Random Walk and Trapping of Interplanetary Magnetic Field Lines: Global Simulation, Magnetic Connectivity, and Implications for Solar Energetic Particles
Rohit Chhiber, David Ruffolo, William H. Matthaeus, Arcadi V. Usmanov, Paisan Tooprakai, Piyanate Chuychai, Melvyn L. Goldstein
The random walk of magnetic field lines is an important ingredient in understanding how the connectivity of the magnetic field affects the spatial transport and diffusion of charged particles. As solar energetic particles (SEPs) propagate away from near-solar sources, they interact with the fluctuating magnetic field, which modifies their distributions. We develop a formalism in which the differential equation describing the field line random walk contains both effects due to localized magnetic displacements and a non-stochastic contribution from the large-scale expansion. We use this formalism together with a global magnetohydrodynamic simulation of the inner-heliospheric solar wind, which includes a turbulence transport model, to estimate the diffusive spreading of magnetic field lines that originate in different regions of the solar atmosphere. We first use this model to quantify field line spreading at 1 au, starting from a localized solar source region, and find rms angular spreads of about 20° - 60°. In the second instance, we use the model to estimate the size of the source regions from which field lines observed at 1 au may have originated, thus quantifying the uncertainty in calculations of magnetic connectivity; the angular uncertainty is estimated to be about 20°. Finally, we estimate the filamentation distance, i.e., the heliocentric distance up to which field lines originating in magnetic islands can remain strongly trapped in filamentary structures. We emphasize the key role of slab-like fluctuations in the transition from filamentary to more diffusive transport at greater heliocentric distances.
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 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…
Solar energetic particles (SEPs) are one of the extreme space weather phenomena. A huge SEP event increases the radiation dose received by aircrews, who should be warned of such events as early as possible. We developed a warning system for aviation exposure to SEPs. This article describes one component of the system, which calculates the temporal evolution of the SEP intensity and the spectrum immediately outside the terrestrial magnetosphere. To achieve this, we performed numerical simulations of SEP transport in interplanetary space, in which interplanetary SEP transport is described by the…
Reproducing measurements of the scattering mean free paths for energetic particles propagating through the solar system has been a major problem in space physics. The pioneering work of Bieber et al. [Astrophys. J. 420, 294 (1994)] provided a theoretical explanation of such observations, which, however, was based on assumptions such as the questionable hypothesis that quasi-linear theory is correct for parallel diffusion. By employing a hybrid plasma-wave/magnetostatic turbulence model, a test-particle code is used to investigate the scattering of energetic particles. The results show excellen…
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 …
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…
Sheaths ahead of coronal mass ejections (CMEs) are large heliospheric structures that form with CME expansion and propagation. Turbulent and compressed sheaths contribute to the acceleration of particles in the corona and in interplanetary space, but the relation of their internal structures to particle energization is still relatively little studied. In particular, the role of sheaths in accelerating particles when the shock Mach number is low is a significant open problem. This work seeks to provide new insights on the internal structure of CME sheaths with regard to energetic particle enhan…
To understand the origin of Solar Energetic Particles (SEPs), we must study their injection time relative to other solar eruption manifestations. Traditionally the injection time is determined using the Velocity Dispersion Analysis (VDA) where a linear fit of the observed event onset times at 1 AU to the inverse velocities of SEPs is used to derive the injection time and path length of the first-arriving particles. VDA does not, however, take into account that the particles that produce a statistically observable onset at 1 AU have scattered in the interplanetary space. We use Monte Carlo test…
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）
We calculate the interplanetary magnetic field path lengths traveled by electrons in solar electron events detected by the WIND 3DP instrument from $1994$ to $2016$. The velocity dispersion analysis method is applied for electrons at energies of $\sim$ $27$ keV to $310$ keV. Previous velocity dispersion analyses employ the onset times, which are often affected by instrumental effects and the pre-existing background flux, leading to large uncertainties. We propose a new method here. Instead of using the peak or onset time, we apply the velocity dispersion analysis to the times that correspond t…
