Particle acceleration and transport at an oblique CME-driven shock

In gradual solar energetic particle (SEP) events, protons and heavy ions are often accelerated to >100 MeV/nucleon at a CME-driven shock. In this work, we study particle acceleration at an oblique shock by extending our earlier particle acceleration and transport in heliosphere (PATH) code to include shocks with arbitrary θ_BN, where θ_BN is the angle between the upstream magnetic field and the shock normal. Instantaneous particle spectra at the shock front are obtained by solving the transport equation using the total diffusion coefficient κ, which is a function of the parallel diffusion coefficient κ_∥ and the perpendicular diffusion coefficient κ_⊥. In computing κ_∥ and κ_⊥, we use analytic expressions derived previously. The particle maximum energy at the shock front as a function of time, the time intensity profiles and particle spectra at 1 AU for five θ_BN’s are calculated for an example shock.     

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.     

Energetic ion acceleration and transport in the upstream region of Jupiter: Voyager 1 and 2

Long-lived upstream energetic ion events at Jupiter appear to be very similar in nearly all respects to upstream ion events at earth. A notable difference between the two planetary systems is the enhanced heavy ion compositional signature reported for the Jovian events. This compositional feature has suggested that ions escaping from the Jovian magnetosphere play an important role in forming upstream ion populations at Jupiter. In contrast, models of energetic upstream ions at earth emphasize $\text{in situ}$ acceleration of reflected solar wind ions within the upstream region itself. Using Voyager 1 and 2 energetic (? 30 keV) ion measurements near the magnetopause, in the magnetosheath, and immediately upstream of the bow shock, we examine the compositional patterns together with typical energy spectra in each of these regions. We find characteristic spectral changes late in ion events observed upstream of the bow shock at the same time that heavy ion fluxes are enhanced and energetic electrons are present. A model involving upstream Fermi acceleration early in events and emphasizing energetic particle escape in the prenoon part of the Jovian magnetosphere late in events is presented to explain many of the features in the upstream region of Jupiter.     

Interplanetary acceleration of low-energy protons as observed during the 25 september 1978 shock event

ISEE-3 observations of a long-lasting low-energy proton intensity increase during the 25 September 1978 shock event are presented as an example for interplanetary particle acceleration in association with shock waves. The observations are discussed in the light of current models for particle acceleration. The particular shape of the time intensity behaviour of the particle intensity increase, the existence of a shock spike and the observed particle distributions indicate that the particles are accelerated at the shock by the induced electric field $\text{E}\text{= ?}\text{1}\text{c}\text{V}\text{×}\text{B}$.     

Modulation of cosmic rays: Perpendicular diffusion and drifts in a heliosphere with a solar wind termination shock

In this study the roles of polar perpendicular diffusion and drifts are illustrated in a model containing a heliosheath and diffusive shock acceleration as applied to the solar wind termination shock. Of particular interest is the relation of polar perpendicular diffusion to particle drifts and how the effectiveness of the termination shock acceleration of galactic and anomalous protons is influenced by this relation. We found that drifts have a more prominent effect than the polar enhancement of perpendicular diffusion so that its omission from termination shock models would produce unrealistically large shock acceleration and consequently also larger modulation effects throughout the heliosphere. The computed spectra at a heliolatitude of 35° are almost similar for the two polarity epochs indicating that the two Voyager spacecraft might not observe differences between the two cycles in future.     

Angular distributions of energetic charged particles observed with HELIOS-1 and -2 between 0.3 amd 1 AU and their relevance to manned interplanetary space missions.

The University of Kiel Cosmic Ray Instrument on board the solar probes HELIOS-1 and -2 measured angular distributions of electrons, protons, and heavier nuclei between 0.3 and 1 AU over one complete solar cycle between 1974 and 1986. Anisotropies are observed mainly during the rising phase of solar particle events or close to the passage of certain interplanetary shocks. The anisotropies are presented as proton data of energies between 27 and 37 MeV. The dependence of the anisotropies on particle energy and distance from the sun is provided based on diffusive propagation in interplanetary space. Strong anisotropies could provide a chance of efficient shielding of the passenger compartment by moving heavier parts of the spacecraft structure into the direction of the highest flux. A reduction of the total radiation dose by less than a factor of 2 might be achievable, however, selection of quiet times for the mission reduces the radiation hazard much more.     

Diffusive shock acceleration at interplanetary perpendicular shock waves: Influence of the large scale structure of turbulence on the maximum particle energy

We calculate the maximum energy that a particle can obtain at perpendicular interplanetary shock waves by the mechanism of diffusive shock acceleration. The influence of the energy range spectral index of the two-dimensional modes of the interplanetary turbulence is explored. We show that changes in this parameter lead to energies that differ in at least one order of magnitude. Therefore, the large scale structure of the turbulence is a key input if the maximum particle energy is calculated.     

