Cosmic-ray diffusive acceleration at shock waves with finite upstream and downstream escape boundaries

In the present paper we discuss the modifications introduced into the first-order Fermi shock acceleration process due to a finite extent of diffusive regions near the shock or due to boundary conditions leading to an increased particle escape upstream and/or downstream of the shock. In the simple example of the planar shock wave considered we idealize the escape phenomenon by imposing a particle escape boundary at some distance from the shock. The presence of such a boundary (or boundaries) leads to coupled steepening of the accelerated particle spectrum and decreasing of the acceleration time scale. It allows for a semi-quantitative evaluation and, in some specific cases, also for modelling of the observed steep particle spectra as a result of the first-order Fermi shock acceleration. We also note that the particles close to the upper energy cut-off are younger than the estimate based on the respective acceleration time scale. In Appendix A we present a new time-dependent solution for infinite diffusive regions near the shock allowing for different constant diffusion coefficients upstream and downstream of the shock.     

A numerical method to determine the electromagnetic field of the pulsar magnetosphere with inclined magnetic moment

A numerical method to determine the electromagnetic field of a steadily rotating magnetosphere with an inclined magnetic moment under a given boundary condition on an arbitrary shaped boundary surface is presented. The region may include the light cylinder. The present method, together with a companion method giving particle motion and creation, makes an iterative scheme to obtain a global model of the pulsar magnetosphere. A key problem for explaining the particle acceleration in pulsars is to solve field-aligned electric field in an accelerating region bounded by an ideal-MHD region. The present method is fit to connect a solution for the non-ideal-MHD region with another solution for the ideal-MHD region on a boundary surface whose location should also be solved (i.e., a floating boundary). The integration scheme is based on the boundary element method and it has great advantage as compared with other methods like the finite difference method and the Fourier transformation method.     

Heliospheric propagation of galactic cosmic rays depending on the scattering characteristics of the turbulent interplanetary magnetic field

The effect of the solar wind on the spectrum of cosmic rays accelerated in the Galaxy is studied. The coefficient of cosmic-ray diffusion in the interplanetary turbulent magnetic field is assumed to be independent of the particle energy and a power-law function of the distance from the Sun. The particle spectrum at the heliospheric boundary is specified as a power-law function of the total particle energy.     

Galactic cosmic ray distribution in the simplest model of termination shock near the heliospheric boundaries

The termination shock at the heliospheric boundary is simulated in terms of a two-layer turbulent medium for which the average radial component of solar wind velocity is nonzero inside the heliosphere and zero for external magnetic inhomogeneities. Galactic cosmic rays (GCRs) are scattered more strongly in the solar wind than in the interstellar medium. A boundary value problem for density is defined to describe GCR propagation in the given two-layer medium. The exact analytical solution of it is derived. The phase density and GCR fluxes in the whole range of the particle energies, as well as the degree of anisotropy of high-energy GCRs, are determined. The qualitative agreement of theoretical calculations and observed GCR distributions is obtained. In particular, in the region near the termination shock, an increase in the high-energy particle density and a decrease in the low-energy particle density are observed.     

Inhomogeneous models of the atmosphere of Saturn

Analyses of ultraviolet, visible, and near-infrared spectra of Saturn lead to an inhomogeneous atmospheric model, having a clear gas layer which lies above an absorbing particle layer which lies above an ammonia haze layer. The boundary between the clear layer and the absorbing particle layer is at a pressure of 0.2 atm in the equatorial region and 0.3 atm in the temperate region. The boundary between the absorbing particle layer and the haze layer is at the radiative-convective boundary. Observations of ammonia absorption lines indicate that sunlight penetrates the haze to the ammonia sublimation level at a depth of 1.1 atm. Absorbing particles cause the observed decrease in reflectivity from visible to ultraviolet wavelengths. Consideration of the wavelength variation of Mie scattering parameters leads to an upper limit of about 0.2 μm for the particle radii and a particle number density of 10³ cm^?3. Some possible particle compositions are discussed. Comparison of computed 3-0 and 4-0 band hydrogen quadropole line equivalent widths with observed values leads to a haze layer optical thickness above the ammonia sublimation level of approximately 10. Equivalent widths computed for an equilibrium distribution of states agree better with observed values than those computed for a normal distribution. Methane 3ν₃ band manifold equivalent widths are in best agreement with measured equivalent widths for a CH₄/H₂ abundance ratio of 2 × 10^?3, which is 4.5 times the solar C/H ratio.     

