Basic concepts of particle scattering. In the upper panel, the particle's pitch-angle is illustrated, which is an important quantity for the description of charged particle scattering. In the lower panel, sample particle trajectories are shown (black solid lines) in a turbulent magnetic field (blue dotted lines) superposing a homogeneous background field (blue arrow). The effects of pitch-angle scattering and perpendicular scattering as described through the coefficients D μμ and κ⊥, respectively, can also be illustrated.
The pitch-angle Fokker-Planck coefficient, D μμ, for slab turbulence, i.e., a simplified turbulent magnetic field that varies only along the mean magnetic field. 53 The solid and dotted lines (the latter is only visible around μ = 0) show analytical results obtained by using quasi-linear and second-order quasi-linear theories. 45 The data points show numerical results obtained with a Monte Carlo simulation code and indicate that D μμ ≠ 0 at μ = ±1. Reproduced by permission from G. Qin and A. Shalchi, Astrophys. J. 707, 61 (2009). Copyright 2009 The American Astronomical Society.
The time-integrated characteristic function, R(μ, μ0) from Eqs. (31a) and (31b) for the case of . Note that the slope of R(μ, μ0) is always discontinuous across μ0, even though it appears to be perfectly smooth.
Same as Fig. 3 but now for the opposite case of .
Article metrics loading...
Full text loading...