Mean free paths of energetic particles at very large heliodistances (Pioneer 11 at 20 AU)

Abstract

Pioneer 11 magnetic field data at 20 AU are analysed by the computational method of Moussas, Quenby, and Webb (1975), Moussas and Quenby (1978), and Moussas, Quenby, and Valdes-Galicia (1982a, b) to obtain the parallel mean free path λ ∥, and the diffusion coefficient parallel to the magnetic field line K ∥. This method is the most appropriate for the mean free path calculation at large heliodistances since the alternative method which is based on fitting of energetic particle intensities cannot be easily and accurately be used because the association of energetic particles with their parent flares is not precise. The results show that the mean free path has values between 0.85 and 0.98 AU, linearly increasing with energy according to λ∥(Tkinetic) = ∧ + MT, where Λ = 0.846 AU and M = 4.44 × 10 −5 AU MeV−1 for energies between 10 MeV and 3 GeV for protons. These values of the parallel mean free path are much larger than the values estimated by previous studies up to 6 AU. The diffusion coefficient dependence upon energy follows a relation which simply reflects an almost constant mean free path and a linear dependence on the velocity of the particle, so that at 20 AU heliodistance K ∥(T kin) = K ∥, 1 MeV(T kin)T kinetic α, with α = 1/2. The distance dependence of the parallel diffusion mean free path follows a power law, λ ∥(R) = λ ∥, 1 AU R λ , where λ is 1 ± 0.1. While the parallel diffusion coefficient obeys a power-law relation with heliodistance R, K ∥ (R, T kin) = K ∥, 1 AU(T kin)R β , with β = 1 ± 0.1. The radial diffusion coefficient of cosmic rays is not expected to strongly depend upon the parallel diffusion coefficient because the nominal magnetic field at these large heliodistances (20 AU) is almost perpendicular to the radial direction and the contribution of the diffusion coefficient perpendicular to the magnetic field is expected to play a dominant role. However, the actual garden hose angle varies drastically and for long time periods and hence the contribution of the diffusion parallel to the field may continue to be important for the small scale structure of intensity gradients.