Estimates of the wind speeds required for particle motion on Mars

We have obtained estimates of the threshold wind speed V_gt near the top of the atmospheric boundary layer on Mars and of the rotation angle α between this wind velocity and the direction of the surface stress. this calculation has been accomplished by combining wind tunnel determinations of the friction velocity with semi-empirical theories of the Earth's atmospheric boundary layer. Calculations have been performed for a variety of values of the surface pressure, ground temperature, roughness height, boundary layer height, atmospheric composition atmospheric stability, particle density, particle diameter, and strength of the cohesive force between the particles.The curve of threshold wind speed as a function of particle diameter monotonically decreases with decreasing particle diameter for a cohesionless soil but has the classical $\text{U}$ shape for a soil with cohesion. Observational data indicate that the latter condition holds on Mars. Under “favorable” conditions minimum threshold wind speeds between about 50 and 100m/sec are required to cause particle motion. These minimum values lie close to the highest wind speeds predicted by general circulation models. Hence, particle motion should be an infrequent occurence and should be strongly correlated with nearness to small topographic features. The latter prediction is in accord with the correlation found between albedo markings and topographic obstacles such as craters. For equal wind speeds at the midpoint of the boundary layer, particle movement occurs more readily in general at night than during the day, more readily in the winter polar areas than the equatorial areas noon, and more readily for ice particles than for silicate particles.The boundary between saltating and suspendable particles is located at a particle diameter of about 100 μm. This value is close to the diameter at which the V_gt curve has its minimum. Hence, the wind can set directly into motion both saltating and larger-sized suspendable particles, but dust-storm-sized particles usually require impact by a saltating particle for motion to be initiated. Albedo changes occur most often in regions containing a mixture of dust-stoorm-sized particles and saltating particles. The threshold wind speed for surfaces containing large, nonerodible roughness elements can either be larger or smaller than the value for surfaces with only erodible material. The former condition for V_gt holds when the roughness height z₀ is less than about 1 cm and may be illustrated by craters that have experienced less erosion than their environs. The latter condition for V_gt may be partly responsible for albedo changes detected on the elevated shield volcano, Pavonis Mons. Values of the angle α generally lie between 10 and 30°. These figures place a modest limitation on the utility of surface albedo streaks as wind direction indicators.     

A note on adiabatic solutions of the one-dimensional current sheet problem

It has recently been shown that adiabatic solutions of the one-dimensional current sheet problem exist provided that magnetically trapped particles are included in the model together with the current-carrying untrapped “beam” particles. We show here that a formulation of the problem in terms of particle velocity and pitch angle is advantageous, and we derive some general properties of the solutions. In particular it is shown that there is, in general, no discontinuity in the value of the particle distribution function ? across the boundary in velocity space between “beam” and trapped particles, but that there will be a discontinuity in the gradients of ?. An example is given in which the beam population is of bi-Maxwellian form at the outer boundary of the current sheet.     

Low-energy particle events associated with sector boundaries

Onsets of some 40 to 45 low-energy proton events during the years 1957–1969 coincided in time with transits of well-defined sector boundaries across the Earth. These events can be interpreted as long-lived proton streams filling up some of the magnetic sectors, indicating an acceleration of protons which is not associated with typical proton-producing flares. The sharp onsets of these particle streams, as well as a deficiency of flare-associated particle events shortly before the boundary transit, indicate that in some cases magnetic sector boundaries can inhibit transverse propagation of low-energy particles in the solar corona or in interplanetary space.     

Wave Transformation and Scattering on Stationary Charged Particles in a Magnetoactive Plasma. I

The scattering and transformation of natural waves of a magnetoactive plasma on a heavy charged particle lying at a plane plasma—vacuum boundary is considered. The angular distribution and cross section for scattering (transformation) of high-frequency ordinary and extraordinary waves are investigated.     

Wave Transformation and Scattering on Stationary Charged Particles in a Magnetoactive Plasma. II

The transformation of upper-hybrid, lower-hybrid, and magnetosonic waves on a heavy charged particle lying at the plane boundary of a magnetoactive plasma is considered. The angular distribution of the radiation resulting from wave transformation is investigated. The transformation of a low-frequency magnetosonic wave is suggested as a possible mechanism for pulsar radio emission.     

Interplanetary diffusive shock acceleration: Exponential or power-law spectra?

A new method for solving the transport equation and boundary condition describing diffusive shock acceleration for interplanetary corotating interaction regions is provided. It involves inverting a quindiagonal matrix. Application of this method to realistic parameters indicates that the parallel diffusion coefficient magnitude is critical in determining whether observed particle distribution functions are exponential or power law.     

Confirmation of quiet pulsar model by the boundary element method

A method for solving the force-free surface problem for the pulsar magnetosphere is outlined. The given formulation is extended to an oblique rotator problem. Since we solve equation subject to the boundary values—i.e., the boundary element method (BEM) developed in Paper I is used—we can directly determine the force-free surface. Another merit of this method rests in the fact that we only use a two-dimensional grid, in spite of the problem being three-dimensional. A numerical calculation has been performed to confirm the solution by the particle method (Krause-Polstorff and Michel, 1985).     

