Energetic particle losses and trapping boundaries as deduced from calculations with a realistic magnetic field model

An interpretation of the stable trapping boundaries of energetic electrons and protons during quiet periods is given basing on a realistic magnetospheric magnetic field model. Particle losses are explained in terms of an ionospheric and drift loss cone filling due to a non-adiabatic pitch-angle scattering in the nightside magnetotail current sheet. The proposed mechanism is shown to provide a good agreement of the observed and calculated positions of the energetic particle trapping boundaries, as well as their energy dependence. The obtained results can be applied as a tool for investigating the magnetospheric magnetic field structure using the particle data of low-altitude satellites.     

Large-scale transport of plasma in the Earth's plasma sheet: comparative analysis for adiabatic and non-adiabatic cases

A system of multi-fluid MHD-equations is used to compare adiabatic and non-adiabatic transport of the energetic particles in the magnetospheric plasma sheet. A “slow-flow” approximation is considered to study large-scale transport of the anisotropic plasma consisting of energetic electrons and protons. Non-adiabatic transport of the energetic plasma is caused by scattering of the particles in the presence of both wave turbulence and arbitrary time-varying electric fields penetrating from the solar wind into the magnetosphere. The plasma components are devided into particle populations defined by their given initial effective values of the magnetic moment per particle. The spatial scales are also given to estimate the non-uniformity of the geomagnetic field along the chosen mean path of a particle. The latters are used to integrate approximately the system of MHD-equations along each of these paths. The behaviour of the magnetic moment mentioned above and of the parameter which characterizes the pitch-angle distribution of the particles are studied self-consistently in dependence on the intensity of non-adiabatic scattering of the particles. It is shown that, in the inner magnetosphere, this scattering influences the particles in the same manner as pitch-angle diffusion does. It reduces the pitch-angle anisotropy in the plasa. The state of the plasma may be unstable in the current sheet of the magnetotail. If the initial state of the plasma does not correspond to the equilibrium one, then, in this case, scattering influences the particles so as to remove the plasma further from the equilibrium state. The coefficient of the particle diffusion across the geomagnetic field lines is evaluated. This is done by employing the Langevin approach to take the stochastic electric forces acting on the energetic particles in the turbulent plasma into account. The behaviour of the energy density of electrostatic fluctuations in the magnetosphere is estimated.     

On the convective mechanism for formation of the plasma sheet in the magnetospheric tail

Calculation of stationary distributions of the most important plasma parameters (particle energy, density, field-aligned and transversal pressure) is performed for a model magnetotail plasma sheet which is formed by convecting plasma mantle particles injected into the closed geomagnetic field line tubes. Computations have been done for two convection models: (i) a model of completely adiabatic particle motion with conservation of the first two invariants and (ii) a model with a strong pitch-angle diffusion which maintains isotropy. It is found that in both cases the heating and compression of the plasma are somewhat more effective than is necessary to account for the observed gradients of magnetic field in the magnetospheric tail. A leakage of accelerated particles through the dawn and dusk edges of the plasma sheet is proposed as a possible mechanism for maintenance of stationary convection in the magnetotail. The question of the dependence of the stationary magnetotail parameters on the solar wind state is discussed briefly.     

SCR Distribution Function in the Radial IMF Approximation

The transport of cosmic rays in the interplanetary medium is considered in terms of the kinetic equation describing the energetic particle scattering by magnetic irregularities and their focusing by the regular interplanetary magnetic field. The analytical expression for solar cosmic ray distribution function in the approximation of radial regular magnetic field is obtained and the evolution of energetic particle angular distribution is analyzed. The obtained results can be used for the analysis of ground-level enhancements of cosmic ray intensity.     

SCR Steady State Distribution Function and Scattering Properties of the Interplanetary Medium

The propagation of energetic particles in the interplanetary space is considered on the basis of kinetic equation describing the scattering of charged particles by magnetic irregularities and the particle focusing by regular magnetic field. Our analysis confirms that angular distribution of solar cosmic rays contains a valuable information about properties of the particle scattering in the interplanetary magnetic field. Steady state solutions of the kinetic equation are applied to the analysis of solar proton events.     

