On the Power-Law Distribution of Pitch-Angle Scattering Times in Solar Wind Turbulence

The propagation of energetic particles in the solar wind depends in a sensitive way on the pitch-angle scattering of particles in the presence of magnetic turbulence. The well-known quasi-linear theory gives an expression for the pitch-angle scattering rate under the assumption of small turbulence levels, but both in the solar wind and in other astrophysical environments the turbulent magnetic field fluctuations can be large. Therefore, a reliable assessment of the pitch-angle scattering requires an investigation that goes beyond the quasi-linear theory. To this end, we employ a recently developed model of synthetic magnetic turbulence, which allows reproduction of a very long spectrum, while varying the turbulence level and the turbulence intermittency. Test particles representing protons with energies in the range 70 keV-1 MeV are injected in the turbulence spectrum plus a background magnetic field, and the pitch-angle scattering rate is determined by following the individual particles. Using turbulence and intermittency levels comparable to those observed in the solar wind, we find a broad power-law distribution of pitch-angle scattering times, which encompasses the quasi-linear value but extends to values both much larger and much smaller. We find that the distribution of pitch-angle scattering times also depends on the intermittency level. This finding shows that a description of parallel transport based on a single value of the pitch-angle scattering time is not sufficient. These numerical results are compared with observations of the distribution of magnetic variances at the particle resonant scale, measured in the solar wind by the Ulysses spacecraft.