Modeling the effects of pitch-angle scattering processes on the transport of solar energetic particles along the interplanetary magnetic field

We present a Monte-Carlo technique to study the time-dependent transport of energetic particles in the interplanetary medium. We use the guiding center approximation between discrete finite pitch-angle scatterings to quantify the competing effects of focusing and pitch-angle scattering on energetic particles propagating along a Parker spiral magnetic field. We consider that the pitch-angle scattering process is produced by small-scale magnetic field irregularities frozen in the expanding solar wind. We also include the effects of both solar wind convection and adiabatic deceleration. We use a joint probability distribution P(h, μ′) = p(h; μ′)q(μ′; μ) to describe both the distance traveled by the particle between two scattering processes and the change in the particle pitch-angle after a scattering process. Here, p(h; μ′) is the conditional probability that the particle travels a distance h along the field line before the next scattering if it had a pitch-angle cosine μ′ after the previous scattering, and q(μ′; μ) is the conditional probability for the pitch-angle cosine μ′ if the pitch-angle cosine was μ before the scattering. We consider several functional forms to describe the processes of pitch-angle scattering, such as an isotropic scattering without any memory of the initial particle’s pitch-angle or processes in which the scattering result depends upon the initial particle’s pitch-angle. The results of our simulations are pitch-angle distributions and time-intensity profiles that can be directly compared to spacecraft observations. Comparison of our simulations with near-relativistic (45–290 keV) electron events observed by the Electron, Proton and Alpha Monitor on board the Advanced Composition Explorer allows us to estimate both the time dependence of the injection of near-relativistic electrons into the interplanetary medium and the conditions for electron propagation along the interplanetary magnetic field.     

Onset study of impulsive solar energetic particleevents

Impulsive solar energetic particle (SEP) events are associated with impulsive X-ray flares, energetic electrons,and enhanced heavy ion abundances. Using instruments on ACE, we have examined the composition and origin of twelve impulsive SEP events from November 1997 to June 2000. All selected impulsive SEP events have enhanced ³He/⁴He ratios compared with the solar wind values. The range of ³He/⁴He ratios varies from 0.01 to 7.8. By assuming scatter-free propagation at zero degree pitch-angle, we fitted the minimum particle path lengths (from 1.2 to 1.4 AU, as expected), and estimated the ion event release time back at the Sun to within better than 30 minutes in most cases. We found only four events in which the release times agree for both 38–50 keV electrons and <1 MeV/nucleon ions. Five of our events have significant differences (>40 minutes) between the electron and ion onset times, all with ions injected later. Three impulsive ion events have no association with any impulsive electron event. Seven events have associated solar electromagnetic signatures (Type III radio bursts and/or X-ray flares).     

Comparing proton fluxes of central meridian SEP events with those predicted by SOLPENCO

We have developed an operational code, SOLPENCO, that can be used for space weather prediction schemes of solar energetic particle (SEP) events. SOLPENCO provides proton differential flux and cumulated fluence profiles from the onset of the event up to the arrival of the associated traveling interplanetary shock at the observer’s position (either 1.0 or 0.4 AU). SOLPENCO considers a variety of interplanetary scenarios where the SEP events develop. These scenarios include solar longitudes of the parent solar event ranging from E75 to W90, transit speeds of the associated shock ranging from 400 to 1700 km s⁻¹, proton energies ranging from 0.125 to 64 MeV, and interplanetary conditions for the energetic particle transport characterized by specific mean free paths. We compare the results of SOLPENCO with flux measurements of a set of SEP events observed at 1 AU that fulfill the following four conditions: (1) the association between the interplanetary shock observed at 1 AU and the parent solar event is well established; (2) the heliolongitude of the active region site is within 30° of the Sun–Earth line; (3) the event shows a significant proton flux increase at energies below 96 MeV; (4) the pre-event intensity background is low. The results are discussed in terms of the transit velocity of the shock and the proton energy. We draw conclusions about both the use of SOLPENCO as a prediction tool and the required improvements to make it useful for space weather purposes.     

