{'fraction_non_alphanumeric': 0.022104332449160036, 'fraction_numerical': 0.0, 'mean_word_length': 5.619883040935672, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
A New Type of Cosmic-Ray Anisotropy from Perpendicular Diffusion. I. Modification of the Spatial Diffusion Tensor and the Diffusion-Convection Cosmic-Ray Transport Equation

Perpendicular spatial diffusion of cosmic rays is particularly important in highly flattened astrophysical objects such as the Galactic disk and in the outer heliosphere. By maintaining perpendicular Fokker-Planck coefficients in the Fokker-Planck equation for the gyrotropic cosmic-ray phase-space density, it is shown that the diffusion approximation gives rise to a new, third contribution to the cosmic-ray anisotropy due to perpendicular spatial diffusion, adding to the well-known streaming anisotropy due to pitch-angle scattering and parallel spatial gradients and the Compton-Getting anisotropy due to momentum gradients. This new anisotropy modifies the transport parameters of the diffusion-convection transport equation for the isotropic gyrotropic part of the cosmic-ray phase-space density; in general, one obtains two new perpendicular rates of adiabatic deceleration and nine nonzero elements of the full cosmic-ray spatial diffusion tensor.