Velocity correlation functions of charged particles derived from the Fokker–Planck equation

An important ingredient in theories for diffusion of charged particles across a mean magnetic field are velocity correlation functions along and across that field. In the current article we present an analytical study of these functions by investigating the two-dimensional Fokker–Planck equation. We show that for an isotropic pitch-angle Fokker–Planck coefficient, the parallel velocity correlation function is an exponential function in agreement with the standard model used previously. For other forms of the pitch-angle diffusion coefficient, however, we find non-exponential forms. Also a new, velocity correlation function based, approach for deriving the so-called Earl-relation is presented. This new derivation is more systematic and simpler than previous derivations. We also discuss higher-order velocity correlations and the applicability of the quasi-normal hypothesis in particle diffusion theory. Furthermore, we compute velocity correlation functions across the mean field and develop an alternative theory for perpendicular diffusion.     

Ion and electron superdiffusive transport in the interplanetary space

We study the propagation of energetic particles, accelerated by interplanetary shock waves, upstream of the shock. By using the appropriate propagator, we show that in the case of superdiffusive transport, the time profile of particles accelerated at a traveling planar shock is a power-law with slope 0<γ<1$0<\gamma <1$, at variance with the exponential profile obtained for normal diffusion. By analyzing data sets of interplanetary shocks in the solar wind observed by the Ulysses and the Voyager 2 spacecraft, we find that the time profiles of energetic electrons correspond to power-laws, with slopes γ?0.30–0.98$\gamma ?0.30''–''0.98$, implying a mean square displacement 〈Δx²〉∝t^α$〈\mathrm{\Delta }{x}^2〉\propto t^{\alpha }$, with α=2-γ>1$\alpha =2-\gamma >1$, i.e., superdiffusion. In addition, the propagation of ions is also superdiffusive, with α=1.07–1.13$\alpha =1.07''–''1.13$.     

Random walk of magnetic field lines: Subdiffusive,diffusive, and superdiffusive regimes

One- and two-dimensional models of magnetic field fluctuations and turbulence are widely used in space-, astrophysical, and laboratory contexts. In the present article we use a generalized form of the turbulence wave spectrum to calculate field line diffusion coefficients analytically and numerically. General conditions are derived for which field line wandering behaves subdiffusively, diffusively, and superdiffusively.     

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.     

Relation between different theories for cosmic ray cross field diffusion

In the past few year several theories have been presented for describing cosmic ray scattering across the mean magnetic field. It is the purpose of the present article to discuss the relation between these different theories in order to improve our understanding of cosmic ray perpendicular scattering and to explore the parameter regimes for which these different theories are valid.     

基于嫦娥一号高能粒子数据的地球磁层屏蔽效应研究

月球绕地球运行轨道约有1/4位于地球磁层内,因此,地球磁层是否会为月球轨道附近高能粒子提供足够的磁场屏蔽对于探索月球活动具有重要影响.嫦娥一号是中国首颗绕月人造卫星,其绕月飞行的工作轨道距离月球表面200 km.通过对嫦娥一号高能粒子探测器(HPD)的探测数据进行分析,比较了当月球位于地球磁层内外6个不同能道(能量范围4～400 MeV)时质子通量的变化,发现当月球位于地球磁层内时,这些能道的质子通量并没有发生显著减少,结果表明地球磁层不能为月球轨道附近高能粒子提供显著的磁屏蔽.     

Model of energetic populations at Ganymede,implications for an orbiter

A model is developed to study the energetic particle populations in Ganymede’s magnetosphere. The main objective is to estimate to what extent the moon could protect an orbiter from radiations. Using Liouville’s theorem, the phase space density of particles coming from Jupiter’s magnetosphere is calculated at any point of Ganymede’s environment. Up to energies of ∼50–100 keV for ions and ∼10–20 MeV for electrons, Ganymede’s magnetic field appears to be able to form distinctive populations as loss-cones over the polar caps and radiation belts. At larger energies, these features are blurred by Larmor radius effects; the moon absorption simply creates a quasi-isotropic layer of ∼500 km thickness where the flux is reduced by ∼40–50%. The predictions are compared to Galileo measurements. In particular, we demonstrate the importance of the moon sweeping in reducing the flux over the polar caps. Interestingly, this can be accounted for by assuming that the particles bouncing between Jupiter and Ganymede are ideally scattered in pitch angle and permanently re-fill the loss-cone, which increases the precipitation on Ganymede’s polar cap. In overall, it is estimated that the radiation dose received by an orbiter of Ganymede will be reduced by more than 50–60% compared to the expected dose at Jupiter/Ganymede distance. This should have a positive impact on the design of a future orbiter of Ganymede.     