Solar energetic particles (SEPs), accelerated during solar eruptions, propagate in turbulent solar wind before being observed with in situ instruments. In order to interpret their origin through comparison with remote-sensing observations of the solar eruption, we thus must deconvolve the transport effects due to the turbulent magnetic fields from the SEP observations. Recent research suggests that the SEP propagation is guided by the turbulent meandering of the magnetic fieldlines across the mean magnetic field. However, the lengthening of the distance the SEPs travel, due to the fieldline me…
Fast interplanetary coronal mass ejections (interplanetary CMEs, or ICMEs) are the drivers of strongest space weather storms such as solar energetic particle events and geomagnetic storms. The connection between space weather impacting solar wind disturbances associated with fast ICMEs at Earth and the characteristics of causative energetic CMEs observed near the Sun is a key question in the study of space weather storms as well as in the development of practical space weather prediction. Such shock-driving fast ICMEs usually expand at supersonic speed during the propagation, resulting in the …
We study how a high-speed solar wind stream embedded in a slow solar wind influences the spread of solar energetic protons in interplanetary space. To model the energetic protons, we used a recently developed particle transport code that computes particle distributions in the heliosphere by solving the focused transport equation in a stochastic manner. The particles are propagated in a solar wind containing a CIR, which was generated by the heliospheric magnetohydrodynamic model, EUHFORIA. We study four cases in which we assume a delta injection of 4 MeV protons spread uniformly over different…
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…
Forecasting Solar Energetic Particle (SEP) fluence, as integrated over an SEP event, is an important element when estimating the effect of solar eruptions on humans and technology in space. Current real-time estimates are based on SEP measurements at a single location in space. However, the interplanetary magnetic field corotates with the Sun approximately 13$^\circ$ each day with respect to Earth, thus in 4 days a near-Earth spacecraft will have changed their connection about 60$^\circ$ from the original SEP source. We estimate the effect of the corotation on particle fluence using a simple p…
A functional form I_{max}(R)=kR^{-α}, where R is the radial distance of spacecraft, was usually used to model the radial dependence of peak intensities I_{max}(R) of solar energetic particles (SEPs). In this work, the five-dimensional Fokker-Planck transport equation incorporating perpendicular diffusion is numerically solved to investigate the radial dependence of SEP peak intensities. We consider two different scenarios for the distribution of spacecraft fleet: (1) along the radial direction line, (2) along the Parker magnetic field line. We find that the index αin the above expression varie…
The acceleration of thermal solar wind protons at spherical interplanetary shocks driven by coronal mass ejections is investigated. The solar wind velocity distribution is represented using $κ$-functions, which are transformed in response to simulated shock transitions in the fixed-frame flow speed, plasma number density, and temperature. These heated solar wind distributions are specified as source spectra at the shock from which particles with sufficient energy can be injected into the diffusive shock acceleration process. It is shown that for shock-accelerated spectra to display the classic…
Solar Energetic Particles (SEPs), a major component of space weather, propagate through the interplanetary medium strongly guided by the Interplanetary Magnetic Field (IMF). In this work, we analyse the implications a flat Heliospheric Current Sheet (HCS) has on proton propagation from SEP release sites to the Earth. We simulate proton propagation by integrating fully 3-D trajectories near an analytically defined flat current sheet, collecting comprehensive statistics into histograms, fluence maps and virtual observer time profiles within an energy range of 1--800 MeV. We show that protons exp…
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 …
We examine the accuracy of a common technique for estimating the start time of solar energetic particle injection based on a linear fit to the observed onset time versus 1/(particle velocity). This is based on a concept that the first arriving particles move directly along the magnetic field with no scattering. We check this by performing numerical simulations of the transport of solar protons between 2 and 2000 MeV from the Sun to the Earth, for several assumptions regarding interplanetary scattering and the duration of particle injection, and analyzing the results using the inverse velocity …
Small 3He-rich solar energetic particle (SEP) events have been commonly associated with extreme-ultraviolet (EUV) jets and narrow coronal mass ejections (CMEs) which are believed to be the signatures of magnetic reconnection involving field lines open to interplanetary space. The elemental and isotopic fractionation in these events are thought to be caused by processes confined to the flare sites. In this study we identify 32 3He-rich SEP events observed by the Advanced Composition Explorer near the Earth during the solar minimum period 2007-2010 and examine their solar sources with the high r…
