Mean free paths of energetic charged particles parallel and antiparallel to the interplanetary magnetic field

A new method to calculate the mean free paths of energetic particles propagating parallel and anti-parallel to the interplanetary magnetic field, based on quasi-linear theory and the complex spectral polarization analysis of the field, is developed and presented. Applications of the method using HEOS 2 (1 AU), Pioneer 10 (5 AU), Pioneer 11 (20 AU), ICE (Giacobini-Zinner's comet) data have been made, showing that: (a) The mean free paths parallel and anti-parallel to the field can be completely different in various regions of the interplanetary medium and different time periods. (b) Particles are preferentially scattered in one direction. (c) The parallel and anti-parallel mean free paths become equal at certain energy. Comparisons with the results from another computational method are made.     

Dynamics of charged particles and perpendicular diffusion in turbulent magnetic field

A test particle code is employed to explore the dynamics of charged particles and perpendicular diffusion in turbulent magnetic field, where a three-dimensional (3D) isotropic turbulence model is used in this paper. The obtained perpendicular diffusion at different particle energies is compared with that of the nonlinear guiding center (NLGC) theory. It is found that the NLGC theory is consistent with test particle simulations when the particle energies are small. However, the difference between the NLGC theory and test particle simulations tends to increase when the particle energy is sufficiently large, and the threshold is related to the turbulence bend-over length. In the NLGC theory, the gyrocenter of a charged particle is assumed to follow the magnetic field line. Therefore, when the particle has sufficiently large energy, its gyroradius will be larger than the turbulence bend-over length. Then the particle can cross the magnetic field lines, and the difference between the test particle simulations and NLGC theory occurs.     

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.     

Saturated magnetic field amplification at supernova shocks

Cosmic ray streaming instabilities at supernova shocks are discussed in the quasi-linear diffusion formalism which takes into account the feedback effect of wave growth on the cosmic ray streaming motion. In particular, the non-resonant instability that leads to magnetic field amplification in the short wavelength regime is considered. The linear growth rate is calculated using kinetic theory for a streaming distribution. We show that the non-resonant instability is actually driven by a compensating current in the background plasma. The non-resonant instability can develop into a non-linear regime generating turbulence. The saturation of the amplified magnetic fields due to particle diffusion in the turbulence is derived analytically. It is shown that the evolution of parallel and perpendicular cosmic ray pressures is predominantly determined by non-resonant diffusion. However, the saturation is determined by resonant diffusion which tends to reduce the streaming motion through pitch angle scattering. The saturated level can exceed the mean background magnetic field.     

Analytic forms of the perpendicular cosmic ray diffusion coefficient for an arbitrary turbulence spectrum and applications on transport of Galactic protons and acceleration at interplanetary shocks

We investigate cosmic ray scattering in the direction perpendicular to a mean magnetic field. Unlike in previous articles we employ a general form of the turbulence wave spectrum with arbitrary behavior in the energy range. By employing an improved version of the nonlinear guiding center theory we compute analytically the perpendicular mean free path. As shown, the energy range spectral index, has a strong influence on the perpendicular diffusion coefficient. If this parameter is larger than one we find for some cases a perpendicular diffusion coefficient that is independent of the parallel mean free path and particle energy. Two applications are considered, namely transport of Galactic protons in the solar system and diffusive particle acceleration at highly perpendicular interplanetary shock waves.     

Electromagnetic radiation from line sources interacting with a moving magnetoplasma slab backed by a finitely conducting medium

The problem of electromagnetic radiation from electric and magnetic line sources interacting with a moving magnetoplasma slab backed by a finitely conducting medium is treated. The local magnetostatic field is aligned parallel with the line source and is perpendicular to the direction of slab motion. For the configuration, theE andH modes are excited independently by a magnetic and an electric line source respectively. Expressions for the far zone radiation fields and the radiation pattern have been obtained for both the line sources. It is found that the radiation due to an electric line source is not affected by the presence of a static magnetic field and the motion of the slab medium. Numerical results for the radiation pattern referring to both the line sources have been presented for a wide range of parameters characterizing the finite magnetostatic field, the conductivity of the medium backing the plasma, the thickness of the slab and the location of the line source.     

