Pitch-angle scattering of energetic particles in the current sheet of the magnetospheric tail and stationary distribution functions

An investigation of pitch-angle scattering of energetic particles in magnetic field configurations with a current sheet similar to that observed in the geomagnetotail has been performed. The magnetic field model is specified by two parameters which are the current sheet thickness in units of particle gyroradius and the angle between the magnetic field lines and the sheet plane. Computations of a considerable number of trajectories (about 20,000 for each model case) has provided the possibility of obtaining the matrix of pitch-angle scattering and the corresponding kernel function of the integral equation for the stationary particle distribution function. Solution of this equation shows that isotropic distributions are formed only in the case of a sufficiently thick current sheet. Particle scattering in a thin field reversal region leads to the formation of an anisotropic stationary distribution. The results can be used for interpretation of the data on the spatial distribution of energetic particle fluxes in the near part of the magnetospheric tail and in the vicinity of the outer boundary of the radiation belt.     

Motion of energetic particles in a magnetospheric model including a convection electric field

A magnetospheric model including convection and corotation electric fields is developed. Drift shells and pitch-angle evolution are obtained through perturbation methods. The asymmetry of the shell is maximum in a plane different from the noon-midnight meridian. As a consequence the dip in fluxes is not maximum in this meridian and the amount of shift is shown to be directly proportional to the convection electric field intensity. It is inversely proportional to the energy or the pitch-angle of the particles.     

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.     

Initial pitch-angle of narrowly beamed electrons injected into a magnetic mirror,formation of trapped and precipitating electron distribution,and asymmetry of hard X-ray and microwave footpoint emissions

A new kind of static distribution function for trapped and precipitating electrons is derived by solving a time-independent Fokker–Planck equation in a magnetic mirror, with injection of initially narrow-beamed electrons at an arbitrary initial pitch-angle. There are two independent parameters to determine the ratio of trapped and precipitating electrons, as well as their emissions, i.e., the mirror ratio and the initial pitch-angle, which is helpful for understanding some new features of asymmetrical hard X-ray and microwave footpoint emissions in solar observations.     

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.     

Particle populations in Mercury's magnetosphere

Observations by Mariner 10 during its first and third flybys showed that Mercury possesses an intrinsic magnetic field resulting in a small magnetosphere that can keep the solar wind from directly interacting with the planet's surface under usual conditions. Since Mercury occupies a large fraction of its magnetosphere, regions of trapped charged particles in the inner magnetosphere, the plasmasphere and the energetic radiation belts, would all be absent. During the first flyby, energetic particle bursts were detected and interpreted as hermean substroms analogous to the terrestrial magnetosphere. Moreover, during this flyby, ULF waves and field-aligned currents were detected in the data. Earth-based observations of Na, K, and Ca populations in the exosphere strongly suggest the existence of dynamic magnetospheric processes at high latitudes interacting with the planet's surface.     

Electron precipitation in a non-uniform glow aurora

Electron intensities at 5 keV >18 keV and >45 keV, were measured on a Petrel rocket flown from Kiruna, Sweden, into a non-uniform glow aurora during the recovery phase of a magnetic bay. The intensities depend on pitch-angle in a way that is consistent with the precipitation being caused by pitch-angle diffusion from reservoirs of geomagnetically-trapped electrons. The scattering process that causes pitch-angle diffusion, and leads to three regions of relatively high intensity, appears to have properties different from the scattering process that leads to two intervening regions of low intensity. A spatial structure in electron reservoir intensity, is attributed mainly to variations in the rate of erosion by pitch-angle diffusion of an initially nearly-uniform reservoir intensity. An expression is derived for the minimum lifetime of trapped electrons undergoing strong pitch-angle diffusion.     

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.     

A theory of VLF emissions

The work attempts to give a theoretical explanation of the triggering of VLF emissions by magnetospheric whistler morse pulses. First studied is the behaviour of resonant particles in a whistler wave train in an inhomogeneous medium. It is found that second order resonant particles become stably trapped in the wave. After 1–2 trapping periods such particles dominate the resonant particle distribution function, and produce large currents that are readily estimated.     

