Frank C. Jones

The plasma physics of shock acceleration

The notion that plasma shocks in astrophysical settings can and do accelerate charged particles to high energies is not a new one. However, in recent years considerable progress has been achieved in understanding the role particle acceleration plays both in astrophysics and in the shock process itself. In this paper we briefly review the history and theory of shock acceleration, paying particular attention to theories of parallel shocks which include the backreaction of accelerated particles on the shock structure. We discuss in detail the work that computer simulations, both plasma and Monte Carlo, are playing in revealing how thermal ions interact with shocks and how particle acceleration appears to be an inevitable and necessary part of the basic plasma physics that governs collisionless shocks. We briefly describe some of the outstanding problems that still confront theorists and observers in this field.

Dissipation of magnetohydrodynamic waves on energetic particles: impact on interstellar turbulence and cosmic ray transport

The physical processes involved in diffusion of Galactic cosmic rays in the interstellar medium are addressed. We study the possibility that the nonlinear MHD cascade sets the power-law spectrum of turbulence which scatters charged energetic particles. We find that the dissipation of waves due to the resonant interaction with cosmic ray particles may terminate the Kraichnan-type cascade below wavelengths 10{sup 13} cm. The effect of this wave dissipation has been incorporated in the GALPROP numerical propagation code in order to asses the impact on measurable astrophysical data. The energy-dependence of the cosmic-ray diffusion coefficient found in the resulting self-consistent model may explain the peaks in the secondary to primary nuclei ratios observed at about 1 GeV/nucleon.

Acceleration rates and injection efficiencies in oblique shocks

The rate at which particles are accelerated by the first-order Fermi mechanism in shocks depends on the angle, \teq{\Tbone}, that the upstream magnetic field makes with the shock normal. The greater the obliquity the greater the rate, and in quasi-perpendicular shocks rates can be hundreds of times higher than those seen in parallel shocks. In many circumstances pertaining to evolving shocks (\eg, supernova blast waves and interplanetary traveling shocks), high acceleration rates imply high maximum particle energies and obliquity effects may have important astrophysical consequences. However, as is demonstrated here, the efficiency for injecting thermal particles into the acceleration mechanism also depends strongly on obliquity and, in general, varies inversely with \teq{\Tbone}. The degree of turbulence and the resulting cross-field diffusion strongly influences both injection efficiency and acceleration rates. The test particle \mc simulation of shock acceleration used here assumes large-angle scattering, computes particle orbits exactly in shocked, laminar, non-relativistic flows, and calculates the injection efficiency as a function of obliquity, Mach number, and degree of turbulence. We find that turbulence must be quite strong for high Mach number, highly oblique shocks to inject significant numbers of thermal particles and that only modest gains in acceleration rates can be expected for strong oblique shocks over parallel ones if the only source of seed particles is the thermal background.

First-order Fermi particle acceleration by relativistic shocks

Monte Carlo calculations of test particle spectra and acceleration times are presented from first-order Fermi particle acceleration for parallel shocks with arbitrary flow velocities and compression ratios r up to seven, shock velocities u1 up to 0.98c, and injection energies ranging from thermal to highly superthermal. Far above the injection energy, the spectra are well-approximated by a power law and the spectra are always harder than for nonrelativistic shocks. Approximate analytic expression are given for the spectral slope as a function of u1 and r. The acceleration time as a function of particle energy is less than for nonrelativistic shocks by a factor that increases with u1 and is about three for u1 = 0.98c. It is confirmed that the spectrum for pitch-angle diffusion is considerably steeper than for large-angle scattering for the same shock parameters. 69 refs.

The Modified Weighted Slab Technique: Models and Results

In an attempt to understand the source and propagation of Galactic cosmic rays, we have employed the modified weighted slab technique along with recent values of the relevant cross sections to compute primary to secondary ratios including B/C and sub-Fe/Fe for different Galactic propagation models. The models that we have considered are the disk-halo diffusion model, the dynamical halo wind model, the turbulent diffusion model, and a model with minimal reacceleration. The modified weighted slab technique will be briefly discussed and a more detailed description of the models will be given. We will also discuss the impact that the various models have on the problem of anisotropy at high energy and discuss what properties of a particular model bear on this issue.