Relationships between energetic storm particle events and interplanetary shocks driven by full and partial halo coronal mass ejections

We have analysed energetic storm particle (ESP) events in 116 interplanetary (IP) shocks driven by front-side full and partial halo coronal mass ejections (CMEs) with speeds $>$400 km s^?1during the years 1996–2015. We investigated the occurrence and relationships of ESP events with several parameters describing the IP shocks, and the associated CMEs, type II radio bursts, and solar energetic particle (SEP) events. Most of the shocks (57 %) were associated with an ESP event at proton energies $>$1 MeV.The shock transit speeds from the Sun to 1 AU of the shocks associated with an ESP event were significantly greater than those of the shocks without an ESP event, and best distinguished these two groups of shocks from each other. The occurrence and maximum intensity of the ESP events also had the strongest dependence on the shock transit speed compared to the other parameters investigated. The correlation coefficient between ESP peak intensities and shock transit speeds was highest (0.73 $\pm$ 0.04) at 6.2 MeV. Weaker dependences were found on the shock speed at 1 AU, Alfvénic and magnetosonic Mach numbers, shock compression ratio, and CME speed. On average all these parameters were significantly different for shocks capable to accelerate ESPs compared to shocks not associated with ESPs, while the differences in the shock normal angle and in the width and longitude of the CMEs were insignificant.The CME-driven shocks producing energetic decametric–hectometric (DH) type II radio bursts and high-intensity SEP events proved to produce also more frequently ESP events with larger particle flux enhancements than other shocks. Together with the shock transit speed, the characteristics of solar DH type II radio bursts and SEP events play an important role in the occurrence and maximum intensity of ESP events at 1 AU.     

“风云一号”(B)星对内辐射带质子的观测结果

本文介绍“风云一号”(B)星上的“宇宙线成份监测器”于1990年11月19至24日对内辐射带质子的观测结果。通过对这些结果的分析, 本文获得了4—23MeV能量范围内辐射带质子垂直强度在磁坐标内的分布特征。同时, 本文还给出了100°E子午面内质子垂直强度的分布。分析表明, 所得结果与辐射带理论一致。     

Perpendicular transport of charged particles: Results for the unified nonlinear transport theory derived from the Newton–Lorentz equation

The perpendicular diffusion coefficient is calculated by combining a recently developed Unified Nonlinear Transport (UNLT) theory with the Newton–Lorentz equation. The total perpendicular mean free path can be described as a combination of a guiding center contribution and a microscopic contribution. It is shown that the total mean free path depends strongly on the energy range of the turbulence power spectrum and on particle energy. Further, a slab/2D composite model is used to investigate the influence of each contribution to the total mean free path for a quasi-3D turbulence model. For pure 2D turbulence the UNLT reduces to the NLGC-theory. For pure slab turbulence the guiding center contribution is subdiffusive in accordance with simulations and the theorem on reduced dimensionality. Conversely, the microscopic contribution is non-zero, which has to be interpreted as normal diffusion.     

Magnetosphere response to the 2005 and 2006 extreme solar events as observed by the Cluster and Double Star spacecraft

The four identical Cluster spacecraft, launched in 2000, orbit the Earth in a tetrahedral configuration and on a highly eccentric polar orbit (4–19.6 R_E). This allows the crossing of critical layers that develop as a result of the interaction between the solar wind and the Earth’s magnetosphere. Since 2004 the Chinese Double Star TC-1 and TC-2 spacecraft, whose payload comprise also backup models of instruments developed by European scientists for Cluster, provided two additional points of measurement, on a larger scale: the Cluster and Double Star orbits are such that the spacecraft are almost in the same meridian, allowing conjugate studies. The Cluster and Double Star observations during the 2005 and 2006 extreme solar events are presented, showing uncommon plasma parameters values in the near-Earth solar wind and in the magnetosheath. These include solar wind velocities up to ∼900 km s⁻¹ during an ICME shock arrival, accompanied by a sudden increase in the density by a factor of ∼5 and followed by an enrichment in He⁺⁺ in the secondary front of the ICME. In the magnetosheath ion density values as high as 130 cm⁻³ were observed, and the plasma flow velocity there reached values even higher than the typical solar wind velocity. These resulted in unusual dayside magnetosphere compression, detection of penetrating high-energy particles in the magnetotail, and ring current development following several successive injections of energetic particles in the inner magnetosphere, which “washed out” the previously formed nose-like ion structures.     