Influence of accelerated particles on the large-scale magnetic field in young supernova remnants

We offer a possible explanation for the observational data on the magnetic-field structure in young supernova remnants (SN 1006, Tycho, Kepler, Cas A) that have been obtained by analyzing the polarizations of electromagnetic radiation in the radio, infrared, and other wavelength ranges. The authors of observational works interpret these data as evidence that the ordered magnetic-field component is predominantly radial, but it can be much smaller in amplitude than the stochastic field component that accounts for the bulk of the total magnetic energy. We calculate the magnetic field in supernova remnants by taking into account the shock compression of the primary field and the generation of a large-scale magnetic field by the particles accelerated at the shock front. The assumption that the field in the supernova remnant is the explosion-compressed primary field near the star is inconsistent with observational data, because the tangential (relative to the shock front) field component perpendicular to the radius must prevail in this case. However, allowing for the generation of an additional magnetic field by the electric current of the particles accelerated by a strong shock front leads us to conclude that the field components parallel to the front are suppressed by accelerated particles by several orders of magnitude. Only the component perpendicular to the front remains. Such a field configuration for uniform injection does not lead to the generation of an additional magnetic field, and, in this sense, it is stable. This explains the data on the radial direction of the ordered field component. As regards the stochastic field component, we show that it is effectively generated by accelerated particles if their injection into acceleration at the shock front is nonuniform along the front. Injection nonuniformity can be caused by upstream density nonuniformities. A relative density nonuniformity of the order of several percent is enough for an observable magnetic field with scales on the order of the density nonuniformity scales to be generated.     

Analytical forms of correlation functions and length scales of astrophysical turbulence

In this article correlation-functions, correlation-scales, and field line diffusion coefficients of magnetic turbulence are discussed. For the slab turbulence model these parameters are calculated analytically for different forms of the wave-spectrum of the magnetic fluctuations. It is also demonstrated in this article that the definition of the correlation-length used previously yields infinity in some cases. Furthermore, correlation-functions and correlation-scales are calculated analytically for the well-established slab/2D composite model. It is demonstrated that the 2D correlation function decays much slower than the slab correlation function. These results are essential for understanding previous theoretical results of superdiffusive field line random walk and very recent spacecraft measurements of magnetic correlations in the solar wind.     

Perpendicular Transport in the Inner Heliosphere: A Quick and Dirty Approach

In previous studies, transport of solar energetic particles in the inner heliosphere was regarded as one-dimensional along the Archimedean field spiral; i.e., any perpendicular transport is neglected. We extend Roelof’s equation of focused transport for solar energetic particles to accommodate perpendicular transport in the plane of the ecliptic. Numerically, this additional term is solved with an implicit Laasonen scheme. In this first approximation, it is solved for azimuthal instead of perpendicular transport – these are similar in the inner heliosphere where the Archimedean field is almost radial. The intent of the study is to estimate the possible influence of perpendicular transport, but not to fit energetic particle events; thus, the particle source stays fixed on the Sun. For typical ratios κ _⊥ /κ _‖ between 0.02 and 0.1 at 1 AU scaled with r ² as suggested in nonlinear guiding-center theory, we find that i) an azimuthal spread over some 10° occurs within a few hours, ii) the variation of maximum intensities with longitude is comparable to the ones inferred from multispacecraft observations, and iii) on a given field line, intensity and anisotropy-time profiles are modified such that fits with the two-dimensional transport model give different combinations of injection profiles and mean free paths. Implications for the interpretation of intensity and anisotropy-time profiles observed in interplanetary space and consequences for our understanding of particle propagation and acceleration in space are discussed.     

