A. Shalchi

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.

A Unified Particle Diffusion Theory for Cross-field Scattering: Subdiffusion, Recovery of Diffusion, and Diffusion in Three-dimensional Turbulence

A new nonlinear theory for cosmic-ray scattering across the mean magnetic field is derived. This theory can be applied for arbitrary turbulence geometry. Previous theories such as the extended nonlinear guiding center theory are deduced as special limits. Furthermore, the new theory can explain subdiffusive transport for slab turbulence and the recovery of diffusion for slab/two-dimensional and three-dimensional turbulence. The nonlinear standard theory for field line wandering can be obtained as a special limit.

Analytic Forms of the Perpendicular Diffusion Coefficient in Magnetostatic Turbulence

Recently, a nonlinear theory for perpendicular diffusion of charged particles was presented. This theory is called the nonlinear guiding center theory and provides an integral equation for the perpendicular mean free path. In this paper we consider analytical solutions of this equation in the case of magnetostatic turbulence. The resulting formulas for the perpendicular mean free path are discussed. We also compare these new results with results of the quasi-linear theory for parallel diffusion and with observational results.

Parallel and Perpendicular Transport of Heliospheric Cosmic Rays in an Improved Dynamical Turbulence Model

By applying a new model for the dynamical magnetic turbulence, we calculate parallel and perpendicular mean free paths of heliospheric cosmic rays. The results are compared with different observations and previous theoretical calculations. It is the main conclusion of this paper that we can achieve agreement between theory and observations if we employ realistic turbulence parameters. Motivated by previous work, we also discuss nonlinear effects in cosmic-ray transport theory.

A New Theory for Perpendicular Transport of Cosmic Rays

We present an improved nonlinear theory for the perpendicular transport of charged particles. This approach is based on an improved nonlinear treatment of field-line random walk in combination with a generalized compound diffusion model. The generalized compound diffusion model employed is more systematic and reliable, in comparison with previous theories. Furthermore, the theory shows remarkably good agreement with test-particle simulations and solar wind observations.

Extended nonlinear guiding center theory of perpendicular diffusion

Recently the nonlinear guiding center theory of cosmic ray perpendicular diffusion was proposed. In this paper it is demonstrated that at least the slab contribution to the perpendicular mean free path is calculated incorrectly within this nonlinear approach. An extended theory which includes an improved treatment of the slab contribution is presented in this paper. Contrary to the original theory, the extended nonlinear guiding center theory shows agreement with numerical simulations for slab and non-slab models.

Second-order quasilinear theory of cosmic ray transport

The problem of pitch-angle diffusion close to 90° is well known in cosmic ray astrophysics. If the pitch-angle Fokker–Planck coefficient for pure slab geometry is calculated, the quasilinear approximation results in vanishing pitch-angle scattering. For a realistic wave spectrum with a steep dissipation range this vanishing coefficient generates an infinitely large parallel mean free path. It is well known from numerical simulations that the 90° problem is a problem of quasilinear theory and not a problem of reality. In the current paper quasilinear theory is used to calculate corrections of the unperturbed orbit. These corrections can be resubstituted into transport theory to calculate a second-order pitch-angle Fokker–Planck coefficient. The second-order quasilinear theory is an applicable theory which agrees with simulations for pitch-angle diffusion.

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.

Solving the 90° Scattering Problem in Isotropic Turbulence

A fundamental problem of cosmic-ray diffusion theory is pitch-angle scattering at 90°. For isotropic and anisotropic turbulence, the 90° problem leads to an infinitely large parallel mean free path. In this Letter, the second-order quasi-linear theory for cosmic-ray scattering parallel to a mean magnetic field is generalized for isotropic turbulence. It is shown that, in contrast to classic quasi-linear theory, the second-order theory provides nonvanishing scattering through 90° even for magnetostatic turbulence. The problem of 90° scattering is thus solved, because the comparison with simulations shows good quantitative agreement. It is also shown that the Fokker-Planck coefficient for pitch-angle scattering has its maximum at 90°.

Analytical description of stochastic field-line wandering in magnetic turbulence

A nonperturbative nonlinear statistical approach is presented to describe turbulent magnetic systems embedded in a uniform mean magnetic field. A general formula in the form of an ordinary differential equation for magnetic field-line wandering (random walk) is derived. By considering the solution of this equation for different limits several new results are obtained. As an example, it is demonstrated that the stochastic wandering of magnetic field-lines in a two-component turbulence model leads to superdiffusive transport, contrary to an existing diffusive picture. The validity of quasilinear theory for field-line wandering is discussed, with respect to different turbulence geometry models, and previous diffusive results are shown to be deduced in appropriate limits.