We present a 2D kinematic model to study the acceleration of solar energetic particles (SEPs) at a shock driven by a coronal mass ejection. The shock is assumed to be spherical about an origin that is offset from the center of the Sun. This leads to a spatial and temporal evolution of the angle between the magnetic field and shock normal direction ($θ_{Bn}$) as it propagates through the Parker spiral magnetic field from the lower corona to 1 AU. We find that the high-energy SEP intensity varies significantly along the shock front due to the evolution of $θ_{Bn}$. Generally, the west flank of the shock preferentially accelerates particles to high energies compared to the east flank and shock nose. This can be understood in terms of the rate of acceleration, which is higher at the west flank. Double power-law energy spectra are reproduced in our model as a consequence of the local acceleration and transport effects. These results will help better understand the evolution of SEP acceleration and provide new insights into large SEP events observed by multi-spacecraft, especially those close to the Sun, such as Parker Solar Probe and Solar Orbiter.
The pickup protons originate as a result of the ionization of hydrogen atoms in the supersonic solar wind, forming the suprathermal component of protons in the heliosphere. While picked by the heliospheric magnetic field and convected into the heliosheath, the pickup protons may suffer the stochastic acceleration by the solar wind turbulence in the region from the Sun up to the heliospheric termination shock, where they can also experience the shock-drift acceleration or the reflection from the cross-shock potential. These processes create a high-energy "tail" in the pickup ion energy distribu…
We revisit the full variety of observed temporal and spatial distributions of energetic solar protons in "gradual" solar energetic-particle (SEP) events resulting from the spatial variations in the shock waves that accelerate them. Differences in the shock strength at the solar longitude of a spacecraft and at the footpoint of its connecting magnetic field line, nominally 55 degrees to the west, drive much of that variation. The shock wave itself, together with energetic particles trapped near it by self-amplified Alfven waves, forms an underlying autonomous structure that can drive across mag…
The acceleration of charged particles by interplanetary shocks can drain a non-negligible fraction of the upstream ram pressure. For a sample of shocks observed in-situ at 1 AU by the ACE and Wind spacecraft, time-series of the non-Maxwellian components (supra-thermal and higher-energy) of the ion and electron energy spectra were acquired for each event. These were averaged for one hour before and after the time of the shock passage to determine their partial pressure. Using the MHD Rankine-Hugoniot jump conditions, we find that the fraction of the total upstream energy flux transferred to non…
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 …
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…
We examine the production of energetic neutral atoms (ENAs) in solar flares and CME-driven shocks and their subsequent propagation to 1 au. Time profiles and fluence spectra of solar ENAs at 1 au are computed for two scenarios: 1) ENAs are produced downstream at CME-driven shocks, and 2) ENAs are produced at large-scale post-flare loops in solar flares. Both the time profiles and fluence spectra for these two scenarios are vastly different. Our calculations indicate that we can use solar ENAs as a new probe to examine the underlying acceleration process of solar energetic particles (SEPs) and …
We study periods of elevated energetic particle intensities observed by STEREO-A when the partial pressure exerted by energetic ($\geq$83 keV) protons ($P_{EP}$) is larger than the pressure exerted by the interplanetary magnetic field ($P_{B}$). In the majority of cases, these periods are associated with the passage of interplanetary shocks. Periods when $P_{EP}$ exceeds $P_{B}$ by more than one order of magnitude are observed in the upstream region of fast interplanetary shocks where depressed magnetic field regions coincide with increases of the energetic particle intensities. When solar win…
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 …
The acceleration of charged particles by interplanetary shocks (IPs) can drain a non-negligible fraction of the plasma pressure. In this study, we have selected 17 IPs observed in-situ at $1\,\text{au}$ by the Advanced Composition Explorer (ACE) and the Wind spacecraft, and 1 shock at $0.8\,\text{au}$ observed by Parker Solar Probe (PSP). We have calculated the time-dependent partial pressure of supra-thermal and energetic particles (smaller and greater than $50\,\text{keV}$ for protons and $30\,\text{keV}$ for electrons, respectively) in both the upstream and downstream regions. The particle …
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…
The latest survey of stellar bow shocks (Peri et al. 2012) lists 28 candidates detected at IR wavelengths, associated with massive, early-type stars up to 3 kpc, along with the geometrical parameters of the structures found. I present here some considerations on the energetics involved, after the estimation of stellar wind power, infrared flux, stellar bolometric luminosity and radio flux limits for each source. The best candidates for relativistic particle acceleration are highlighted.