Production of pulses and interpulses in pulsars

Pulsars accelerate the charged particles moving along their magnetic field lines due to their rapidly spinning motion. Particles gain maximum energy from pulsars within the light cylinder when they are moving along the field lines perpendicular to the rotation velocity. In pulsars with non-aligned rotation and magnetic axes, the production of two intense and sharp pulses (main pulse and interpulse) separated by 180° longitude occur at the two regions near the light cylinder where the rotation velocity is perpendicular to the magnetic field. Since the radiating particles move radially along the relativistically compressed magnetic field lines, the observer in the stationary frame receives beamed and transversely compressed radiation pulse. Near the light cylinder position angle varies smoothly during pulsar rotation in a way as Radhakrishnan and Cook (1969) expect its variation near the magnetic pole, as the field lines experience relativistic compression in the direction of rotation. The motion of two charge species along the field lines produce orthogonal modes at each pulse longitude.     

Observations in the earth's magnetotail relating to magnetic merging

For more than a decade there has been growing conviction that the burst of energy from a solar flare is first stored in magnetic fields and is then released rapidly by magnetic field annihilation (magnetic merging). There has also been recognition that magnetic merging may be responsible for the energy release manifested in auroral phenomena at the Earth. The most substantial evidence that magnetic merging does indeed occur in the Earth's magnetosphere and causes the auroral phenomena is provided by recent observations, in the magnetotail, of very rapid (500 km s^–1) tailward, then earthward, flow of plasma during magnetospheric substorms. The observations, made with the Vela and IMP satellites, reveal also that the component of the tail magnetic field perpendicular to the tail neutral sheet changes polarity at the time of the reversal of plasma flow. These features are interpreted as indicative of passage of a magnetic neutral line, at which magnetic merging is proceeding, past the observing satellite. This paper describes an example of such observations made with IMP 6. It is anticipated that such systematic measurements of the plasma, energetic particles and magnetic field in the neighborhood of the passing neutral line on many such occasions will provide a general understanding of the magnetic merging process which can then be applied to studies of solar flares and other astrophysical phenomena.Work performed under the auspices of the U.S. Energy Research and Development Administration.     

Acceleration of relativistic charged particles by supersonic hydromagnetic turbulence

The acceleration of relativistic particles is considered during their intersection with hydromagnetic shock fronts in the presence of randomly distributed large-scale magnetic fields. In a series of astronomical objects, the Larmor radius of the relativistic particles exceeds the width of the shock front. In this case there is a change in the adiabatic invariant which results in an increase in the energy of the particle when it crosses the front in any direction. We have proved that the adiabatic part of the energy change will be partially or completely compensated by its reverse change in the weaker regions of the magnetic field. The acceleration mechanism considered is found to be more effective than the Fermi mechanism.If the mean free path of the particles is much less than the distance between the shock fronts, magnetic small-scale fluctuations cause further scattering of the particles. In this case the particles following and crossing the front will return to it. After reversed crossing, a fraction of the particles-defined by the ratio of the front speed to the particle velocity or of the distance between the fronts to the free path — will not return to the front. It is proved that for both large and small free paths the rates at which the particle gains energy are nearly the same.     

Particle dynamics in reconnection field configurations

Trajectories of test particles are studied numerically in two types of reconnection magnetic field configurations, a single X-line magnetic field configuration and a tearing magnetic field configuration. Both adiabatic and nonadiabatic motions are examined, with special emphasis on net energy gain and time spent in the neutral line regions. They spend typically one characteristic gyroperiod in the X-line region and are ejected predominantly along field lines in the vicinity of the separatrix. Both adiabatic and nonadiabatic test particles in the tearing-type field configuration are channelled into and accelerated along the O-line region. It may be inferred from these test particle results that particle energizations are significant along the O-line region, but not along the X-line region. These results are in qualitative agreement with those obtained by a self-consistent particle simulation.     

Magnetic field rearrangement by accelerated particles near a shock front

We solve the self-consistent problem of the generation of a static magnetic field by the electric current of accelerated particles near a strong plane MHD shock front. We take into account the back reaction of the field on the particle diffusion tensors and the background plasma parameters near the front. Various states that differ significantly in static magnetic-field strength are shown to be possible near a strong front. If the initial field has a component normal to the front, then its components parallel to the front are suppressed by accelerated particles by several orders of magnitude. Only the component perpendicular to the front remains. This field configuration for uniform particle injection at the front does not lead to the generation of an additional field, and, in this sense, it is stable. If the initial field is parallel to the front, then either its significant enhancement by two or three orders of magnitude or its suppression by several orders of magnitude is possible. The phenomenon under consideration is an example of the self-organization of plasma with a magnetic field in a strongly nonequilibrium system. It can significantly affect the efficiency of particle acceleration by the shock front and the magnetobremsstrahlung of the accelerated particles.     