The mass density of dust particles that form from asteroids and comets in the interplanetary medium of the solar system is, near 1 AU, comparable to the mass density of the solar wind. It is mainly contained in particles of micrometer size and larger. Dust and larger objects are destroyed by collisions and sublimation and hence feed heavy ions into the solar wind and the solar corona. Small dust particles are present in large number and as a result of their large charge to mass ratio deflected by electromagnetic forces in the solar wind. For nano dust particles of sizes 1 - 10 nm, recent calcu…
The event-averaged charge state of heavy ion Solar Energetic Particles (SEPs), measured at 1 AU from the Sun, typically increases with the ions' kinetic energy. The origin of this behaviour has been ascribed to processes taking place within the acceleration region. In this paper we study the propagation through interplanetary space of SEP Fe ions, injected near the Sun with a variety of charge states that are uniformly distributed in energy, by means of a 3D test particle model. In our simulations, due to gradient and curvature drifts associated with the Parker spiral magnetic field, ions of d…
Drifts in the Parker spiral interplanetary magnetic field are known to be an important component in the propagation of galactic cosmic rays, while they are thought to be negligible for Solar Energetic Particles (SEPs). As a result they have so far been ignored in SEP propagation modelling and data analysis. We examine drift velocities in the Parker spiral within single particle first-order adiabatic theory, in a local coordinate system with an axis parallel to the magnetic field. We show that, in the presence of scattering in interplanetary space, protons at the high end of the SEP energy rang…
Coronal mass ejections (CMEs) are intense solar explosive eruptions. CMEs are highly important players in solar-terrestrial relationships, and they have important consequences for major geomagnetic storms and energetic particle events. It has been unclear how CMEs evolve when they propagate in the heliosphere. Here we report an interplanetary coronal mass ejection (ICME) consisting of multiple magnetic flux ropes measured by WIND on March 25-26, 1998. These magnetic flux ropes were merging with each other. The observations indicate that internal interactions (reconnections) within multi-flux-r…
Energetic particle transport in the interplanetary medium is known to be affected by magnetic structures. It has been demonstrated for solar energetic particles in near-Earth orbit studies, and also for the more energetic cosmic rays. In this paper, we show observational evidence that intensity variations of solar energetic particles can be correlated with the occurrence of helical magnetic flux tubes and their boundaries. The analysis is carried out using data from Parker Solar Probe orbit 5, in the period 2020 May 24 to June 2. We use FIELDS magnetic field data and energetic particle measure…
Understanding the transport of Solar Energetic Particles (SEPs) from acceleration sites at the Sun into interplanetary space and to the Earth is an important question for forecasting space weather. The Interplanetary Magnetic Field (IMF), with two distinct polarities and a complex structure, governs energetic particle transport and drifts. We analyse for the first time the effect of a wavy Heliospheric Current Sheet (HCS) on the propagation of SEPs. We inject protons close to the Sun and propagate them by integrating fully 3D trajectories within the inner heliosphere in the presence of weak sc…
Impulsive solar energetic particle events are widely believed to be due to the prompt escape into the interplanetary medium of flare-accelerated particles produced by solar eruptive events. According to the standard model for such events, however, particles accelerated by the flare reconnection should remain trapped in the flux rope comprising the coronal mass ejection. The particles should reach the Earth only much later, along with the bulk ejecta. To resolve this paradox, we have extended our previous axisymmetric model for the escape of flare-accelerated particles to fully three-dimensiona…
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 …
Kiel University（基尔大学）；European Space Agency (ESA)（欧洲空间局）；European Space Astronomy Centre (ESAC)（欧洲航天天文中心）；Institut de Recherche en Astrophysique et Planétologie (IRAP)（天体物理与行星学研究所在）
We draw a comparison between a solar energetic particle event associated with the release of a slow coronal mass ejection close to the sun, and the energetic particle population produced in high current density field-aligned current structures associated with auroral phenomena in planetary magnetospheres. We suggest that this process is common in CME development and lift-off in the corona, and may account for the electron populations that generate Type III radio bursts, as well as for the prompt energetic ion and electron populations typically observed in interplanetary space.