Statistical properties of SEP event flux declines

The interplanetary space is not a passive medium, which merely constitutes a scene for the propagation of previously accelerated energetic particles, but influences the distribution of particles by changing their energies as well due to interactions with magnetic field inhomogeneities. Such processes manifest themselves in the energy spectra of solar energetic particle (SEP) events. In this paper the fluxes of protons with energies of 4–60 MeV are investigated on the basis of two data sets. Both sets are homogeneous, obtained by the CPME instrument aboard the IMP 8 satellite between 1974 and 2001. The first includes all SEP events where the integral fluxes of >4 MeV protons exceeded 2 particle/cm² s sr. The other set consists of fluxes recorded in differential energy windows between 0.5 and 48 MeV. Important characteristics of SEP events include the rates of decrease of particle flux, which, as well as peak flux time, is an integral feature of the interplanetary medium within a considerable region, surrounding the observation point. The time intervals selected cover the decay phases of SEP events following flares, CMEs and interplanetary shocks of different origin. Only those parts of declines were selected, that could reasonably be described by exponential dependence, irrespective of the gradual/impulsive character of the events. It is shown that the average values of characteristic decay time, τ, and energy spectral index, γ, are all changing with the solar activity phase. Distributions of τ and γ values are obtained in SEPs with and without shocks and during different phases of events: just after peak flux and late after maximum.     

Relativistic proton production at the Sun in the 20 January 2005 solar event

Based on the concept of multiple acceleration of solar energetic particles (SEP) we analyzed the super-event of 20 January 2005 by the data of ground level, balloon and spacecraft observations. The main characteristics of relativistic solar protons (energy spectra, anisotropy directions and pitch-angle distributions) are derived and their dynamics during the event is studied. It is shown that the flux of relativistic solar protons may consist of two distinct components, the so-called prompt and delayed ones. Within a two-source model of particle generation, one of which is associated with an expanding magnetic loop, we solved the transport equation in energy phase space, including adiabatic losses simultaneously with the stochastic acceleration process, and calculate the expected spectra of the delayed component at the source. The confrontation of experimental spectra with theoretical ones shows that the delayed component may be correctly described by stochastic acceleration, but not the prompt component. The required acceleration efficiencies turned out to be rather high, so that, for this particular event, adiabatic cooling is practically negligible. Our results provide a new support to the existence of two populations of relativistic solar protons in some SEP events.     

两个临近脉冲型太阳能量电子事件的观测与拟合

WIND飞船在2010年11月15日观测到两个临近的脉冲型太阳能量电子事件, 这两个事件在1AU处呈现出不同类型的通量-时间曲线. 事件一的通量表现出快速上升及快速下降的特性; 事件二则表现为缓慢上升, 更缓慢下降, 事件二的持续时间是事件一的5～17倍. 以往的解释认为事 件二中的电子在行星际受到了更强的散射. 本文引入等腰三角形的释放函数并 求解电报方程, 利用得到的解对1AU处的观测进行拟合. 根据最佳拟合结果 反推两事件在太阳上的释放函数和在行星际传播的平均自由程, 发现造成两事 件在1AU处能谱和通量-时间曲线形状不同的原因是太阳上电子 加速过程的不同而非行星际散射. 结合SOHO卫星的白光观测, 发现两事件可能 与一个CME (日冕物质抛射)相关, 并进一步推测了这两个太阳电子事件可能 的加速图像.      

On the early phase of relativistic solar particle events: Are there signatures of acceleration mechanism?

Many physical processes precede and accompany the solar energetic particles (SEP) occurrence on the Earth’s orbit. Explosive energy release on the Sun gives rise to a flare and a coronal mass ejection (CME). X-ray and gamma emissions are believed to be connected with flares. Radio emission is signature of disturbances traveling through the corona and interplanetary space. Particles can gain energy both in the flare and the accompanying wave processes. The beginning of the SEP events has the advantage of being the phase most close to the time of acceleration. Influence of interplanetary transport is minimal in the case of first arriving relativistic solar protons recorded by ground based neutron monitors in so called ground-level enhancements (GLE). The early phase of the SEP events attracts attention of many scientists searching for the understanding of particle acceleration. However, they come to the opposite conclusions. While some authors find arguments for coronal mass ejections as a sole accelerator of SEPs, others prove a flare to be the SEP origin. Here, the circumstances of SEP generation for several GLEs of the 23rd solar cycle are considered. Timing of X-ray, CME, and radio emissions shows a great variety from event to event. However, the time of particle ejection from the Sun is closer to maximum of X-ray emission than to any other phenomena considered. No correlation is found between the particle fluxes and the CME characteristics.     

