Joe Giacalone

The Transport of Cosmic Rays across a Turbulent Magnetic Field

We present a new analysis of the transport of cosmic rays in a turbulent magnetic field that varies in all three spatial dimensions. The analysis utilizes a numerical simulation that integrates the trajectories of an ensemble of test particles from which we obtain diffusion coefficients based on the particle motions. We find that the diffusion coefficient parallel to the mean magnetic field is consistent with values deduced from quasi-linear theory, in agreement with earlier work. The more interesting and less understood transport perpendicular to the average magnetic field is found to be enhanced (above the classical scattering result) by the random walk, or braiding, of the magnetic field. The value of κ⊥ obtained is generally larger than the classical scattering value but smaller than the quasi-linear value. The computed values of κ⊥/κ∥, for a representation of the interplanetary magnetic field, are 0.02-0.04; these values are of the same general magnitude as those assumed in recent numerical simulations of cosmic-ray modulation and transport in the heliosphere, and give reasonable agreement with spacecraft observations of cosmic rays. Some consequences of these results for the interpretation of heliospheric observations are discussed.

Interplanetary magnetic field line mixing deduced from impulsive solar flare particles

We have studied fine-scale temporal variations in the arrival profiles of approximately 20 keV nucleon-1 to approximately 2 MeV nucleon-1 ions from impulsive solar flares using instrumentation on board the Advanced Composition Explorer spacecraft at 1 AU between 1997 November and 1999 July. The particle events often had short-timescale ( approximately 3 hr) variations in their intensity that occurred simultaneously across all energies and were generally not in coincidence with any local magnetic field or plasma signature. These features appear to be caused by the convection of magnetic flux tubes past the observer that are alternately filled and devoid of flare ions even though they had a common flare source at the Sun. Thus, we have used the particles to study the mixing of the interplanetary magnetic field that is due to random walk. We deduce an average timescale of 3.2 hr for these features, which corresponds to a length of approximately 0.03 AU.

Magnetic Field Amplification by Shocks in Turbulent Fluids

We consider the effect of preexisting, large-scale, broadband turbulent density fluctuations on propagating hydromagnetic shock waves. We present results from several numerical simulations that solve the two-dimensional magnetohydrodynamic equations. In our simulations, a plasma containing large-scale, low-amplitude density and magnetic field turbulence is forced to flow into a rigid wall, forming a shock wave. We find that the density fluctuations not only distort the shape of the shock front and lead to a turbulent postshock fluid, but they also produce a number of important changes in the postshock magnetic field. The average downstream magnetic field is increased significantly, and large fluctuations in the magnetic vector occur, with the maximum field strength reaching levels such that magnetic stresses are important in the postshock region. The downstream field enhancement can be understood in terms of the stretching and forcing together of the magnetic field entrained within the turbulent fluid of the postshock flow. We suggest that these effects of the density fluctuations on the magnetic field are observed in astrophysical shock waves such as supernova blast waves and the heliospheric termination shock.

Perpendicular transport in 1‐ and 2‐dimensional shock simulations

We consider the foundations of 1- and 2-dimensional shock simulations in which the physical quantities are independent of a coordinate which is not parallel to the magnetic field. We show analytically that in such simulations the ions are effectively tied to the convected magnetic lines of force because of the presence of an ignorable spatial coordinate. This conclusion has important consequences. In particular we conclude that the acceleration of energetic charged particles at quasi-perpendicular shocks cannot be properly studied in such simulations because the role of perpendicular diffusion cannot be properly evaluated.

Particle Acceleration at Shocks Moving through an Irregular Magnetic Field

We use nondiffusive, nonrelativistic, test-particle numerical simulations to address the physics of particle acceleration by collisionless shocks. We focus on the importance of the shock normal angle, θBn, in determining the energy spectrum of the accelerated particles. For reasonable parameters, we find that the injection velocity is weakly dependent on the mean shock normal angle and that low-energy particles are readily accelerated to high energies irrespective of θBn. Our results are applicable for shocks that are nearly planar on scales larger than the coherence scale of the upstream magnetic turbulence and for particles whose gyroradii are smaller than this scale. We confirm previous results showing that the acceleration rate is larger for nearly perpendicular shocks compared to parallel shocks. However, we also find that the acceleration rate at parallel shocks moving through large-scale magnetic fluctuations is larger than that predicted by simple first-order Fermi acceleration. Our results can be understood in terms of the nature of the large-scale fluctuations and their effect on particle transport.