Context. Interplanetary (IP) shocks are known to be accelerators of energetic charged particles observed in-situ in the heliosphere. However, the acceleration of near-relativistic electrons by shocks in the interplanetary medium is often questioned. On 9 August 2011 a Corotating Interaction Region (CIR) passed STEREO B (STB) that resulted in a flux increase in the electron and ion channels of the Solar Electron and Proton Telescope (SEPT). Because electron measurements in the few keV to several 100 keV range rely on the so-called magnet foil technique, which is utilized by SEPT, ions can contr…
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…
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…
August 1 to November 15, 2016 period was characterized by the presence of Corotating Interaction Regions (CIRs) and a few weak Coronal Mass Ejections (CMEs) in the heliosphere. In this study we show recurrent energetic electron and proton enhancements observed near Earth (1 AU) and Mars (1.43-1.38 AU) during this period. The observations near Earth are using data from instruments aboard ACE, SOHO, and SDO whereas those near Mars are by the SEP, SWIA, and MAG instruments aboard MAVEN. During this period, the energetic electron fluxes observed near Earth and Mars showed prominent periodic enhanc…
As solar energetic particles (SEPs) stream outward along the interplanetary magnetic field after acceleration by shock waves near the Sun, their intensities are limited by scattering against self-generated Alfvén waves, trapping the particles near their source. This streaming limit varies with the magnetic rigidity of the particle and with distance from the source. Pitch-angle coupling can cause higher-energy protons to suppress the intensities of lower-energy ions causing flattened low-energy spectra on the early SEP intensity plateau. At sufficiently high energies, particle flow and wave tra…
Solar Energetic Particles (SEPs) are an important component of Space Weather, including radiation hazard to humans and electronic equipment, and the ionisation of the Earth's atmosphere. We review the key observations of SEPs, our current understanding of their acceleration and transport, and discuss how this knowledge is incorporated within Space Weather forecasting tools. Mechanisms for acceleration during solar flares and at shocks driven by Coronal Mass Ejections are discussed, as well as the timing relationships between signatures of solar eruptive events and the detection of SEPs in inte…
We propose a model for interpreting highly variable ion composition ratios in solar energetic particles (SEP) events recently observed by Parker Solar Probe (PSP) at $0.3 - 0.45$ astronomical unit. We use numerical simulations to calculate SEP propagation in a turbulent interplanetary magnetic field with a Kolmogorov power spectrum from large scale down to the gyration scale of energetic particles. We show that when the source regions of different species are offset by a distance comparable to the size of the source regions, the observed energetic particle composition He/H can be strongly vari…
We compare the characteristics of flare-accelerated energetic electrons at the Sun with those injected into interplanetary space. We have identified 17 energetic electron events well-observed with the SEPT instrument aboard STEREO which show a clear association with a hard X-ray (HXR) flare observed with the RHESSI spacecraft. We compare the spectral indices of the RHESSI HXR spectra with those of the interplanetary electrons. Because of the frequent double-power-law shape of the in situ electron spectra, we paid special attention to the choice of the spectral index used for comparison. The ti…