Why should the latitude of the observer be considered when modeling gradual proton events? An insight using the concept of cobpoint

The shape of flux profiles of gradual solar energetic particle (SEP) events depends on several not well-understood factors, such as the strength of the associated shock, the relative position of the observer in space with respect to the traveling shock, the existence of a background seed particle population, the interplanetary conditions for particle transport, as well as the particle energy. Here, we focus on two of these factors: the influence of the shock strength and the relative position of the observer. We performed a 3D simulation of the propagation of a coronal/interplanetary CME-driven shock in the framework of ideal MHD modeling. We analyze the passage of this shock by nine spacecraft located at ∼0.4 AU (Mercury’s orbit) and at different longitudes and latitudes. We study the evolution of the plasma conditions in the shock front region magnetically connected to each spacecraft, that is the region of the shock front scanned by the “cobpoint” (Heras et al., 1995), as the shock propagates away from the Sun. Particularly, we discuss the influence of the latitude of the observer on the injection rate of shock-accelerated particles and, hence, on the resulting proton flux profiles to be detected by each spacecraft.     

Relation of decline characteristics of 2–4.6 MeV protons in SEP events to solar wind parameters

The shape of the particle flux decline in solar energetic particle (SEP) events is of particular importance in understanding the propagation of energetic particles in the interplanetary medium. Power-law time profiles indicate the dominance of diffusive propagation, whereas exponential-law decline emphasizes convection transport and adiabatic deceleration. Values obtained theoretically for the decay time in the latter case are reasonably close to the fitted slopes in nearly half of all events when the solar wind speed stays nearly constant. Dependencies of characteristic decay time τ and spectral index γ on environmental plasma parameters are considered. Parts of exponential-law declines when solar wind speed: (a) decreases with time, (b) is constant, and (c) increases with time through the interval are analyzed separately. Both average values and dispersions of size distributions of τ for these three groups markedly differ in accordance with theoretical expectations.     

Energetic particle signatures of geoeffective coronal mass ejections

We have studied statistically associations of moderate and intense geomagnetic storms with coronal mass ejections (CMEs) and energetic particle events. The goal was to identify specific energetic particle signatures, which could be used to improve the predictions of the geoeffectiveness of full and partial halo CMEs. Protons in the range 1–110 MeV from the ERNE experiment onboard SOHO are used in the analysis. The study covers the time period from August 1996 to July 2000. We demonstrate the feasibility of energetic particle observations as an additional source of information in evaluating the geoeffectiveness of full and partial halo CMEs. Based on the observed onset times of solar energetic particle (SEP) events and energetic storm particle (ESP) events, we derive a proxy for the transit times of shocks driven by the interplanetary counterparts of coronal mass ejections from the Sun to the Earth. For a limited number of geomagnetic storms which can be associated to both SEP and ESP signatures, we found that this transit time correlates with the strength of geomagnetic storms.     

Simulation of ASTROD I test mass charging due to solar energetic particles and interplanetary electrons

As ASTROD I travels through space, its test mass will accrue charge due to exposure of the spacecraft to high-energy particles. This test mass charge will result in Coulomb forces between the test mass and the surrounding electrodes. In earlier work, we have used the GEANT 4 toolkit to simulate charging of the ASTROD test mass due to cosmic-ray protons of energies between 0.1 and 1000 GeV at solar maximum and at solar minimum. Here we use GEANT 4 to simulate the charging process due to solar energetic particle events and interplanetary electrons. We then estimate the test mass acceleration noise due to these fluxes. The predicted charging rates range from 2247 e⁺/s to 47,055 e⁺/s, at peak intensity, for the four largest SEP events in September and October 1989. Although the noise due to charging exceeds the ASTROD I budget for the two larger events, it can be suppressed through continuous discharging. The acceleration noise during the two small events is well below the design target. The charging rate of the ASTROD I test mass due to interplanetary electrons in this simulation is about −11% of the cosmic-ray protons at solar minimum, and over −37% at solar maximum. In addition to the Monte Carlo uncertainty, an error of ±30% in the net charging rates should be added to account for uncertainties in the spectra, physics models and geometry implementations.     