The influence of in situ pitch-angle cosine coverage on the derivation of solar energetic particle injection and interplanetary transport conditions

Modelization of solar energetic particle (SEP) events aims at revealing the general scenario of SEP injection and interplanetary propagation and relies on in situ measurements of SEP distributions. In this paper, we study to what extent the LEFS60 and LEMS30 electron telescopes of the Electron Proton Alpha Monitor (EPAM) on board the Advanced Composition Explorer are able to scan pitch-angle distributions during near-relativistic electron events. We estimate the percentage of the pitch-angle cosine range scanned by both telescopes for a given magnetic field configuration. We obtain that the pitch-angle coverage is always higher for LEFS60 than for LEMS30. Therefore, LEFS60 provides more information of the directional distribution of the observed particles. The aim of the paper is to study the relevance of the coverage when fitting LEFS60 particle measurements in order to infer the solar injection and the interplanetary transport conditions. By studying synthetic electron events, we obtain that at least 70% of the pitch-angle cosine range needs to be scanned by the telescope. Otherwise, multiple scenarios can explain the data.     

Solar cycle and latitude dependence of high-beta suprathermal plasma conditions in interplanetary space between 1.3 and 5.4 AU

The analysis of energetic particles and magnetic field measurements from the Ulysses spacecraft has shown that in a series of events, the energy density contained in the suprathermal tail particle distribution is comparable to or larger than that of the magnetic field, creating conditions of high-beta plasma. In this work we analyze periods of high-beta suprathermal plasma occurrences (β_ep > 1) in interplanetary space, using the ratio (β_ep) of the energetic particle (20 keV to ∼5 MeV) and magnetic field energy densities from measurements covering the entire Ulysses mission lifetime (1990–2009) in order to reveal new or to reconfirm some recently defined interesting characteristics. The main key-results of the work are summarized as follows: (i) we verify that high-beta events are detected within well identified regions corresponding mainly to the vicinity of shock surfaces and magnetic structures, and associated with energetic particle intensity enhancements due to (a) reacceleration at shock-fronts and (b) unusually large magnetic field depressions. (ii) We define three considerable features for the high-beta events, concentrated on the next points: (a) there is an appreciable solar-activity influence on the high-beta events, during the maximum and middle solar-cycle phase, (b) the annual peak magnitude and the number of occurrences of high events are well correlated with the sunspot number, (c) the high-beta suprathermal plasma events present a spatial distribution in heliographic latitudes (HL) up to ∼±80°, and a specific important concentration on the low (−25° ? HL < −6°, 6° < HL ? 25°) and median (−45° ? HL < −25°, 25° < HL ? 45°) latitudes. We also reconfirm by a statistical analysis the results of Marhavilas and Sarris (2011), that the high-beta suprathermal plasma (β_ep > 1) events are characterized by a very large parameter β_ep (up to 1732.5), a great total duration (406 days) and a large percentage of the Ulysses-mission lifetime (which is equal to 6.34% of the total duration with usable measurements, and 11.3% of the duration in presence of suprathermal particles events).     

Cluster observations showing the indication of the formation of a modified-two-stream instability in the geomagnetic tail

This study presents several observations of the Cluster spacecraft on September 24, 2003 around 15:10 UT, which show necessary prerequisites and consequences for the formation of the so-called modified-two-stream instability (MTSI). Theoretical studies suggest that the plasma is MTSI unstable if (1) a relative drift of electrons and ions is present, which exceeds the Alfvèn speed, and (2) this relative drift or current is in the cross-field direction. As consequences of the formation of a MTSI one expects to observe (1) a field-aligned electron beam, (2) heating of the plasma, and (3) an enhancement in the B-wave spectrum at frequencies in the range of the lower-hybrid-frequency (LHF). In this study we use prime parameter data of the CIS and PEACE instruments onboard the Cluster spacecraft to verify the drift velocities of ions and electrons, FGM data to calculate the expected LHF and Alfvèn velocity, and the direction of the current. The B-wave spectrum is recorded by the STAFF instrument of Cluster. Finally, a field aligned beam of electrons is observed by 3D measurements of the IES instrument of the RAPID unit. Observations are verified using a theoretical model showing the build-up of a MTSI under the given circumstances.     

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.