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…
Energetic particle-mediated interplanetary shocks observed by Solar Orbiter
European Space Agency (ESA), European Space Astronomy Centre (ESAC)（欧洲空间局（ESA），欧洲空间天文中心（ESAC））；Heliospheric Physics Laboratory, Heliophysics Division, NASA Goddard Space Flight Center（NASA戈达德太空飞行中心，日球物理部，日球物理实验室）；Max-Planck-Institut für Kernphysik（马克斯·普朗克核物理研究所）；Johns Hopkins University Applied Physics Laboratory（约翰斯·霍普金斯大学应用物理实验室）；Istituto per la Scienza e Tecnologia dei Plasmi (ISTP), Consiglio Nazionale delle Ricerche（意大利国家研究委员会等离子体科学与技术研究所（ISTP））；Department of Physics and Astronomy, Queen Mary University of London（伦敦大学玛丽女王学院物理与天文学系）；Lunar and Planetary Laboratory, University of Arizona（亚利桑那大学月球与行星实验室）；Institute of Experimental and Applied Physics, Kiel University（基尔大学实验与应用物理研究所）
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…
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…
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…
In-situ spacecraft observations recently suggested that the transport of energetic particles accelerated at heliospheric shocks can be anomalous, i.e. the mean square displacement can grow non-linearly in time. In particular, a new analysis technique has permitted the study of particle transport properties from energetic particle time profiles upstream of interplanetary shocks. Indeed, the time/spatial power laws of the differential intensity upstream of several shocks are indicative of superdiffusion. A complete determination of the key parameters of superdiffusive transport comprises the pow…
A data-driven physics-based transport model of solar energetic particles accelerated by coronal mass ejection shocks propagating through the solar coronal and heliospheric magnetic fields
We have performed 2D hybrid simulations of non-relativistic collisionless shocks in the presence of pre-existing energetic particles ("seeds"); such a study applies, for instance, to the re-acceleration of Galactic cosmic rays (CRs) in supernova remnant (SNR) shocks and solar wind energetic particles in heliospheric shocks. Energetic particles can be effectively reflected and accelerated regardless of shock inclination via a process that we call \emph{diffusive shock re-acceleration}. We find that reaccelerated seeds can drive the streaming instability in the shock upstream and produce effecti…
We present numerical modelling of particle acceleration at coronal shocks propagating through a streamer-like magnetic field by solving the Parker transport equation with spatial diffusion both along and across the magnetic field. We show that the location on the shock where the high-energy particle intensity is the largest, depends on the energy of the particles and on time. The acceleration of particles to more than 100 MeV mainly occurs in the shock-streamer interaction region, due to perpendicular shock geometry and the trapping effect of closed magnetic fields. A comparison of the particl…
We find that element abundances in energetic ions accelerated by shock waves formed at corotating interaction regions (CIRs) mirror the abundances of the solar wind modified by a decreasing power-law dependence on the mass-to-charge ratio A/Q of the ions. This behavior is similar in character to the well-known power-law dependence on A/Q of abundances in large gradual solar energetic particles (SEP). The CIR ions reflect the pattern of A/Q, with Q values of the source plasma temperature or freezing-in temperature of 1.0 - 1.2 MK typical of the fast solar wind in this case. Thus the relative io…
The dearth of observations between 1 au and 3 au limits our understanding of energetic particle acceleration processes in interplanetary space. We present the first-of-their-kind observations of the energetic particle acceleration in a Corotating Interaction Region (CIR) using data from two vantage points, 1 au (near Earth) and 1.5 au (near Mars). The CIR event of June 2015 was observed by the particle detectors aboard the Advanced Composition Explorer (ACE) satellite as well as the SEP (Solar Energetic Particle) instrument aboard the Mars Atmosphere and Volatile EvolutioN (MAVEN) spacecraft s…
Globally-propagating shocks in the solar corona have long been studied to quantify their involvement in the acceleration of energetic particles. However, this work has tended to focus on large events associated with strong solar flares and fast coronal mass ejections (CMEs), where the waves are sufficiently fast to easily accelerate particles to high energies. Here we present observations of particle acceleration associated with a global wave event which occurred on 1 October 2011. Using differential emission measure analysis, the global shock wave was found to be incredibly weak, with an Alfv…
Nonthermal loop-top sources in solar flares are the most prominent observational signature that suggests energy release and particle acceleration in the solar corona. Although several scenarios for particle acceleration have been proposed, the origin of the loop-top sources remains unclear. Here we present a model that combines a large-scale magnetohydrodynamic simulation of a two-ribbon flare with a particle acceleration and transport model for investigating electron acceleration by a fast-mode termination shock at the looptop. Our model provides spatially resolved electron distribution that …
We reexamine the relationship between energy spectral indices and element abundance enhancements in solar energetic particle (SEP) events at energies of a few MeV/amu. We find a correlated behavior only in the largest gradual SEP4 events when all ions are accelerated from the ambient coronal plasma by shock waves driven by fast, wide coronal mass ejections (CMEs). This correlated abundance behavior can track complex time variations in the spectral indices during an event. In other (SEP3) events, CME-driven shock waves, days apart, sample seed particles from a single pool of suprathermal impuls…
The solar eruption on 2012 January 27 resulted in a wide-spread solar energetic particle (SEP) event observed by STEREO A and the near-Earth spacecraft (separated by 108\degree). The event was accompanied by an X-class flare, extreme-ultraviolet (EUV) wave and fast coronal mass ejection (CME). We investigate the particle release by comparing the release times of particles at the spacecraft and the times when magnetic connectivity between the source and the spacecraft was established. The EUV wave propagating to the magnetic footpoint of the spacecraft in the lower corona and the shock expandin…
The author has been fortunate to observe and participate in the rise of the field of solar energetic particles (SEPs), from the early abundance studies, to the contemporary paradigm of shock acceleration in large SEP events, and element abundance enhancements that are power laws in mass-to-charge ratios from H to Pb. Through painful evolution the "birdcage" model and the "solar-flare myth" came and went, leaving us with shock waves and solar jets that can interact as sources of SEPs.