Nonlinear Particle Acceleration in Oblique Shocks

The solution of the nonlinear diffusive shock acceleration problem, where the pressure of the non-thermal population is sufficient to modify the shock hydrodynamics, is widely recognized as a key to understanding particle acceleration in a variety of astrophysical environments. We have developed a Monte Carlo technique for self-consistently calculating the hydrodynamic structure of oblique, steady state shocks, together with the first-order Fermi acceleration process and associated nonthermal particle distributions. This is the first internally consistent treatment of modified shocks that includes cross-field diffusion of particles. Our method overcomes the injection problem faced by analytic descriptions of shock acceleration and the lack of adequate dynamic range and artificial suppression of cross-field diffusion faced by plasma simulations; it currently provides the most broad and versatile description of collisionless shocks undergoing efficient particle acceleration. We present solutions for plasma quantities and particle distributions upstream and downstream of shocks, illustrating the strong differences observed between nonlinear and test particle cases. It is found that, for strong scattering, there are only marginal differences in the injection efficiency and resultant spectra for two extreme scattering modes, namely large-angle scattering and pitch-angle diffusion, for a wide range of shock parameters, i.e., for nonper-pendicular subluminal shocks with field obliquities less than or equal to 75° and de Hoffmann-Teller frame speeds much less than the speed of light.

Charged-particle motion in electromagnetic fields having at least one ignorable spatial coordinate

We give a rigorous derivation of a theorem showing that charged particles in an arbitrary electromagnetic field with at least one ignorable spatial coordinate remain forever tied to a given magnetic field line. Such a situation contrasts with the significant motions normal to the magnetic field that are expected in most real three-dimensional systems. It is pointed out that while the significance of the theorem has not been widely appreciated, it has important consequences for a number of problems and is of particular relevance for the acceleration of cosmic rays by shocks.

Partially averaged field approach to cosmic ray diffusion

The kinetic equation for particles interacting with turbulent fluctuations is derived by a new nonlinear technique which successfully corrects the difficulties associated with quasi‐linear theory. In this new method the effects of the fluctuations are evaluated along particle orbits which themselves include the effects of a statistically averaged subset of the possible configurations of the turbulence. The new method is illustrated by calculating the pitch angle diffusion coefficient Dμμ for particles interacting with ’’slab model’’ magnetic turbulence, i.e., magnetic fluctuations linearly polarized transverse to a mean magnetic field 〈B〉. Results are compared with those of quasi‐linear theory and also with those of Monte Carlo calculations reported in a companion paper. The major effect of the nonlinear treatment in this illustration is the determination of Dμμ in the vicinity of 90° pitch angles where quasi‐linear theory breaks down. The spatial diffusion coefficient κ∥ parallel to 〈B〉 is evaluated usin...

Computer simulation of the velocity diffusion of cosmic rays

Monte Carlo simulation experiments have been performed in order to study the velocity diffusion of charged particles in a static turbulent magnetic field. By following orbits of particles moving in a large ensemble of random magnetic field realizations with suitably chosen statistical properties, a pitch‐angle diffusion coefficient is derived. Results are presented for a variety of particle rigidities and rms random field strengths and compared with the predictions of standard quasi‐linear theory and the nonlinear partially averaged field theory.

The generalized diffusion-convection equation

Starting from the Boltzmann equation, a transport equation is derived for energetic particles in a moving magnetized plasma in which the scattering centers that keep the particles quasi-isotropic are moving with a velocity that is not necessarily the same as that of the plasma. The scattering is characterized by three very loose constraints: (1) there is a rest frame for each scatterer in which the particles scatter elastically; (2) in this frame the scattering will not disturb an isotropic distribution; and (3) the momentum transfer in an average collision may be described by a tensor operating on the particles original momentum. Since the strength of the scattering is not specified, the derivation should be as valid for plasma microturbulence as for hard-sphere scattering. The results show clearly which phenomena are responsible for tying the particles to the plasma in the transport equation. 31 refs.