Energetic particle acceleration by coronal mass ejections

The current paradigm for the source of large, gradual solar energetic particle (SEP) events is that theyare accelerated in coronal/interplanetary shocks driven by coronal mass ejections (CMEs). Early studies established that there is a rough correlation between the logs of the CME speed and the logs of the SEP intensities. Here I review two topics challenging the basic paradigm, the recent discovery that CMEs are also associated with impulsive, high-Z rich SEP events and the search for gradual SEP sources other than CME-driven shocks. I then discuss three topics of recent interest dealing with the relationship between the shock or CME properties and the resulting SEP events. These are the roles that CME accelerations, interactions between fast and preceding slow CMEs, and widths of fast CMEs may play in SEP production.     

Coronal mass ejection interaction and particle acceleration during the 2001 April 14–15 events

Two successive solar energetic particle (SEP) events associated with fast and wide coronal mass ejections (CMEs) on 2001 April 14 and 15 are compared. The weak SEP event of April 14 associated with an 830 km/s CME and an M1.0 flare was the largest impulsive event of cycle 23. The April 15 event, the largest ground level event of cycle 23, was three orders of magnitude more intense than the April 14^th event and was associated with a faster CME (1200 km/s) and an X14.4 flare. We compiled and compared all the activities (flares, CMEs, interplanetary conditions and radio bursts) associated with the two SEP events to understand the intensity difference between them. Different coronal and interplanetary environments of the two events (presence of preceding CME and seed particles ahead of the April 15 event) may explain the intensity difference.     

Cone model-based SEP event calculations for applications to multipoint observations

The problem of modeling solar energetic particle (SEP) events is important to both space weather research and forecasting, and yet it has seen relatively little progress. Most important SEP events are associated with coronal mass ejections (CMEs) that drive coronal and interplanetary shocks. These shocks can continuously produce accelerated particles from the ambient medium to well beyond 1 AU. This paper describes an effort to model real SEP events using a Center for Integrated Space weather Modeling (CISM) MHD solar wind simulation including a cone model of CMEs to initiate the related shocks. In addition to providing observation-inspired shock geometry and characteristics, this MHD simulation describes the time-dependent observer field line connections to the shock source. As a first approximation, we assume a shock jump-parameterized source strength and spectrum, and that scatter-free transport occurs outside of the shock source, thus emphasizing the role the shock evolution plays in determining the modeled SEP event profile. Three halo CME events on May 12, 1997, November 4, 1997 and December 13, 2006 are used to test the modeling approach. While challenges arise in the identification and characterization of the shocks in the MHD model results, this approach illustrates the importance to SEP event modeling of globally simulating the underlying heliospheric event. The results also suggest the potential utility of such a model for forcasting and for interpretation of separated multipoint measurements such as those expected from the STEREO mission.     

Periods of quasi-stationary conditions in interplanetary space according to sequences of SEP events

The values of the characteristic decay time of particle fluxes in SEP events vary, as a rule, considerably from event to event. We point out, however, that at times sequences of events having similar decay times were observed over long time intervals (up to one month, and even longer in a few cases). The values of the decay times, however, differed among different sequences. The constancy of the decay phase in each consecutive event of these series suggests that the interplanetary medium was in steady state during the event series, and, because of solar rotation, its uniformity within sectors extended to 90–180° in heliolongitude. The very rarely observed long series (up to 2–3 solar rotations) indicate the steadiness and homogeneity of the plasma and the interplanetary magnetic field (IMF) in the entire inner solar system in the course of this time span. It is pointed out that the neutral current sheet of the IMF does not represent a substantial obstacle for energetic charged particles. Both hemispheres are (above and below the current sheet), at least during the series of solar events, invariant with time, uniform and alike from the viewpoint of the propagation of charged particles. The investigation of such sequences of events can also be useful for forecasting characteristics of SEP events.     