We have developed a simulation model of particle acceleration in coronal shock waves. The model is based on a Monte Carlo method, where particles are traced in prescribed large-scale electromagnetic fields utilizing the guiding center approximation. The particles are scattered in the turbulence according to quasilinear theory, with the scattering amplitude directly proportional to the intensity of Alfvén waves at gyro-resonant wavenumbers. The Alfvén waves are traced simultaneously with the particles, so that the wave field is propagated outwards from the Sun using WKB propagation supplemented…
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 …
Diffusive shock acceleration at collisionless shocks is thought to be the source of many of the energetic particles observed in space. Large-scale spatial variations of the magnetic field has been shown to be important in understanding observations. The effects are complex, so here we consider a simple, illustrative model. Here, we solve numerically the Parker transport equation for a shock in the presence of large-scale sinusoidal magnetic-field variations. We demonstrate that the familiar planar-shock results can be significantly altered as a consequence of large-scale, meandering magnetic l…
Recent observations have shown that in many large solar energetic particle (SEP) events the event-integrated differential spectra resemble double power laws. We perform numerical modeling of particle acceleration at coronal shocks propagating through a streamer-like magnetic field by solving the Parker transport equation, including protons and heavier ions. We find that for all ion species the energy spectra integrated over the simulation domain can be described by a double power law, and the break energy depends on the ion charge-to-mass ratio as $E_B \sim (Q/A)^α$, with $α$ varying from 0.16…
One of the earliest indicators of the importance of shock acceleration of solar energetic particles (SEPs) was the broad spatial extent of the "gradual" SEP events produced as the shock waves, driven by wide, fast coronal mass ejections (CMEs), expand across the Sun with cross-field transport mediated by the shocks. Contrasting "impulsive" SEP events, with characteristic enhancements of 3He and of heavy elements, are now associated with magnetic reconnection on open field lines in solar jets. However, large shock waves can also traverse pools of residual impulsive suprathermal ions and jets ca…
In solar energetic particle (SEP) events, the power-law dependence of element abundance enhancements on their mass-to-charge ratios A/Q provides a new tool that measures the combined rigidity dependences from both acceleration and transport. Distinguishing these two processes can be more challenging. However, the effects of acceleration dominate when SEP events are small or when the ions even propagate scatter-free, and transport can dominate the time evolution of large events with streaming-limited intensities. Magnetic reconnection in solar jets produces positive powers of A/Q from +2 to +7 …
We present the implementation of coupling the EUropean Heliospheric FORcasting Information Asset (EUHFORIA) and the improved Particle Acceleration and Transport in the Heliosphere (iPATH) model and simulate the widespread solar energetic particle (SEP) event of 2020 November 29. We compare the simulated time intensity profiles with measurements at Parker Solar Probe (PSP), the Solar Terrestrial Relations Observatory (STEREO)-A, SOlar and Heliospheric Observatory (SOHO) and Solar Orbiter (SolO). We focus on the influence of the history of shock acceleration on the varying SEP time intensity pro…
Recent observations have shown that coronal shocks driven by coronal mass ejections can develop and accelerate particles within several solar radii in large solar energetic particle (SEP) events. Motivated by this, we present an SEP acceleration study including the process that a fast shock propagates through a streamer-like magnetic field with both closed and open field lines in the low corona region. The acceleration of protons is modeled by numerically solving the Parker transport equation with spatial diffusion both along and across the magnetic field. We show that particles can be suffici…
This paper presents a stochastic three-dimensional (3D) focused transport simulation of solar energetic particles (SEPs) produced by a data-driven coronal mass ejection (CME) shock propagating through a data-driven model of coronal and heliospheric magnetic fields. The injection of SEPs at the CME shock is treated using diffusive shock acceleration of post-shock superthermal solar wind ions. A time backward stochastic simulation is employed to solve the transport equation to obtain the SEP time-intensity profile at any location, energy, and pitch angle. The model is applied to a SEP event on 2…