Precipitation of charged particles by a parallel electric field

A time-dependent model of the effect of a parallel electric field on particle precipitation from a closed field-line has been constructed and the results are presented. A pattern of field-aligned pitch-angle distributions and energy peaks develops rapidly and then persists unchanged in shape while the intensity decreases for a time of the order of the bounce period of the energetic particles. It is shown that the structures in velocity space are created by the juxtaposition of particles from different source populations. Four sources are found to be sufficient to reproduce the principal features observed frequently by rockets and satellites. They are, a trapped plasma sheet distribution, a loss-cone partially filled by pitch-angle diffusion at the equator, cold ionospheric plasma which has flowed outward along the field line and particles backscattered from the precipitation into the atmosphere.The model develops density gradients and discontinuities far sharper than any observed, so that any parallel electric field actually occurring in an aurora must be accompanied by strong wave-particle interactions either as part of the accelerating mechanism or as a result of the density gradients produced by it.     

磁重联电流片的参数变化对电子加速的影响

通过采用试验粒子的方法,研究了在有引导磁场Bz存在的磁重联电流片中,电子被super-Dreicer电场Ez加速后的运动特征.首先,考虑了引导磁场恒定且与电场有不同方向时对粒子加速的影响.在这种情况下,Bz方向的改变直接改变了电子的运动轨迹,使其沿着不同的路径离开电流片.在Bz和Ez同向时,高能电子的pitch-angle接近于180°.然而,当2者反向时,高能电子的pitch-angle接近0°.引导磁场的取向只是使电场有选择地对不同区域的电子进行加速,不会最终影响电子的能量分布,最终得到的能谱是普遍的幂率谱E-γ.在典型的日冕条件下, γ大约等于2.9.进一步的研究表明γ的大小依赖于引导磁场及磁重联电场的强弱,以及电流片的尺度.随后,也研究了包含多个X-点和O-点电流片中被加速粒子的运动特征.结果表明X-点和O-点的存在使得粒子被束缚在加速区并获得最大的加速,而且最终的能谱具有多幂率谱的特征.     

Energetic particle acceleration in a three-dimensional magnetic field reconnection model: the role of magnetohydrodynamic turbulence

The role of magnetohydrodynamic (MHD) turbulence in the cosmic ray acceleration process in a volume with a reconnecting magnetic field is studied by means of Monte Carlo simulations. We performed modelling of proton acceleration, with the three-dimensional analytic model of stationary reconnection of Craig et al. providing the unperturbed background conditions. Perturbations of particle trajectories resulting from a turbulent magnetic field component were simulated using small-amplitude pitch-angle momentum scattering, enabling modelling of both small- and large-amplitude turbulence in a wide wavevector range. Within the approach, no second-order Fermi acceleration process is allowed. Comparison of the acceleration process in models involving particle trajectory perturbations with the unperturbed model reveals that the turbulence can substantially increase the acceleration efficiency, enabling much higher final particle energies and flat particle spectra.     

Field-aligned beams and reconnection in the jovian magnetotail

The release of plasma in the jovian magnetotail is observed in the form of plasmoids, travelling compression regions, field-aligned particle beams and flux-rope like events. We demonstrate that electrons propagate along the magnetic field lines in the plasma sheet boundary layer (PSBL), while close to the current sheet center the electron distribution is isotropic. The evidences of the counterstreaming electron beams in the PSBLs are also presented. Most of the field-aligned energetic ion beams are associated with the field-aligned electron beams and about half of them have the bipolar fluctuation of the meridional magnetic field component. Moreover they often show a normal velocity dispersion for the different species which fits well in the scenario of particle propagation from a single source. All features above are observed during jovian reconfiguration events which are typically bonded with plasma flow reversals. From all these characteristics, which are based on energetic particle and magnetic field measurements, we believe that the reconfiguration processes in the jovian magnetotail are associated with reconnection.     