Discrete VLF emissions (7–9 kHz) displaying unusual banded and periodic structure

Rising frequency VLF emissions having unusually high frequency and exhibiting banded structure were recorded between 14.55 and 15.30 U.T. on 28 June 1972 by the VLF goniometer receiver at Halley, Antarctica. The risers were split into two frequency groups, one with frequencies in the range 6.0–7.7 kHz and the other with frequencies between 7.8 and 9.4 kHz, the former being more numerous. The gap between the lower and upper frequency risers is superficially similar to, though at a higher frequency than, the missing bands in emissions observed by satellites. However, it is found to be unlikely that the risers received at Halley can be explained by any of the mechanisms advanced to explain the banded satellite-observed emissions. Several other explanations are considered and it is shown that the most likely is partial suppression by magnetospheric line radiation propagating in the same duct.The risers are interpreted as being generated via cyclotron resonance with counterstreaming electrons. A computer program based on Helliwell's (1967) phenomenological theory is used to determine the generation region and electron energies involved.Both frequency groups of risers display a 4 min periodicity in occurrence. It is shown that this time period is consistent with that required to replenish the flux of resonant electrons, by eastwards drift into the duct, after the emissions have been quenched due to the reduction of the flux by pitch-angle diffusion into the loss cone.     

Gyrosynchrotron Emission from Anisotropic Pitch-Angle Distribution of Electrons in 3-D Solar Flare Sources

We present calculations, made for the first time, of the gyrosynchrotron emission by mildly relativistic electrons with anisotropic pitch-angle distribution using a realistic magnetic loop model in three dimensions. We investigated the intensity, spectral index of the optically thin region of the spectrum, the spatial morphology and the dependency on the source position on the solar disk. The method to describe a three-dimensional source and the procedure to perform the calculations are presented. We have modified the Ramaty’s gyrosynchrotron code to allow the evaluation of anisotropic pitch-angle electron distributions, as described in the complete formalism. We found that anisotropic electron distributions affect the intensity of the radiation, spatial morphology and spectrum of spatially resolved sources. However, the spatially integrated spectrum of the emission seems to be insensitive to the electron pitch-angle distribution, as the magnetic field inhomogeneity smooths out the effects of the anisotropic distribution in the produced radiation, in contrast to homogeneous sources.     

Magnetospheric environments of outer planet rings: Influence of Saturn's axially symmetric magnetic field

The Jovian and Uranian rings exist within severe energetic particle and plasma environments where magnetosphere-related losses of small ring particles and surface reflectance alteration by sputtering are likely to be important. In contrast, the main Saturnian rings exist within a zone where magnetospheric losses and surface alteration effects are negligible, primarily because of solid-body absorption of inwardly diffusing magnetospheric particles. It is shown here that solid-body absorption of radially diffusing ions is a much more efficient process in the inner Saturnian magnetosphere than in the inner Jovian and Uranian magnetospheres because of the near axial symmetry of the planetary magnetic field with respect to the rotational equatorial plane. This is especially true for continuous rings (as opposed to satellites) for which the approximate time scale against absorption is the particle bounce period in an axially symmetric field, whereas it is the particle drift period in an asymmetric field. Assuming comparable diffusion rates, inward transport of magnetospheric particles is much more strongly inhibited in the inner Saturnian magnetosphere than in the inner magnetospheres of Jupiter and Uranus. This remains true when only rings of comparable widths and optical depths are considered (e.g., the F ring at Saturn and the ϵ ring at Uranus). The most extreme possible consequence of this difference in solid-body absorption efficiency may have been the preferential development of a radially extensive, optically thick ring system at Saturn where magnetospheric losses are minimized in comparison to those at Jupiter and Uranus. A more definite consequence is that the Uranian rings are most probably directly exposed to nearly the same proton fluxes measured at Voyager 2's closest approach. Exposure of ring particle surfaces to radiation belt ion fluxes therefore remains as a viable explanation for the low albedos of the Uranian rings.     

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.     

