Interplanetary propagation of relativistic solar protons

Particle fluxes and pitch angle distributions of relativistic solar protons at Earth's orbit have been determined by Monte Carlo calculations. The analysis covers two hours after the release of the particles from the Sun and total of 8 × 10⁶ particle trajectories were simulated. The pitch angle scattering was assumed to be isotropic and the scattering mean free path was varied from 0.1 to 4 AU.The intensity-time profiles after a delta-like injection from the Sun show that the interplanetary propagation is clearly non-diffusive at scattering mean-free paths above 0.5 AU. All pitch angle distributions have a steady minimum at 90 °, and they become similar about 20 min after the arrival of first particles.As an application, the solar injection profile and the interplanetary scattering mean-free path of particles that gave rise to the GLE on 7 May, 1978 were determined. In contrast to the values of 3–5 AU published by other authors, the average scattering mean-free path was found to be about 1 AU.     

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.     

Proton observations supporting the ion cyclotron wave heating theory of SAR arc formation

Low altitude satellite observations of precipitated and locally mirroring protons during periods of ground-based SAR arc observations are presented. The SAR arcs are found to be located in a region with significantly enhanced proton pitch angle scattering and enhanced electron temperature, but inside the plasmapause where the proton pitch angle distribution is anisotropic. The increase in the pitch angle scattering takes place in a localized region having a width of a few tenths of a L-value. The observations can favourably be accounted for by the Cornwall et al. (1971) theory for the SAR arc formation. Using observed proton fluxes and typical energy spectra, the expected Hβ intensity in the SAR arc region is estimated to be a few Rayleighs, and the energy flux from precipitated protons above a few keV to be 10^?2?10^?1erg/cm²s. These estimates are in reasonable agreement with previously published theoretical and experimental values. Simultaneous groundbased observations of Hα emissions were found in the region of intense, isotropic proton precipitation located outside the plasmapause.     

3-Dimensional Energetic Particle Distribution Past an Instantaneous Uni-Directional Injection

The exact analytic expression for the density of energetic charged particles, which were injected by an instantaneous point source at a particular pitch angle into the interplanetary medium, has been derived. We start from the Boltzmann kinetic equation with the collision integral describing the isotropic particle scattering by "massive" magnetic clouds. The solution has been obtained without any expansion parameters in the 3-dimensional vector form, then it was projected into the cylindrical coordinate system. The space-time particle distribution is disscussed. This revised version was published online in July 2006 with corrections to the Cover Date.     

Pitch angle diffusion by bounce resonance

The paper aims at removing the restriction x ? 1 (where x is the cosine of the equatorial pitch angle) in the theory of pitch angle diffusion by bounce resonance. When the fourth order anharmonicity term is included in the expansion of the magnetic field around the equator, the parallel displacement of a particle becomes a superposition of the first and third harmonics of the fundamental frequency. The diffusion coefficient for pitch angle scattering by bounce resonance has been evaluated by taking into consideration the anharmonicity effects, and this expression can be expected to be valid for particles which mirror at higher latitudes also.     

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.     

Energy and pitch angle distributions for auroral ions using the current sheet acceleration model

Using a dipole plus tail magnetic field model, H⁺, He⁺⁺ and O ₁₆ ⁺⁶ ions are followed numerically, backward in time, from an output plane perpendicular to the axis of the geomagnetic tail, to their point of entrace to the magnetosphere as solar wind particles in the magnetosheath. An adiabatic or guiding center approximation is used in regions where the particles do not interact directly with the current sheet. A Maxwellian distribution with bulk flow is assumed for solar wind particles in the magnetosheath. Bulk velocity, density, and temperature along the magnetopause are taken from the fluid calculations of Spreiter. Using Liouville's theorem, and varying initial conditions at the output plane, the distribution function is found as a function of energy and pitch angle at the output plane. These results are then mapped to the auroral ionosphere using guiding center theory. Results show that the total precipitation rate is sufficient only for particles which enter the magnetosphere near the edges of the current sheet. Small pitch angles are favored at the output plane, but mappings to the auroral ionosphere indicate isotropic pitch angle distributions are favored with some peaking of the fluxes parallel or at other angles to the field lines. Perpendicular auroral pitch angle anisotropies are at times produced by the current sheet acceleration mechanism. Therefore, caution must be used in interpreting all such observations as ‘loss cone-trapping’ distributions. Energy spectra appear to be quite narrow for small cross-tail electric fields, and a little broader as the electric field increases. Comparisons of these results with experimental observations are presented.     