A study of the magnetic helicity during eight HELIOS-observed solar proton events

We have studied the influence of the magnetic helicity on solar particle propagation using the IMF data observed by the HELIOS spacecraft in the range 0.31–0.95 AU, during eight solar proton events. For this, we have derived power and helicity spectra of the turbulence of the magnetic field during the time of the events. These are used to compute the particle pitch-angle scattering coefficients according to the quasi-linear theory (QLT) treatment of particle propagation in turbulent magnetic fields. The results show that in all the cases the helicity effects are negligible and the particle's mean free paths deduced from the pitch-angle diffusion coefficients are the same regardless of whether or not helicity effects are included in the calculations. The computed mean free paths are quite different in each case.Deceased 10 April, 1995.     

Diffuse auroral precipitation in the jovian upper atmosphere and magnetospheric electron flux variability

The deposition of energetic electrons in Jupiter's upper atmosphere provides a means, via auroral observations, of monitoring electron and plasma wave activity within the magnetosphere. Not only does particle precipitation indicate a potential change in atmospheric chemistry, it allows for the study of episodic, pronounced flux enhancements in the energetic electron population. A study has been made of the effects of such electron injections into the jovian magnetosphere and of their ability to provide the source population for variations in diffuse auroral emissions. To identify the source region of precipitating auroral electrons, we have investigated the pitch-angle distributions of high-resolution Galileo Energetic Particle Detector (EPD) data that indicate strong flux levels near the loss cone. The equatorial source region of precipitating electrons has been determined from the locations of Galileo's in situ measurements by tracing magnetic field lines using the KK97 model. The primary source region for Jupiter's diffuse aurora appears to lie in the magnetic equator at 15-40 RJ, with the predominant contribution to precipitation flux (tens of ergs cm⁻² s⁻¹ sr⁻¹) stemming from <30 RJ. Variability of flux for energetic electrons in this region is also important to the irradiation of surfaces and atmospheres for the Galilean moons: Europa, Ganymede, and Callisto. The average diffuse auroral precipitation flux has been shown to vary by as much as a factor of six at a given radial location. This variability appears to be associated with electron injection events that have been identified in high-resolution Galileo EPD data. These electron flux enhancements are also associated with increased whistler-mode wave activity and magnetic field perturbations, as detected by the Galileo Plasma Wave Subsystem (PWS) and Magnetometer (MAG), respectively. Resonant interactions with the whistler-mode waves cause electron pitch-angle scattering and lead to pitch-angle isotropization and precipitation.     

The Formation of Large-Scale Current Sheets within Magnetic Clouds

Magnetic clouds are a class of interplanetary coronal mass ejections (CME) predominantly characterised by a smooth rotation in the magnetic field direction, indicative of a magnetic flux rope structure. Many magnetic clouds, however, also contain sharp discontinuities within the smoothly varying magnetic field, suggestive of narrow current sheets. In this study we present observations and modelling of magnetic clouds with strong current sheet signatures close to the centre of the apparent flux rope structure. Using an analytical magnetic flux rope model, we demonstrate how such current sheets can form as a result of a cloud’s kinematic propagation from the Sun to the Earth, without any external forces or influences. This model is shown to match observations of four particular magnetic clouds remarkably well. The model predicts that current sheet intensity increases for increasing CME angular extent and decreasing CME radial expansion speed. Assuming such current sheets facilitate magnetic reconnection, the process of current sheet formation could ultimately lead a single flux rope becoming fragmented into multiple flux ropes. This change in topology has consequences for magnetic clouds as barriers to energetic particle propagation.     

The different transport regimes of pitch-angle scattering of energetic particles

Recently an advanced nonlinear diffusion theory for particle transport across the mean magnetic field has been developed. The method used in the derivation of the latter theory is based on the cosmic ray Fokker-Planck equation. In the present article we use the same approach to describe pitch-angle scattering and parallel spatial diffusion nonlinearly. Furthermore, we derive the quasilinear transport theory, the weakly nonlinear theory as well as the Bohm limit as special cases from our more general approach.     