Energization of charged particle in a time-dependent chaotic magnetic field with an implication of the production of seed particles in solar energetic particle events

We investigate the acceleration of charged particles in a time-dependent chaotic magnetic field in this work. In earlier works, it has been demonstrated that in an asymmetric wire-loop current systems (WLCSs), the magnetic field is of chaotic in nature. Furthermore, observations also showed that there exist time-varying current loops and current filaments in solar corona. It is therefore natural to conceive that the magnetic field on the solar surface is chaotic and time-dependent. Here, we develop a numerical model to study the acceleration process of charged particles in a time-varying chaotic magnetic field that is generated by an ensemble of 8 WLCSs. We found that the motion of energetic particles in the system is of diffusive in nature and a power law spectrum can quickly develop. The mechanism examined here may serve as an efficient pre-acceleration mechanism that generates the so-called seed particles for diffusive shock acceleration at a coronal mass ejection (CME) driven shock in large solar energetic particle (SEP) events.     

Interplanetary acceleration of low energy protons in association with shock waves: The 11 February 1979 event

The problem of interplanetary acceleration of low energy protons in association with shock waves is examined in the context of the specific event observed on 11 February 1979 on board the ISEE-3 spacecraft. This event has been selected for special study as it apparently was not associated with a solar flare event. The low energy proton telescope system on ISEE-3 measures the proton distribution function with good spectral, directional and temporal resolution from E_p = 35 keV. The evolution of the anisotropies and of the energy spectrum during the event are consistent with particle acceleration taking place in the vicinity of the shock wave.     

2008年4月24日行星际激波事件相关联的超热电子90°投掷角的增强

利用测试粒子数值模拟的方法研究了与STEREO-A卫星观测到的2008年4月24日行星际激波事件相关联的超热电子90°投掷角的增强.根据激波到达前给定时刻超热电子的观测分布,拟合得到不同投掷角的初始分布函数;在给定的激波参数下,采用时间向后的方法计算特定能道上激波下游超热电子的投掷角分布.由于超热电子具有较高的共振频率,模拟采用的磁场湍流谱包含了低能电子发生共振的耗散区.对以215.76,151.67,106.63,eV为中心的三个能道进行了模拟.结果表明,不同能道上超热电子在激波下游的投掷角分布均在90°投掷角附近出现峰值,呈现出明显的90°投掷角增强,这与观测结果符合得很好.可以认为在激波对电子的加速过程中,电子与湍流耗散区的共振对90°投掷角的增强具有重要作用.      

Injection mechanism for cosmic ray acceleration

The quasilinear theory of MHD waves excitation by cosmic rays accelerated at a front of supernova shock has been constructed. It is shown that the energetic particles excite the waves propagating from the shock front, the intensity and the spectrum of these waves is obtained. The role of nonlinear Landau damping in the formation of such spectrum has been analysed. The diffusive scattering length of the high energy particles in the preshock region has been calculated and it is shown with the help of these formulae that the effective Fermi acceleration at the shock front is possible upto the values of the relativistic factor = 10⁴ - 10⁵. The injection mechanism for cosmic rays acceleration has been proposed. It is based on stochastic Fermi acceleration of the thermal plasma by MHD waves excited in the preshock region. Different possibilities for wave phase velocity dispersion needed for stochastic Fermi acceleration are analysed, those are the excitation of the oblique magnetosonic waves as well as the excitation of parallel Alfven waves propagating in opposite directions. The distribution function of the suprathermal particles accelerated by MHD waves is obtained, the cosmic rays density as well as the lower boundary of their energy spectrum realised in the proposed mechanism are also calculated.     

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.     

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.     

Effects of solar modulation on the cosmic ray positron fraction

We implemented a 2D Monte Carlo model to simulate the solar modulation of galactic cosmic rays. The model is based on the Parker’s transport equation which contains diffusion, convection, particle drift and energy loss. Following the evolution in time of the solar activity, we are able to modulate a local interstellar spectrum (LIS), that we assumed isotropic beyond the termination shock, down to the Earth position inside the heliosphere. In this work we focused our attention to the cosmic ray positron fraction at energy below ∼10 GeV, showing how the particle drift processes could explain different results for AMS-01 and PAMELA. We compare our modulated spectra with observations at Earth, and then make a prediction of the cosmic ray positron fraction for the AMS-02 experiment.     

