On the heliospheric diffusion tensor and its effect on 26-day recurrent cosmic-ray variations
Engelbrecht, Nicholas Eugéne
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A first attempt at an ab initio steady-state three-dimensional modulation model for galactic cosmic ray electrons, utilizing expressions adapted from the work of Teufel and Schlickeiser  and Shalchi et al. [2004a] for the parallel and perpendicular mean free paths dependent on basic turbulence quantities is presented. A similar model for galactic protons is also presented. Various models for the dissipation range breakpoint presented by Leamon et al.  are implemented. Applying a Fisk-Parker hybrid field, 26-day recurrent galactic proton and electron variations are investigated via a three-dimensional numerical modulation code in an attempt to understand the effects the varying of basic turbulence quantities would have on them. Only solar minimum conditions are considered here, and no attempts are made to fit data in any way whatsoever. At higher rigidities, the relationship between changes in cosmic ray intensities and changes in the modulation parameter first postulated by Zhang  was found to adequately explain the linear relationship between these quantities first observed by the same author. Effective diffusion for both galactic electrons and protons was dominated by the ratio of the perpendicular to parallel mean free paths, whilst typically the relationship of Zhang was found to no longer hold for electrons when this ratio dropped below a critical value with a sufficiently small perpendicular mean free path. With this small mean free path, combined with the fact that drift effects are not effective at low energies, electrons would be significantly influenced by transport along the magnetic field. In general, results for electrons were found to be very sensitive to the ratio of the perpendicular to parallel mean free paths. Constants of proportionality for relative amplitudes as function of latitude gradients were typically found to be ordered by the sign of the latitude gradient, being larger when it is positive than when it is negative. Only in one case, for electrons, was a clear ordering by the sign of the magnetic polarity found, with the constants of proportionality larger for qA > 0 than for qA<0.
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