent feedback of press…
The capability to predict the parameters of an SEP event such as its onset, peak flux, and duration is critical to assessing any potential space weather impact. We present a new flexible modelling system simulating the propagation of Solar Energetic Particles (SEPs) from locations near the Sun to any given location in the heliosphere to forecast the SEP flux profiles. SPARX uses an innovative methodology, that allows implementation within an operational framework, to overcome the time constraints of test particle modelling of SEP profiles, allowing the production of near real time SEP nowcasts…
Turbulence is ubiquitous in astrophysics. It radically changes many astrophysical phenomena, in particular, the propagation and acceleration of cosmic rays. We present the modern understanding of compressible magnetohydrodynamic (MHD) turbulence, in particular its decomposition into Alfvén, slow and fast modes, discuss the density structure of turbulent subsonic and supersonic media, as well as other relevant regimes of astrophysical turbulence. All this information is essential for understanding the energetic particle acceleration that we discuss further in the review. For instance, we show h…
The influence of adiabatic focusing on particle diffusion is an important topic in astrophysics and plasma physics. In the past several authors have explored the influence of along-field adiabatic focusing on parallel diffusion of charged energetic particles. In this paper by using the Unified NonLinear Transport (UNLT) theory developed by Shalchi (SH2010) and the method of He and Schlickeiser (HS2014) we derive a new nonlinear perpendicular diffusion coefficient for non-uniform background magnetic field. This formula demonstrates that particle perpendicular diffusion coefficient is modified b…
After introduction we focus on: the transport of charged particles, the acceleration of ions at shocks, and the acceleration of electrons at shocks. Chapter 2 studies the propagation of solar energetic particles(SEPs) in turbulent magnetic fields. Particle trajectories in turbulent magnetic fields are numerically integrated. The turbulence includes a Kolmogorov-like power spectrum containing a broad range of scales. Small-scale variations in particle intensities(dropouts) and velocity dispersions can be reproduced. The result gives a constraint on the error of onset analysis for inferring SEP …
Strong gradients in plasma flows play a major role in space and astrophysical plasmas. A typical situation is that a static plasma equilibrium is surrounded by a plasma flow, which can lead to strong plasma flow gradients at the separatrices between field lines with different magnetic topologies, e.g., planetary magnetospheres, helmet streamers in the solar corona, or at the boundary between the heliosphere and interstellar medium. Within this work we make a first step to understand the influence of these flows towards the occurrence of current sheets in a stationary state situation. We concen…
We investigate the spatial distribution of charged particles accelerated by non-relativistic oblique fast collisionless shocks using three-dimensional test-particle simulations. We find that the density of low-energy particles exhibit a localised enhancement at the shock, resembling the "spike" measured at interplanetary shocks. In contrast to previous results based on numerical solutions to the focused transport equation, we find a shock spike for any magnetic obliquity, from quasi-perpendicular to parallel. We compare the pitch-angle distribution with respect to the local magnetic field and …
Solar energetic particles (SEPs) affect the solar-terrestrial space environment and become a very important aspect in space weather research. In this work, we numerically investigate the transport processes of SEPs in three-dimensional interplanetary magnetic field, with an emphasis on the longitudinal distribution of SEPs in the heliosphere. We confirm our previous finding that there exists an east-west longitudinal asymmetry in the SEP intensities, i.e., with the same longitude separations between the solar source centers and the magnetic footpoint of the observer, the fluxes of SEP events o…
The spatial and temporal invariance in the spectra of energetic particles in the gradual solar events is reproduced in the simulations. Based on a numerical solution of the focused transport equation, we obtain the intensity time profiles of solar energetic particles (SEPs) accelerated by an interplanetary shock in the three-dimensional interplanetary space. The shock is treated as a moving source of energetic particles with a distribution function. The time profiles of particle flux with different energies are calculated in the ecliptic at $1$ AU. According to our model, we find that shock ac…
The physical evolution of Young Stellar Objects (YSOs) is accompanied by an enrichment of the molecular complexity, mainly triggered by the heating and energetic processing of the astrophysical ices. In this paper, a study of how the ice column density varies across the protostellar evolution has been performed. Tabulated data of H$_2$O, CO$_2$, CH$_3$OH, HCOOH observed by ground- and space-based telescopes toward 27 early-stage YSOs were taken from the literature. The observational data shows that ice column density and spectral index ($α$), used to classify the evolutionary stage, are well c…
Multi-spacecraft constraints on relativistic solar energetic particle transport in the widespread 28 October 2021 event
National & Kapodistrian University of Athens（雅典国立卡波迪斯特里安大学）；Institute for the Management of Information Systems, "Athena" Research Center（雅典研究中心信息管理研究所）；Institute for Astronomy, Astrophysics, Space Applications and Remote Sensing (IAASARS), National Observatory of Athens（雅典国家天文台天文学、天体物理学、空间应用和遥感研究所）；Space Research Laboratory, University of Turku（图尔库大学空间研究实验室）；Centre for Space Research, North-West University（西北大学空间研究中心）；National Institute for Theoretical and Computational Sciences (NITheCS)（国家理论与计算科学研究所）；The Johns Hopkins University Applied Physics Laboratory（约翰斯·霍普金斯大学应用物理实验室）
While a growing body of research indicates that relativistic magnetic reconnection is a prodigious source of particle acceleration in high-energy astrophysical systems, the dominant acceleration mechanism remains controversial. Using a combination of fully kinetic simulations and theoretical analysis, we demonstrate that Fermi-type acceleration within the large-scale motional electric fields dominates over direct acceleration from non-ideal electric fields within small-scale diffusion regions. This result has profound implications for modeling particle acceleration in large-scale astrophysical…
Shock acceleration is considered one of the most important mechanisms for the acceleration of astrophysical energetic particles. In this work, we calculate the trajectories of a large number of test charged particles accurately in a parallel shock with magnetic turbulence. We investigate the time evolution of the accelerated-particle energy spectrum in the downstream of the shock in order to understand the acceleration mechanism of energetic particles. From simulation results we obtain power-law energy spectra with a bend-over energy, $E_0$, increasing with time. With the particle mean acceler…
Magnetic reconnection is an important driver of energetic particles in many astrophysical phenomena. Using kinetic particle-in-cell (PIC) simulations, we explore the impact of three-dimensional reconnection dynamics on the efficiency of particle acceleration. In two-dimensional systems, Alfvénic outflows expel energetic electrons into flux ropes where they become trapped and disconnected from acceleration regions. However, in three-dimensional systems these flux ropes develop axial structure that enables particles to leak out and return to acceleration regions. This requires a finite guide fie…
Particle acceleration in stellar flares is ubiquitous in the Universe, however, our Sun is the only astrophysical object where energetic particles and their source flares can both be observed. The acceleration mechanism in solar flares, tremendously enhancing (up to a factor of ten thousand) rare elements like 3He and ultra-heavy nuclei, has been puzzling for almost 50 years. Here we present some of the most intense 3He- and Fe-rich solar energetic particle events ever reported. The events were accompanied by non-relativistic electron events and type III radio bursts. The corresponding high-re…