The relationship between the harang discontinuity and the substorm injection boundary

A correlative study of characteristic features observed in the ATS-5 particle data, in the Chatanika electric field and ionospheric conductivity data has been performed. It is found that distinct variations in the electric field are observed at Chatanika at the onset of a precipitation event at geostationary orbit. This is probably the effect of the transient electric field inferred by McIlwain (1973). A turn in the meridional component from north to south is observed at Chatanika at about the same local time as the ATS-5 satellite is crossing the injection boundary. This turn in the electric field at Chatanika which is also related to strong particle precipitation is probably due to the crossing of the Harang discontinuity.     

The Leedey,Oklahoma, chondrite: Fall,petrology, chemistry and an unusual Fe,Ni-FeS inclusion

Abstract— The Leedey, Oklahoma, meteorite shower fell on 1943 November 25, following a fireball which was visible across much of southwestern Oklahoma and northcentral Texas. The shower produced 24 stones with a total mass of ～51.5 kg. The stones formed a strewnfield ～18 km in length in the same direction as the observed path of the meteor (N50°W). Leedey is classified as an L6(S3) ordinary chondrite. We report bulk major element chemical analyses from four separate laboratories. Leedey contains an unusual 6 by 8 mm composite Fe,Ni-FeS grain, which is composed of a 3 mm kamacite grain adjacent to a 5 mm troilite grain. A 50–100 μm rim of high-Ni (45–55 wt%) taenite (tetrataenite) occurs at the boundary between kamacite and troilite. A single, zoned pyrophanite grain is observed at the boundary between the inclusion troilite and host silicates. An origin as a foreign particle incorporated after metamorphism or during impact melting appears unlikely. This particle likely formed by a complex set of processes, including melting in the nebula, parent body metamorphism and reheating by later shock, mirroring the history of the host chondrite.     

The dawn polar cap boundary at high altitude

Comparison of hot plasma data from ATS-6 and GEOS-1 when the satellites were near dawn L.T. conjunction reveals the presence of strong gradients separating plasmas differing by more than two orders of magnitude in keV particle fluxes. These gradients are observed at off-equatorial geomagnetic latitudes of 25–30° on field lines outside the synchronous orbit. They are associated with magnetic storms and are distinct from magnetopause crossings. Interpretation of these events in terms of a boundary between magnetospheric and polar-cap plasma leads to the following conclusions: (1) the polar cap/lobe region is essentially devoid of keV plasma at these times; (2) the field lines defining this boundary are significantly distorted from a dipolar to a more stretched form consistent with the presence of a storm-ring current, (3) smaller substorm-scale motions are superposed on the gross motion of the boundary with some evidence present for structure in the plasma spatial profile, and (4) magnetosheath-like plasma finds access to the inner magnetosphere at dawn L.T., much as it does near noon, along polar-cap boundary-layer field lines which close through the low latitude magnetospheric boundary layer.     

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.     

Comment on element fractionation in the solar atmosphere driven by ionization-diffusion processes

It is emphasized that one-dimensional, steady-state models of a photoionization layer in which incoming photon fluxes ionize neutral particle fluxes cannot give rise to enhancements or depletions of one element over another. The so-called fractionation mechanism proposed by Marsch, von Steiger, and Bochler (1995) and Peter (1996, 1998) is shown to be a fallacy arising from applying an incorrect boundary condition at an arbitrary point.     

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.     

Persistent particle anisotropies and magnetospheric models

The influence of an interplanetary particle anisotropy on the asymmetry of solar particle entry into the magnetotail is analysed in the diffusion as well as in the reconnection model. By time dependent diffusion calculations with an asymmetric boundary condition in a cylindrical tail lobe it can be shown that a north-south interplanetary anisotropy leads in the open as well as in the closed magnetosphere to essentially the same polar cap structures when observed with a dawn-dusk polar orbiting satellite. However, depending on the satellite orbit, an east-west interplanetary anisotropy can serve to distinguish between rival magnetospheric models. Comparison of our diffusion calculations with polar cap measurements during an east-west interplanetary anisotropy, as presented in Morfill and Scholer (1972), show a large discrepancy, whereas an open tail model fits these observations best.     

Solar wind access to the plasma sheet along the flanks of the magnetotail

Low-energy particle trajectories in an idealized magnetotail magnetic field are investigated to determine the accessibility of magnetosheath protons and electrons to the plasma sheet along the flanks of the tail magnetopause. The drift motion of the positively (negatively) charged particles incident on the dawn (dusk) magnetotail flank causes such particles to penetrate deeper into the magnetotail. For certain combinations of particle energy, incident velocity vector and initial penetration point on the tail magnetopause, the incident particles can become trapped in the plasma sheet, after which their net drift motion then provides a current capable of supporting the entire observed magnetotail field. The results further indicate that the bulk of the solar wind plasma just outside the distant tail boundary, which streams preferentially in a direction along the magnetopause away from the Earth at velocities around 400 km s^?1, can be caught up in the tail if the initial penetration point is within about 2R_E, of the quasi-neutral sheet. It is suggested that a large fraction of the magnetotail plasma is composed of former solar wind particles which have penetrated the magnetospheric boundary at the tail flanks.