Solar Energetic Particle (SEP) acceleration and injection into interplanetary space during gradual SEP events is thought to take place at Coronal Mass Ejection (CME)-driven shocks. Features of measured intensity profiles at 1 au have been attributed to properties of the radial and longitudinal/latitudinal injections at the shock. Focussed transport models are typically used to model acceleration at a CME-shock and subsequent propagation. Test particle simulations are an alternative approach but so far they have been carried out only with instantaneous injection near the Sun. We develop the fir…
Shock properties for solar energetic particle events with signatures of inverse velocity arrival
The Johns Hopkins University Applied Physics Laboratory（约翰斯·霍普金斯大学应用物理实验室）；NASA Goddard Space Flight Center（美国国家航空航天局戈达德太空飞行中心）；Southwest Research Institute（西南研究所）；KU Leuven Campus Kulak（荷语鲁汶大学库拉克校区）；University of Michigan（密歇根大学）；Christian-ALbrechts-University Kiel（基尔大学）；University of Turku（图尔库大学）；Predictive Science Inc. (PSI)（预测科学公司）；Princeton University（普林斯顿大学）
研究太阳高能粒子事件中冲击波特性及逆速度到达特征，通过分析Solar Orbiter和Parker Solar Probe的数据，揭示冲击波属性和磁场连接对高能粒子延迟到达和谱变硬的影响。
Two solar type II radio bursts, separated by ~24 hours in time, are examined together. Both events are associated with coronal mass ejections (CMEs) erupting from the same active region (NOAA 11176) beneath a well-observed helmet streamer. We find that the type II emissions in both events ended once the CME/shock fronts passed the white-light streamer tip, which is presumably the magnetic cusp of the streamer. This leads us to conjecture that the closed magnetic arcades of the streamer may play a role in electron acceleration and type II excitation at coronal shocks. To examine such a conjectu…
We model the energetic storm particle (ESP) event of 14 July 2012 using the energetic particle acceleration and transport model named PARADISE, together with the solar wind and coronal mass ejection (CME) model named EUHFORIA. The simulation results illustrate both the capabilities and limitations of the utilised models. We show that the models capture some essential structural features of the ESP event; however, for some aspects the simulations and observations diverge. We describe and, to some extent, assess the sources of errors in the modelling chain of EUHFORIA and PARADISE and discuss ho…
As the most energetic eruptions in the solar system, coronal mass ejections (CMEs) can produce shock waves at both their front and flanks as they erupt from the Sun into the heliosphere. However, the amount of energy produced in these eruptions, and the proportion of their energy required to produce the waves, is not well characterised. Here we use observations of a solar eruption from 2014 February 25 to estimate the energy budget of an erupting CME and the globally-propagating "EIT wave" produced by the rapid expansion of the CME flanks in the low solar corona. The "EIT wave" is shown using …
Three-dimensional properties of a coronal shock and the longitudinal distribution of its related solar energetic particles
Key Laboratory of Dark Matter and Space Astronomy, Purple Mountain Observatory, Chinese Academy of Sciences（中国科学院紫金山天文台暗物质与空间天文重点实验室）；School of Astronomy and Space Science, University of Science and Technology of China（中国科学技术大学天文与空间科学学院）；National Key Laboratory of Deep Space Exploration/School of Earth and Space Sciences, University of Science and Technology of China（中国科学技术大学深空探测全国重点实验室/地球与空间科学学院）；CAS Center for Excellence in Comparative Planetology, University of Science and Technology of China（中国科学技术大学中科院比较行星学卓越创新中心）；School of Physics and Optoelectronic Engineering, Institute of Space Weather, Nanjing University of Information Science and Technology（南京信息工程大学物理与光电工程学院空间天气研究所）；State Key Laboratory of Solar Activity and Space Weather, National Space Science Center, Chinese Academy of Sciences（中国科学院国家空间科学中心太阳活动与空间天气国家重点实验室）
Gradual solar energetic particle (SEP) events, usually attributed to shock waves driven by coronal mass ejections (CMEs), show a wide variety of temporal behaviors. For example, TO, the >10 MeV proton onset time with respect to the launch of the CME, has a distribution of at least an order of magnitude, even when the source region is not far from the so-called well-connected longitudes. It is important to understand what controls TO, especially in the context of space weather prediction. Here we study two SEP events from the western hemisphere that are different in TO on the basis of >10 MeV p…