Jovian magnetosphere-ionosphere current system characterized by diurnal variation of ionospheric conductance

We developed a new numerical model of the Jovian magnetosphere-ionosphere coupling current system in order to investigate the effects of diurnal variation of ionospheric conductance. The conductance is determined by ion chemical processes that include the generation of hydrogen and hydrocarbon ions by solar EUV radiation and auroral electrons precipitation. The model solves the torque equations for magnetospheric plasma accelerated by the radial currents flowing along the magnetospheric equator. The conductance and magnetospheric plasma then change the field-aligned currents (FACs) and the intensity of the electric field projected onto the ionosphere. Because of the positive feedback of the ionospheric conductance on the FAC, the FAC is the maximum on the dayside and minimum just before sunrise. The power transferred from the planetary rotation is mainly consumed in the upper atmosphere on the dayside, while it is used for magnetospheric plasma acceleration in other local time (LT) sectors. Further, our simulations show that the magnetospheric plasma density and mass flux affect the temporal variation in the peak FAC density. The enhancement of the solar EUV flux by a factor of 2.4 increases the FAC density by 30%. The maximum density of the FAC is determined not only by the relationship between the precipitating electron flux and ionospheric conductance, but also by the system inertia, i.e., the inertia of the magnetospheric plasma. A theoretical analysis and numerical simulations reveal that the FAC density is in proportion to the planetary angular velocity on the dayside and to the square of the planetary angular velocity on the nightside. When the radial current at the outer boundary is fixed at values above 30 MA, as assumed in previous model studies, the peak FAC density determined at latitude 73°-74° is larger than the diurnal variable component. This result suggests large effects of this assumed radial current at the outer boundary on the system.     

Specific features of VLF wave propagation in the earth’s inner magnetosphere

The ray trajectories of waves in the very low frequency (VLF) range in the case of nonducted propagation in the earth’s inner magnetosphere are studied as functions of location of their source region, frequency, and initial angle between the vector of wave normal and intensity vector of external magnetic field. Simulation is performed on the basis of geometric ray tracing approach in multicomponent plasma. The parameters of the magnetospheric medium were calculated using a diffusion model of the concentration distribution of plasma components and the International Geomagnetic Reference Field (IGRF) model. It is shown that the magnetospheric wave reflection can occur if the lower hybrid resonance frequency is greater than its own wave frequency (ω _LHF > ω), i.e., at the latitudes λ ≈ 50°. The simulation results confirm that the quasi-longitudinal approximation cannot be used to describe the magnetospheric whistler propagation. We present simulations of propagation of chorus-type wave magnetospheric emissions that were performed using realistic wave distributions over initial parameters. In particular, we present distributions of chorus waves over directions of wave vector as functions of geomagnetic latitude; these distributions are required to study the particle scattering and acceleration processes in the radiation belts. Our results well agree with CLUSTER satellite measurements.     

Plasma magnetosphere of rotating magnetized neutron star in the braneworld

Plasma magnetosphere surrounding rotating magnetized neutron star in the braneworld has been studied. For the simplicity of calculations Goldreich-Julian charge density is analyzed for the aligned neutron star with zero inclination between magnetic field and rotation axis. From the system of Maxwell equations in spacetime of slowly rotating star in braneworld, second-order differential equation for electrostatic potential is derived. Analytical solution of this equation indicates the general relativistic modification of an accelerating electric field and charge density along the open field lines by brane tension. The implication of this effect to the magnetospheric energy loss problem is underlined. It was found that for initially zero potential and field on the surface of a neutron star, the amplitude of the plasma mode created by Goldreich-Julian charge density will increase in the presence of the negative brane charge. Finally we derive the equations of motion of test particles in magnetosphere of slowly rotating star in the braneworld. Then we analyze particle motion in the polar cap and show that brane tension can significantly change conditions for particle acceleration in the polar cap region of the neutron star.     

The satellites of Jupiter as a source of very energetic magnetospheric particles

The Jovian satellites and ring are continuously bombarded by high-energy galacic cosmic rays and magnetospheric ions. Nuclear interactions will create very energetic neutrons and pions. The decay of some of these unstable particles within the Jovian magnetosphere wil result in trapped protons and ultrarelativistic electrons and positrons. Although this source is weak compared to those that yield lower-energy magnetospheric particles, it is expected to generate the most energetic Jovian particles. These processes are briefly described.