G. Qin

Nonlinear Collisionless Perpendicular Diffusion of Charged Particles

A nonlinear theory of the perpendicular diffusion of charged particles is presented, including the influence of parallel scattering and dynamical turbulence. The theory shows encouraging agreement with numerical simulations. Subject headings: diffusion — turbulence

Perpendicular Transport of Charged Particles in Composite Model Turbulence: Recovery of Diffusion

The computation of charged particle orbits in model turbulent magnetic fields is used to investigate the properties of particle transport in the directions perpendicular to the large-scale magnetic field. Recent results by Qin, Matthaeus, & Bieber demonstrate that parallel scattering suppresses perpendicular diffusion to a subdiffusive level when the turbulence lacks transverse structure. Here numerical computations are used to show that in turbulence in which there is substantial transverse structure, a second regime of diffusive transport can be established. In both the subdiffusion regime and this second diffusion regime, perpendicular transport is intrinsically nonlinear. The regime of second diffusion persists for long times and may therefore be of interest in astrophysical transport problems such as the scattering and solar modulation of cosmic rays.

Nonlinear parallel and perpendicular diffusion of charged cosmic rays in weak turbulence

The problem of particle transport perpendicular to a magnetic background field is well known in cosmic-ray astrophysics. Whereas it is widely accepted that quasi-linear theory (QLT) of particle transport does not provide the correct results for perpendicular diffusion, it was assumed for a long time that QLT is the correct theory for parallel diffusion. In the current paper we demonstrate that QLT is in general also incorrect for parallel particle transport if we consider composite turbulence geometry. Motivated through the recent success of the so-called nonlinear guiding center theory of perpendicular diffusion, we present a new theory for parallel and perpendicular diffusion of cosmic rays. This new theory is a nonlinear extension of QLT and provides us with a coupled system of nonlinear Fokker-Planck coefficients. By solving the resulting system of integral equations we obtain new results for the pitch-angle Fokker-Planck coefficient and the Fokker-Planck coefficient of perpendicular diffusion. By integrating over pitch angle we calculate the parallel and perpendicular mean free path. To our knowledge the new theory is the first that can deal with both parallel and perpendicular diffusion in agreement with simulations.

PROPAGATION OF SOLAR ENERGETIC PARTICLES IN THREE-DIMENSIONAL INTERPLANETARY MAGNETIC FIELDS

This paper presents a model calculation of solar energetic particle propagation in a three-dimensional interplanetary magnetic field. The model includes essentially all the particle transport mechanisms: streaming along magnetic field lines, convection with the solar wind, pitch-angle diffusion, focusing by the inhomogeneous interplanetary magnetic field, perpendicular diffusion, and pitch-angle dependent adiabatic cooling by the expanding solar wind. We solve the Fokker–Planck transport equation with simulation of backward stochastic processes in a fixed reference frame in which any spacecraft is roughly stationary. As an example we model the propagation of those high-energy (E 10 MeV) solar energetic particles in gradual events that are accelerated by large coronal mass ejection shocks in the corona and released near the Sun into interplanetary space of a Parker spiral magnetic field. Modeled with different scenarios, the source of solar energetic particles can have a full or various limited coverages of latitude and longitude on the solar surface. We compute the long-term time profiles of particle flux and anisotropy at various locations in the heliosphere up to 3 AU, from the ecliptic to high latitudes. Features from particle perpendicular diffusion are revealed. Our simulation reproduces the observed reservoir phenomenon of solar energetic particles with constraints on either solar particle source or the magnitude of perpendicular diffusion.

NONLINEAR PARALLEL DIFFUSION OF CHARGED PARTICLES: EXTENSION TO THE NONLINEAR GUIDING CENTER THEORY

A nonlinear theory of the parallel diffusion of charged particles with perpendicular scattering and dynamical turbulence is obtained. The combination of the new parallel diffusion theory and the nonlinear guiding center theory shows good agreement with numerical simulations using typical parameters for a solar wind. Furthermore, the combination of the theories has a simpler mathematical form and is more computationally tractable than the weakly nonlinear theory.

PITCH-ANGLE DIFFUSION COEFFICIENTS OF CHARGED PARTICLES FROM COMPUTER SIMULATIONS

Pitch-angle diffusion is a key process in the theory of charged particle scattering by turbulent magnetic plasmas. This process is usually assumed to be diffusive and can, therefore, be described by a pitch-angle diffusion or Fokker-Planck coefficient. This parameter controls the parallel spatial diffusion coefficient as well as the parallel mean free path of charged particles. In the present paper, we determine pitch-angle diffusion coefficients from numerical computer simulations. These results are then compared with results from analytical theories. Especially, we compare the simulations with quasilinear, second-order, and weakly nonlinear diffusion coefficients. Such a comparison allows the test of previous theories and will lead to an improved understanding of the mechanism of particle scattering.