Shock acceleration of energetic particles in wave heated corona

The solar wind wave heating models require substantial amount of wave power in order to efficiently heat and accelerate solar wind. The level of fluctuations is however limited by energetic particle observations. The simplest cyclotron sweep models result in convection-dominated transport, contradicting observations. However, models incorporating wave-wave -interactions, which cause wave energy to cascade in wavenumber, allow more reasonable energetic particle transport in the interplanetary space. The mean free path of the energetic particles remains still relatively short in the corona, providing favorable conditions for coronal mass ejection (CME) related shock acceleration. We study the consequences of this scenario on the energetic particle production related to CMEs. The role of self-generated waves is also discussed.     

Using gamma-ray burst prompt emission to probe relativistic shock acceleration

It is widely accepted that the prompt transient signal in the 10 keV–10 GeV band from gamma-ray bursts (GRBs) arises from multiple shocks internal to the ultra-relativistic expansion. The detailed understanding of the dissipation and accompanying acceleration at these shocks is a currently topical subject. This paper explores the relationship between GRB prompt emission spectra and the electron (or ion) acceleration properties at the relativistic shocks that pertain to GRB models. The focus is on the array of possible high-energy power-law indices in accelerated populations, highlighting how spectra above 1 MeV can probe the field obliquity in GRB internal shocks, and the character of hydromagnetic turbulence in their environs. It is emphasized that diffusive shock acceleration theory generates no canonical spectrum at relativistic MHD discontinuities. This diversity is commensurate with the significant range of spectral indices discerned in prompt burst emission. Such system diagnostics are now being enhanced by the broad-band spectral coverage of bursts by the Fermi Gamma-Ray Space Telescope; while the Gamma-Ray Burst Monitor (GBM) provides key diagnostics on the lower energy portions of the particle population, the focus here is on constraints in the non-thermal, power-law regime of the particle distribution that are provided by the Large Area Telescope (LAT).     

垂直激波条件下能量粒子加速机制的模拟研究

在具有湍动的磁场和垂直激波条件下对大量测试粒子的轨迹进行了数值计算,研究了激波强度和粒子初始能量对于粒子穿越激波的平均能量变化的影响,分析了漂移加速(SDA)在不同条件下对粒子加速的贡献,并给出了一个与数值结果相符合的漂移加速理论公式△E=amvivup(1-1/s).结果表明,加入磁场湍流后,垂直激波条件下粒子仍主要受到漂移加速作用,而基于粒子引导中心的耗散漂移加速理论在此条件下失效.      

Fluctuations of cosmic rays and IMF in the vicinity of interplanetary shocks

Fluctuations of cosmic rays and interplanetary magnetic field upstream of interplanetary shocks are studied using data of ground-based polar neutron monitors as well as measurements of energetic particles and solar wind plasma parameters aboard the ACE spacecraft. It is shown that coherent cosmic ray fluctuations in the energy range from 10 keV to 1 GeV are often observed at the Earth’s orbit before the arrival of interplanetary shocks. This corresponds to an increase of solar wind turbulence level by more than the order of magnitude upstream of the shock. We suggest a scenario where the cosmic ray fluctuation spectrum is modulated by fast magnetosonic waves generated by flux of low-energy cosmic rays which are reflected and/or accelerated by an interplanetary shock.     

Modeling of “gradual” solar energeticparticle events using a stochastic differential equation method

We have modeled “gradual” solar energetic particle events through numerical simulations using a StochasticDifferential Equation (SDE) method. We consider that energetic particle events are roughly divided into two groups: (1) where the shock was driven by coronal mass ejections (CMEs) associated with large solar flares, and (2) where they have no related solar events apart from the CMEs. (The detailed classification of energetic particle events was discussed in our previous paper.) What we call “gradual” solar energetic particle events belong to the former group. Particles with energies greater than 10 MeV are observed within several hours after the occurrence of flares and CMEs in many gradual events. By applying the SDE method coupled with particle splitting to diffusive acceleration, we found that an injection of high energy particles is necessary for early enhancement of such a high-energy proton flux and that it should not be presumed that the solar wind particles act as the seed population.     

Long lasting energetic particle injection from a weak flare

A relatively weak solar cosmic ray event registered at the Earth orbit following the flare of December 17, 1976 is discussed. The main feature of the event is the existence of a prolonged unusually high proton and electron anisotropy; even at the end of the decay phase of the flare the motion of the particles were mainly directed away from the Sun. The durations of proton and electron anisotropies were different. If prolonged particle injection is neglected the value of the anisotropy considerable exceeds all diffusive estimates. Time-intensity and anisotropy profiles of electrons and protons are fitted by a diffusive model including prolonged particle injection at the Sun. The best agreement with the data is obtained if the duration of injection equals about 20 and 7 hours for protons and electrons, respectively.