Cosmic Ray Pitch Angle Scattering in Isotropic Turbulence II: Sensitive Dependence on the Dissipation Range Spectrum
C. W. Smith, J. W. Bieber and W. H. Matthaeus
The Astrophysical Journal, 363, 283-291 (1990)
Turbulence theory provides compelling reasons to believe that magnetic turbulence must be strongly damped at sufficiently small scales, thereby giving rise to a dissipation range for the fluctuations where the turbulent energy spectrum decreases more rapidly than the inertial range. The dissipation range is expected to play a decisive role in the resonant scattering of low-energy particles and particles of any energy with pitch angles near 90 degrees, yet the influence of the dissipation range has commonly been neglected in cosmic-ray transport studies. This work employs dissipation range spectra of Gaussian, exponential, and power-law forms in an analysis of the leading order quasilinear expressions for cosmic-ray pitch angle scattering in isotropic magnetic turbulence. For exponential and Gaussian dissipation range spectra, we recover the ``slab'' form of the Fokker-Planck coefficient for pitch angle scattering at sufficiently low energies, but for power-law dissipation range spectra, we obtain a new form for the Fokker-Planck coefficient in the low-energy limit, which reduces to the ``slab'' form only for extremely steep dissipation range spectra. We also find that particle scattering in the critical 90 degree pitch angle regime is quite sensitive to the form of the dissipation range spectrum for particles of all energies. However, in all cases the Fokker-Planck coefficient goes to zero more rapidly as the pitch angle nears 90 degrees than was indicated in earlier theories that ignored dissipation, thereby causing the spatial diffusion coefficient calculated from the magnetostatic theory to be infinite. The singularity is present in both isotropic and slab geometries. This result follows directly from the presence of dissipation, is applicable to particles of any energy, and points once again to the need to identify the correct higher order theory (including effects of the dissipation range) of pitch angle scattering for particles near 90 degrees.
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