Interpretation and consequences of large‐scale magnetic variances observed at high heliographic latitude

We consider recent Ulysses observations of the large-scale variances in the transverse components of the interplanetary magnetic field. A previously-suggested theory is shown to provide a good fit to the observed spatial variation and level of the fluctuations. The transport of cosmic rays in the heliosphere will be significantly affected by these fluctuations. In addition to impeding the inward, radial diffusive and drift access of cosmic rays over the poles, the magnetic fluctuations imply a large latitudinal diffusion, caused primarily by the field-line mixing, or random walk.

Small-scale gradients and large-scale diffusion of charged particles in the heliospheric magnetic field

We have carried out numerical simulations of the propagation of energetic charged particles in a turbulent magnetic field similar to that observed in the solar wind. If the particles are released impulsively near the Sun, in a region small compared with the field coherence scale (a solar flare, for example), they exhibit characteristic fluctuations in intensity at 1 AU (dropouts) associated with very steep localized gradients. These numerical simulations are quantitatively very similar to recent observations by the Advanced Composition Explorer spacecraft and are the result of the convection of alternatively filled and empty flux tubes past the spacecraft. These fluctuations occur naturally as part of the particle transport in the same field, which results in large-scale cross field diffusion and which has previously been used to study the propagation of corotating interaction region-associated particles to high heliographic latitudes.

Charged-particle motion in multidimensional magnetic-field turbulence

We present a new analysis of the fundamental physics of charged-particle motion in a turbulent magnetic field using a numerical simulation. The magnetic field fluctuations are taken to be static and to have a power spectrum which is Kolmogorov. The charged particles are treated as test particles. It is shown that when the field turbulence is independent of one coordinate (i.e., k lies in a plane), the motion of these particles across the magnetic field is essentially zero, as required by theory. Consequently, the only motion across the average magnetic field direction that is allowed is that due to field-line random walk. On the other hand, when a fully three-dimensional realization of the turbulence is considered, the particles readily cross the field. Transport coefficients both along and across the ambient magnetic field are computed. This scheme provides a direct computation of the Fokker-Planck coefficients based on the motions of individual particles, and allows for comparison with analytic theory.

Particle Acceleration in Solar Wind Compression Regions

We present the results of a theoretical investigation of the acceleration of charged particles in regions of gradual solar wind compression. The mechanism we describe is similar to diffusive shock acceleration, except that it invokes a gradual compression of the plasma over many gyroradii rather than a shock. Recent observations of energetic particles associated with corotating interaction regions (CIRs) at 1 AU suggest that the particles were accelerated within the compression region between the fast and slow solar wind rather than at the associated forward and reverse shocks, which are at larger heliocentric distances. We show that nondiffusive effects such as magnetic mirroring are important in the inner heliosphere, particularly the injection of low-energy particles (e.g., pickup ions and suprathermal solar wind ions). We integrate the trajectories of an ensemble of test particles moving in synthesized electromagnetic fields, which are similar to what is currently known about corotating interaction regions in the inner heliosphere, prior to the formation of the forward and reverse shocks. We show that compression regions associated with CIRs at 1 AU with widths ~0.03 AU can accelerate particles up to ~10 MeV and produce energy spectra which are remarkably similar to recent observations.

Hybrid simulations of protons strongly accelerated by a parallel collisionless shock

We present initial results from one-dimensional hybrid simulations which directly address the problems of using such methods to simulate the acceleration of ions to high energy by parallel shocks. As particles are accelerated from the thermal population, they are repeatedly “split,” thereby ensuring statistically valid energy spectra covering a wide dynamic range. In order to model the complex foreshock, as expected if the simulation domain were large enough, and as seen in observations, we introduce a source of upstream turbulence. This turbulence produces an enhanced high energy tail in the upstream particle distribution extending to over a hundred times the plasma flow energy, and a prominent shoulder downstream.