缓变型太阳高能粒子事件特征时间及其经向分布

利用SOHO,STEREO高能粒子观测数据,对2011-2014年30个通量短时间内显著增强的缓变型太阳高能粒子（SEP）事件的两个特征时间（局地爆发时间,起始释放时间）及其经向分布进行统计分析.研究结果显示,多颗卫星同时观测到的SEP事件伴随的日冕物质抛射（CME）角宽明显较一般事件大,且基本都为Halo CME;不同卫星观测到的粒子通量局地增强时间差与卫星位置经度差明显线性正相关且东西不对称;局地爆发时间和起始释放时间相对于耀斑时间的延迟与卫星相对经度正相关;卫星所有能量通道的两个特征时间极差与卫星相对经度呈现较好的正相关,这表明不同能量SEP释放的时间跨度具有明显经度差异;高低能释放时间差与CME速度正相关.这些结论表明,SEP事件的两个特征时间具有明显的经向依赖性,并都与CME速度相关.      

Acceleration and transport of energeticparticles at CME-driven shocks

Historically, solar energetic particle (SEP) events are classified in two classes as “impulsive” and “gradual”. Whether there is a clear distinction between the two classes is still a matter of debate, but it is now commonly accepted that in large “gradual” SEP events, Fermi acceleration, also known as diffusive shock acceleration, is the underlying acceleration mechanism. At shock waves driven by coronal mass ejections (CMEs), particles are accelerated diffusively at the shock and often reach > MeV energies (and perhaps up to GeV energies). As a CME-driven shock propagates, expands and weakens, the accelerated particles can escape ahead of the shock into the interplanetary medium. These escaping energized particles then propagate along the interplanetary magnetic field, experiencing only weak scattering from fluctuations in the interplanetary magnetic field (IMF). In this paper, we use a Monte-Carlo approach to study the transport of energetic particles escaping from a CME-driven shock. We present particle spectra observed at 1 AU. We also discuss the particle “crossing number” at 1AU and its implication to particle anisotropy. Based on previous models of particle acceleration at CME-driven shocks, our simulation allows us to investigate various characteristics of energetic particles arriving at various distances from the sun. This provides us an excellent basis for understanding the observations of high-energy particles made at 1 AU by ACE and WIND.     

Temporal profiles of solar energetic particle events from SOHO/EPHIN data

Temporal profiles of energetic ions and electrons observed at 1 AU during solar energetic particle events are mainly determined by particle injection features, the observer location relative to the source region at the Sun, and the interplanetary space plasma and field conditions during particle transport. In this work, temporal profiles of 18 solar energetic particle events have been analyzed by fitting a pulse function to them in order to find a set of parameters which can be used to characterize the events.     

太阳高能粒子的电荷态和粒子强度间的相关性

本文发表了在太阳高能粒子事件中,元素氦、碳、氮、氧、氖、镁、硅、硫和铁的离子电荷态的分布。研究结果表明,除氦之外上述元素的电荷态分布的不同离子价的数目是随元素的质量而增大。核子能量在2—3MeV范围内,这些元素的平均粒子强度相对于碳的平均粒子强度之间的相关性能够用离子价的数目随元素质量的增加来解释,而不能用日冕温度确定的电荷态平衡模型来解释。且得出结论,太阳高能粒子的离子电荷是在太阳耀斑区而不是在星际激波区产生。      

Particle acceleration by coronal and interplanetary shock waves

Utilizing many years of observation from deep space and near-earth spacecraft a theoretical understanding has evolved on how ions and electrons are accelerated in interplanetary shock waves. This understanding is now being applied to solar flare-induced shock waves propagating through the solar atmosphere. Such solar flare phenomena as γ-ray line and neutron emissions, interplanetary energetic electron and ion events, and Type II and moving Type IV radio bursts appear understandable in terms of particle accleration in shock waves.