Observations of energetic ions in inverted V events

Simultaneous measurements of keV ions and electrons with the ESRO 1A satellite have shown the following ion characteristics among others. Ions of about 6 keV energy are strongly field-aligned on the flanks of the inverted V events (mainly through the disappearance of the ion flux near 90° pitch angle). Field-aligned electron fluxes are often found in the same regions of the inverted V events where the ions are field-aligned. At the centre of inverted V events isotropization occurs (except in some small events). The 1 keV ion flux at large pitch angles (80°) is generally not reduced very much when the 6 keV, 80° ion flux shows strongly decreased values. The ratio of the 1 to 6 keV ion flux has a maximum near the centre of an inverted V event where the electron spectrum is hardest and the 6 keV ions are isotropic (or nearly isotropic).The observations are interpreted in terms of a model with two oppositely directed field-aligned electrostatic potential drops: one upper accelerating electrons downward and one lower, produced by the electron influx, which accelerates ions downward. Ion scattering in turbulent wave fields is proposed to be responsible for the observation that the 1 keV ion flux at large pitch angles does not decrease strongly where the 6 keV ion flux does and as an explanation of the isotropization at the centre of the event. The source problem for the ions is eliminated by the precipitating electrons ionizing continuously the thin neutral atmosphere even at altitudes of a few thousand kilometers.     

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.     

Field line topology in the dayside cusp region inferred from low altitude particle observations

Dayside low altitude satellite observations of the pitch angle and energy distribution of electrons and protons in the energy range 1 eV to 100 eV during quite geomagnetic conditions reveal that at times there is a clear latitudinal separation between the precipitating low energy (keV) electrons and protons, with the protons precipitating poleward of the electrons. The high energy (100 keV) proton precipitation overlaps both the low energy (keV) electron and proton precipitation. These observations are consistent with a model where magnetosheath particles stream in along the cusp field lines and are at the same time convected poleward by an electric field.The electrons with energies of a few keV move fast and give the “ionospheric footprint” of the distant cusp. The protons are partly convected poleward of the cusp and into the polar cap. Here the mirroring protons populate the plasma mantle. Equatorward of the cusp the pitch angle distribution of both electrons and protons with energies above a few keV is pancake shaped indicating closed geomagnetic field lines. The 1 keV electrons, penetrate, however, into this region of closed field line structure maintaining an isotropic pitch angle distribution. The intensity is, however, reduced with respect to what it was in the cusp region. It is suggested that these electrons, the lowest energies measured on the satellite, are associated with the entry layer.     

Pitch-angle distributions in and near the loss cone of (100–350) keV protons

The pitch-angle distributions in and near the loss cone, of ～ (100–200) and ～ (200–350) keV protons observed by the ESRO IB satellite during the period 7–15 October 1969 are presented. The data include periods of relative quiet as well as more disturbed geomagnetic conditions. Spatial characteristics and dynamics of the protons, both on the night-and dayside of the Earth are described. The actual pitch-angle distribution is interpreted as produced by wave-particle interactions, and the diffusion coefficient and lifetime against pitch angle scattering have been estimated from existing theories. During slightly disturbed conditions, the observations suggest an average random walk in pitch angle made by a particle during a crossing of the diffusion region of about one half of the loss cone half angle for 4 ? L ? 6. The lifetime against pitch angle scattering into the loss cone is found to be somewhat less than the charge exchange lifetime for these (100–350) keV protons. The spectral density of interacting waves is tentatively estimated to about 0·1 $\text{γ}{}^2\text{Hz}$, and compares with estimates arrived at from completely different approaches.     

The self-consistent geomagnetic tail under static conditions

A self-consistent calculation of the magnetic field and plasma distribution in the magnetotail has been undertaken for static conditions. We find the best agreement with experimental observations by satellite in the tail for an isotropic particle pitch angle distribution, a slow decrease of magnetic field intensity as a function of distance from the Earth |x|^−0.3, and a northward field in the equatorial plane of about 1 gamma at the position of the lunar orbit. Knowing the field and plasma distribution we calculate the sources of the electrical current and find that the magnetic field in the tail can be supported entirely by solar wind drifting into the curved and diminishing magnetic field of the magnetotail. Furthermore the plasma present in the tail at any one instant is swept out in a very short time due to its large curvature drift velocity; the constant plasma sheet is maintained by constant renewal of entering solar wind plasma.     