PROPAGATION OF SOLAR ENERGETIC PARTICLES IN THREE-DIMENSIONAL INTERPLANETARY MAGNETIC FIELDS: IN VIEW OF CHARACTERISTICS OF SOURCES

In this paper, a model of solar energetic particle (SEP) propagation in the three-dimensional Parker interplanetary magnetic field is calculated numerically. We study the effects of the different aspects of particle sources on the solar surface, which include the source location, coverage of latitude and longitude, and spatial distribution of source particle intensity, on propagation of SEPs with both parallel and perpendicular diffusion. We compute the particle flux and anisotropy profiles at different observation locations in the heliosphere. From our calculations, we find that the observation location relative to the latitudinal and longitudinal coverage of particle source has the strongest effects on particle flux and anisotropy profiles observed by a spacecraft. When a spacecraft is directly connected to the solar sources by the interplanetary magnetic field lines, the observed particle fluxes are larger than when the spacecraft is not directly connected. This paper focuses on the situations when a spacecraft is not connected to the particle sources on the solar surface. We find that when the magnetic footpoint of the spacecraft is farther away from the source, the observed particle flux is smaller and its onset and maximum intensity occur later. When the particle source covers a larger range of latitude and longitude, the observed particle flux is larger and appears earlier. There is east-west azimuthal asymmetry in SEP profiles even when the source distribution is east-west symmetric. However, the detail of particle spatial distribution inside the source does not affect the profile of the SEP flux very much. When the magnetic footpoint of the spacecraft is significantly far away from the particle source, the anisotropy of particles in the early stage of an SEP event points toward the Sun, which indicates that the first arriving particles come from outside of the observer through perpendicular diffusion at large radial distances.

Effects of Perpendicular Diffusion on Energetic Particles Accelerated by the Interplanetary Coronal Mass Ejection shock

In this work, based on a numerical solution of the focused transport equation, we obtained the intensity and anisotropy time profiles of solar energetic particles (SEPs) accelerated by an interplanetary shock in the three-dimensional Parker magnetic field. The shock is treated as a moving source of energetic particles with an assumed particle distribution function. We computed the time profiles of particle flux and anisotropy as measured by an observer at 1 AU, equatorial plane, and various longitudes with respect to the shock propagation direction. With perpendicular diffusion, energetic particles can cross magnetic field lines. Particles may be detected before the observers field line is connected to the shock. After the observers field line breaks from the shock front, the observer still can see more particles are injected into its field line. Our simulations show that the particle onset time, peak time, peak intensity, decay rate, and duration of SEP event could be significantly influenced by the effect of perpendicular diffusion. The anisotropy with perpendicular diffusion is almost the same as that without perpendicular diffusion, but there is an obvious difference at the moment when the observers field line begins to be connected to the shock.

TRANSPORT OF SOLAR ENERGETIC PARTICLES ACCELERATED BY ICME SHOCKS: REPRODUCING THE RESERVOIR PHENOMENON

In this work, gradual solar energetic particle (SEP) events observed by multiple spacecraft are investigated with model simulations. Based on a numerical solution of the Fokker–Planck focused transport equation including perpendicular diffusion of particles, we obtained the fluxes of SEPs accelerated by an interplanetary coronal mass ejection driven shock as it propagates outward through the three-dimensional Parker interplanetary magnetic field. The shock is treated as a moving source of energetic particles with an assumed particle distribution function. We look at the time profiles of particle flux as they are observed simultaneously by multiple spacecraft located at different locations. The dependence of particle fluxes on different levels of perpendicular diffusion is determined. The main purpose of our simulation is to reproduce the reservoir phenomenon, during which it is frequently observed that particle fluxes are nearly the same at very different locations in the inner heliosphere, up to 5 AU, during the decay phase of gradual SEP events. The reservoir phenomenon is reproduced in our simulation under a variety of conditions of perpendicular diffusion of particles estimated from the nonlinear guiding center theory (NLGC). As the perpendicular diffusion coefficient increases, the nonuniformity of particle fluxes becomes smaller, making the reservoir phenomenon more prominent. However, if the shock acceleration strength decreases slower than r −2.5 with the radial distance r, the reservoir phenomenon might disappear, with limited perpendicular diffusion constrained by the NLGC theory. Therefore, observation of the reservoir phenomenon in gradual SEP events can be used to test qualitatively theories of particle diffusion and shock acceleration.

Energetic Particles From Three-Dimensional Magnetic Reconnection Events In The Swarthmore Spheromak Experiment

Measurements are presented from the Swarthmore Spheromak Experiment (SSX) [M. R. Brown, Phys. Plasmas 6, 1717 (1999)] showing a population of superthermal, super-Alfvenic ions with Ē≅90 eV and Emax⩾200 eV accelerated by reconnection activity in three-dimensional magnetic structures. These energetic ions are temporally and spatially correlated with three-dimensional magnetic reconnection events (measured with a 3D probe array) and are accelerated along the X-line normal to the local 2D plane of reconnection. In a typical SSX discharge, the peak reconnection electromotive force E=vBL⩽(105 m/s)(0.05 T)(0.1 m)=500 V consistent with our observations. In addition, test particle simulations using magnetohydrodynamic (MHD) data from SSX simulations and run with dimensionless parameters similar to the experiment (S=1000, β=0.1) show acceleration of ions up to 2vAlf in a few Alfven times consistent with the measurement. The process includes two phases—a strong but short duration direct acceleration in the quasi-ste...