Pitch-angle scattering of energetic protons in the magnetotail current sheet as the dominant source of their isotropic precipitation into the nightside ionosphere

Characteristics of the nightside isotropic precipitation of energetic protons during a period of 4 quiet days has been studied using data from the ESRO 1A satellite. The observed features of the equatorward precipitation boundary (its thickness, energy dependence, dynamics, dependence of its latitudinal position on the magnetic field at the geosynchronous orbit, etc.) were found to be in good agreement with calculations based on recent magnetospheric magnetic field models. We argue that the mechanism of non-adiabatic pitchangle scattering in the equatorial current sheet is a dominant source of isotropic precipitation of energetic protons observed in the nightside auroral zone. Observations of the isotropic precipitation boundary can be used for monitoring the changes in the magnetotail current intensity.     

On the non-adiabatic particle scattering in the earth''s magnetotail current sheet

The empirical model of disturbed magnetosphere of Tsyganenko and Usmanov (1982) and the semi-empirical model of the storm-time magnetospheric configuration of Tsyganenko (1981) are used to find the critical energy for non-adiabatic particle scattering in the midnight sector. Computed values of E_crit vs L are compared with the appropriate experimental data of Imhof et al. (1977). It is found that none of the considered models is able to reproduce the observed steep decrease of E_crit with L. The steepest slope is given by the Tsyganenko model which includes a current sheet with the finite thickness. The current sheet thickness is a crucial parameter in the non-adiabatic scattering problem. In discussion we point to natural limitations of an empirical model as far as the current sheet thickness is to be determined. Imhof et al.'s data as well as some magnetic field data sets seem to indicate that magnetosphere models incorporating a thin current sheet and allowing for the thickness dependence on the geocentric distance would probably be closer to reality than the considered models, at least during higher levels of magnetic activity.     

Nonlinear perturbation theory for cosmic ray propagation in random magnetic fields

A nonlinear perturbation theory is applied to the problem of pitch angle diffusion of energetic particles in random magnetic fields. To keep the analysis simple, the discussion is restricted to fluctuation fields, consisting of Alfvén waves. It is shown that the failure of quasilinear theory at small particle velocities parallel to the average field can be overcome by a statistically exact treatment of the particle orbits in the first order fields. In fact, for spherical power spectra which, in addition, do not fall off too steeply with increasing frequency, the conventional perturbation theory also leads to formally convergent expressions for the scattering mean free path. These results are shown to be quite satisfactory, even in a quantitative sense. For more general physically realistic power spectra, however, a divergence-free diffusion theory is indispensible. A simple representation for the resulting pitch-angle diffusion coefficient is suggested.     

Chaos-induced resistivity of collisionless magnetic reconnection in the presence of a guide field

One of the most puzzling problems in astrophysics is to understand the anomalous resistivity in collisionless magnetic reconnection that is believed extensively to be responsible for the energy release in various eruptive phenomena. The magnetic null point in the reconnecting current sheet, acting as a scattering center, can lead to chaotic motions of particles in the current sheet, which is one of the possible mechanisms for anomalous resistivity and is called chaos-induced resistivity. In many interesting cases, however, instead of the magnetic null point, there is a nonzero magnetic field perpendicular to the merging field lines, usually called the guide field, whose effect on chaos-induced resistivity has been an open problem. By use of the test particle simulation method and statistical analysis, we investigate chaos-induced resistivity in the presence of a constant guide field. The characteristics of particle motion in the reconnecting region, in particular, the chaotic behavior of particle orbits and evolving statistical features, are analyzed. The results show that as the guide field increases, the radius of the chaos region increases and the Lyapunov index decreases. However, the effective collision frequency, and hence the chaos-induced resistivity, reach their peak values when the guide field approaches half of the characteristic strength of the reconnection magnetic field. The presence of a guide field can significantly influence the chaos of the particle orbits and hence the chaos-induced resistivity in the reconnection sheet, which decides the collisionless reconnection rate. The present result is helpful for us to understand the microphysics of anomalous resistivity in collisionless reconnection with a guide field.