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Cosmic-ray diffusion modeling: Solutions using variational methods
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View: Figures


Image of FIG. 1.
FIG. 1.

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 and κ, respectively, can also be illustrated.

Image of FIG. 2.
FIG. 2.

The pitch-angle Fokker-Planck coefficient, , for slab turbulence, i.e., a simplified turbulent magnetic field that varies only along the mean magnetic field. 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. The data points show numerical results obtained with a Monte Carlo simulation code and indicate that ≠ 0 at μ = ±1. Reproduced by permission from G. Qin and A. Shalchi, Astrophys. J. , 61 (2009). Copyright 2009 The American Astronomical Society.

Image of FIG. 3.
FIG. 3.

The time-integrated characteristic function, (μ, μ) from Eqs. (31a) and (31b) for the case of . Note that the slope of (μ, μ) is always discontinuous across μ, even though it appears to be perfectly smooth.

Image of FIG. 4.
FIG. 4.

Same as Fig. 3 but now for the opposite case of .


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Cosmic-ray diffusion modeling: Solutions using variational methods