Cosmic‐Ray Diffusion Approximation with Weak Adiabatic Focusing

Abstract

Large-scale spatial variations of the guide magnetic field of interplanetary and interstellar plasmas give rise to the adiabatic focusing term in the Fokker-Planck transport equation of cosmic rays. The consequences of the adiabatic focusing term for the diffusion approximation to cosmic-ray transport are investigated in the weak focusing limit, where the focusing length L is much larger than the parallel scattering length. Whereas the cosmic-ray anisotropy is unaffected, three new transport terms arise in the diffusion-convection transport equation that represent convective transport terms parallel to the guide field, perpendicular to the guide field, and in momentum space. The convective terms perpendicular to the guide field only occur in nonaxisymmetric electromagnetic turbulence. The new convection term in momentum space represents a continuous momentum loss term or a first-order Fermi-type acceleration term depending on the product a11L of the focusing length L and the rate of adiabatic deceleration a11, which depends sensitively on the cross helicity and magnetic helicity of the magnetic field turbulence. © 2008. The American Astronomical Society. All rights reserved.