Cosmic ray diffusion approximation with weak adiabatic focusing

Large-scale spatial variations of the guide magnetic field of interplanetary and interstellar plasmas give rise to the additional adiabatic focusing term in the Fokker-Planck transport equation of cosmic rays. The consequences of the additional 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, respectively. The convective terms perpendicular to the guide field only occur in non-axisymmetric 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. For the illustrative example of undamped slab Alfvenic plasma waves first-order Fermi acceleration of cosmic ray particles occurs both in a converging guide magnetic field with a majority of forward moving slab Alfven waves, and in a diverging guide magnetic field with a majority of backward moving slab Alfven waves. Alternatively, momentum losses of cosmic ray particles result in a converging guide magnetic field with a majority of backward moving slab Alfven waves, and in a diverging guide magnetic field with a majority of backward moving slab Alfven waves. The consequences for cosmic ray dynamics in the solar wind, at shock waves and in static halos of galaxies are discussed