Electron reflectometry in the martian atmosphere

The technique of electron reflectometry, a method for remote estimation of planetary magnetic fields, is expanded from its original use of mapping crustal magnetic fields at the Moon to achieving the same purpose at Mars, where the presence of a substantial atmosphere complicates matters considerably. The motion of solar wind electrons, incident on the martian atmosphere, is considered in detail, taking account of the following effects: the electrons' helical paths around the magnetic field lines to which they are bound, the magnetic mirror force they experience due to converging field lines in the vicinity of crustal magnetic anomalies, their acceleration/deceleration by electrostatic potentials, their interactions with thermal plasma, their drifts due to magnetic field line curvature and perpendicular electric fields and their scattering off, and loss of energy through a number of different processes to, atmospheric neutrals. A theoretical framework is thus developed for modeling electron pitch angle distributions expected when a spacecraft is on a magnetic field line which is connected to both the martian crust and the interplanetary magnetic field. This framework, along with measured pitch angle distributions from the Mars Global Surveyor (MGS) Magnetometer/Electron Reflectometer (MAG/ER) experiment, can be used to remotely measure crustal magnetic field magnitudes and atmospheric neutral densities at ∼180 km above the martian datum, as well as estimate average parallel electric fields between 200 and 400 km altitude. Detailed analysis and full results, concerning the crustal magnetic field and upper thermospheric density of Mars, are left to two companion papers.     

Some implications of low altitude observations of isotropic precipitation of ring current protons beyond the plasmapause

The precipitation patterns of 6 keV protons at 10° and 80° pitch angles have been mapped at altitudes <1500 km from the ESRO 1A and 1B spacecraft. Equatorward of the trapping boundary, a region of isotropic precipitation, bounded on its equatorward border by a region of anisotropic (depleted loss cone) precipitation, is always observed. The latitudinal location of this transition appears to be nearly spatially coincident with the plasmapause. Similar precipitation patterns are shown to exist for higher energy protons. The general absence of enhanced precipitation at the plasmapause suggests that the inner boundary of the ring current is not usually produced by an enhanced proton pitch angle diffusion process. The isotropic precipitation observed beyond the plasmapause is most consistent with the occurence of an electrostatic instability throughout the ring current zone. It is doubtful whether the proposed cold Li plasma seeding experiments beyond the plasmapause could significantly increase the observed natural proton precipitation rates.     

Solar protons on closed magnetospheric field lines after an interplanetary flux decrease

Particle measurements from the low altitude polar-orbiting satellite GRS-A/Azur and from Explorer 41 in the magnetosheath during a time period after the sudden commencement at 14:30 UT on 8 March 1970, have been used in order to study the access mode of solar particles into the closed field line region of the magnetosphere. A particle decrease in the magnetosheath and over the central polar cap but not in the stable trapping region indicates that solar particles are temporarily trapped and can complete several drifts around the Earth. A single loss cone distribution ～2° inside of the stable trapping region cannot be explained by strong pitch angle scattering but is probably due to non-adiabatic particle motion.     

Rocket observation of conjugate photoelectrons in the predawn ionosphere

Photoelectron flux in the energy range 6–70 eV coming from the sunlight conjugate ionosphere has been measured directly by the rocket borne low energy electron spectrometer in the altitude region of 210–350 km. Pitch angle distribution of the measured flux is nearly isotropic, the flux decreasing slightly with pitch angle. The photoelectron fluxes measured at 350 km at the energies of 15 and 30 eV are 3 × 10⁶ and 1 × 10⁶ (cm² s str eV)^?1 respectively which decrease to 1 × 10⁶ and 1 × 10⁵ at 250 km at the same energies. These values are consistent with the vertical profile of the 630 nm airglow intensity measured simultaneously. The fluxes obtained near apogee show peaks in the range 20–30 eV which also appear in the daytime photoelectron flux, indicating reduced loss of electrons during the passage from the conjugate ionosphere through the plasmasphere at the low geomagnetic latitude where observation was made. Photoelectron fluxes observed below the apogee height are compared to the calculated fluxes to investigate the interaction of electrons with the atmospheric species during the passage in the ionosphere. Calculated fluxes obtained by using continuous slowing-down approximation and neglecting pitch angle scattering are in good agreement with the observations although there still remain disagreements in detailed comparison which may be ascribed to the assumptions inherent in the calculation and/or to the uncertainties of the input data for the calculation.     