Ion-cyclotron waves in solar coronal hole

We investigate the effect of the plume/interplume lane (PIPL) structure of the solar polar coronal hole (PCH) on the propagation characteristics of ion-cyclotron waves (ICW). The gradients of physical parameters determined by SOHO and TRACE satellites both parallel and perpendicular to the magnetic field are considered with the aim of determining how the efficiency of the ICR process varies along the PIPL structure of PCH. We construct a model based on the kinetic theory by using quasi-linear approximation. We solve the Vlasov equation for O VI ions and obtain the dispersion relation of ICW. The resonance process in the interplume lanes is much more effective than in the plumes, agreeing with the observations which show the source of fast solar wind is interplume lanes. The solution of the Vlasov equation in PIPL structure of PCH, the physical parameters of which display gradients along and perpendicular direction to the external magnetic field, is thus obtained in a more general form than the previous investigations.     

Effect of rotation and finite Larmor radius on magneto-gravitational instability of Hall plasma in the presence of suspended particles

The effect of rotation on the self-gravitational instability of an infinite homogeneous magnetized Hall plasma is considered with the inclusion of finite Larmor radius corrections and the effect of suspended particles. A general dispersion relation is obtained from the linearized set of equations. The particular cases of the effect of rotation along and perpendicular to the direction of the magnetic field are considered. The effects of Hall current, finite Larmor radius, and suspended particles on the waves propagated parallel and perpendicular to the uniform magnetic field are investigated along with the uniform rotation of the medium. It is found that in the presence of suspended particles, magnetic field, Hall current, rotation and finite Larmor radius, the Jeans criterion determines the condition of gravitational instability of a gas-particle medium.     

Compound diffusion of energetic particles: a Kappa model for the parallel distribution function

One can assume that energetic particles follow magnetic field lines while they propagate through a magnetized plasma. The latter scenario is usually described by the so-called field line random walk limit. This limit, however, is only valid if parallel diffusion is suppressed. As soon as the latter effect is taken into account, perpendicular transport becomes subdiffusive. This physical scenario is usually called compound diffusion or compound subdiffusion and can be described by a Chapman-Kolmogorov equation. In the latter equation the parallel distribution function is an essential ingredient. In the present paper we replace the standard Gaussian model by a Kappa distribution to compute distribution functions and mean square displacements across the field.     

Lorentz scattering of interplanetary dust

Charged dust grains in a turbulent magnetic field will see a Lorentz force due to the convection of the solar magnetic field past them at the solar wind velocity. Since the sign of this magnetic field is randomly varying, the direction of the force will be random, and the net effect will be to randomly scatter the orbital elements of these particles. The square roots of the mean square change in semimajor axis, inclination, and eccentricity are determined as a function of the particles' original orbital elements. Particles 3 μm in radius and smaller will have their motions strongly perturbed or dominated by Lorentz scattering. This scattering will have an effect comparable to, or greater than, the Poynting-Robertson effect on these particles for time scales comparable to their Poynting-Robertson lifetimes.     

Particle acceleration in reconnecting current sheets

We study motions of charged particles in reconnecting current sheets (CS) which have both transverse (perpendicular to the current sheet plane) and longitudinal (parallel to the electric current inside the sheet) components of the magnetic field. Such CS, called non-neutral, are formed in regions of magnetic field line reconnection in the solar atmosphere. We develop an analytical technique which allows us to reproduce previous results concerning the influence of transverse fields on particle motion and acceleration. This technique also allows us to evaluate the effect of the longitudinal field. The latter increases considerably the efficiency of particle acceleration in CS. The energizing of electrons during the main phase of solar flares can be interpreted as their acceleration in non-neutral CS.