Pitch angle scattering of solar particles: Comparison of ?particle? and ?field? approach

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In the quasi-linear theory of pitch angle scattering the power spectrum of magnetic field fluctuations is related to the shape of the pitch angle diffusion coefficient D(μ), the absolute value of the mean free path λ, and the rigidity dependence of the mean free path λ(R). We discuss these relations in detail during the solar particle event of 11 April, 1978 which was observed on HELIOS-2 at a distance of 0.49 AU from the Sun. Magnetic field measurements obtained during the time of the event are used as a basis for the ‘layer model’ in which the method of particle trajectories in an actually measured field is used to simulate pitch angle diffusion. The values of D(μ) and λ based on the trajectory simulation for 100 MeV protons (‘field’ approach) are compared with results obtained from solar proton data (‘particle’ approach) and with predictions from quasi-linear theory based on the additional assumption of the slab model for magnetic field fluctuations (‘QLT’ approach). The time of the event is characterized by a high level of field fluctuations, the observed mean free path of about 0.03 AU for 100 MeV protons is smaller than the average value near 1 AU. Results from the ‘field’ and ‘particle’ approaches agree surprisingly well. The remaining difference in the mean free path of about a factor of 2 could be due to tangential discontinuities which are measured by the magnetometer, but not seen by the real particles traveling along the average field. The results from the ‘field’ and ‘QLT’ approaches based on the same set of magnetic field measurements differ by about a factor of 4. One of the reasons for this discrepancy is that the conditions for resonance scattering are only marginally valid. In addition, the wave vectors representing Alfven-type fluctuations may not be totally field aligned. This deviation from the slab model would cause an increase of the theoretically predicted mean free path and lead to better agreement with the other two approaches.