Motion of charged particles in the magnetosphere

The adiabatic motion of charged particles in the magnetosphere has been investigated using Mead-Fairfield magnetospheric field model (Mead and Fairfield, 1975). Since the motion of charged particles in a dipolar field geometry is well understood, we bring out in this paper some important features in characteristic motion due to non-dipolar distortions in the field geometry. We look at the tilt averaged picture of the field configuration and estimate theoretically the parameters like bounce period, longitudinal invariant and the bounce averaged drift velocities of the charged particle in the Mead-Fairfield field geometry. These parameters are evaluated as a function of pitch angle and azimuthal position in the region of ring current (5 to 7 Earth radii from the centre of the Earth) for four ranges of magnetic activity. At different longitudes the non-dipolar contribution as a percentage of dipole value in bounce period and longitudinal invariant show maximum variation for particles close to 90° pitch angles. For any low pitch angle, these effects maximize at the midnight meridian. The radial component of the bounce averaged drift velocity is found to be greatest at the dawn-dusk meridians and the contribution vanishes at the day and midnight meridians for all pitch angles. In the absence of tilt-dependent terms in the model, the latitudinal component of the drift velocity vanishes. On the other hand, the relative non-dipolar contribution to bounce averaged azimuthal drift velocity is very high as compared to similar contribution in other characteristic parameters of particle motion. It is also shown that non-dipolar contribution in bounce period, longitudinal invariant and bounce averaged drift velocities increases in magnitude with increase in distance and magnetic activity.     

Angular distribution of photoelectrons from atomic oxygen,nitrogen and carbon

The angular distributions of photoelectrons from atomic oxygen, nitrogen and carbon are calculated. Both Hartree-Fock and Hartree-Slater (Herman-Skillman) wave functions are used for oxygen and the agreement is excellent; thus only Hartree-Slater functions are used for carbon and nitrogen. The pitch angle distribution of photoelectrons is discussed and it is shown that previous approximations of energy independent isotropic or sin² θ distributions are at odds with our results, which vary with energy. This variation with energy is discussed as is the reliability of these calculations.     

Exact solution of the equation of radiative transfer for semi-infinite plane-parallel isotropic scattering atmosphere with scattering albedo ω0 ≤ 1 by a method based on Laplace transform and Wiener-Hopf technique

By performing the one-sided Laplace transform on the scalar integro-differential equation for a semi-infinite plane-parallel isotropic scattering atmosphere with a scattering albedo ₀ 1, an integral equation for the emergent intensity has been derived. Application of the Wiener-Hopf technique to this integral equation will give the emergent intensity. The intensity at any optical depth for a positive scattering angle is also derived by inversion. The intensity at any optical depth for a negative scattering angle is also derived in terms of Cauchy's principal value using Plemelj's formulae.     

Electrostatic electron cyclotron harmonic instability near Ganymede

Jupiter’s moon—Ganymede—is the largest satellite in our solar system. Galileo spacecraft made six close flybys to explore Ganymede. More information was acquired about particle population, magnetic field and plasma waves during these encounters. In this paper, our aim is to study the generation of electrostatic electron cyclotron harmonic (ECH) emissions in the vicinity of Ganymede using the observed particle data. The calculated ECH wave’s growth rates are analyzed in the light of observations of plasma waves along the path of Galileo near Ganymede. Dispersion relation for electrostatic mode is solved to obtain the temporal growth rates. A new electron distribution function, fitted to distribution observed near Ganymede, is used in the calculations. A parametric study is performed to evaluate the effect of loss-cone angle and the ratio of plasma to gyro-frequency on growth rates. It is found that ECH waves growth rates generally decrease as the loss-cone angle is increased. However, the ratio plasma to gyro-frequency has almost no effect on the growth rates. These parameters vary considerably along the Galileo trajectory near Ganymede. This is the first study which relates the occurrence of ECH waves with the particle and magnetic field data in the vicinity of Ganymede. The study of ECH wave growth rate near Ganymede is important for the calculation of pitch angle scattering rates of low-energy electrons and their subsequent precipitation into the thin atmosphere of Ganymede producing ultraviolet emissions. Results of the present study may also be relevant for the upcoming JUNO and JUICE missions to Jupiter.