Until recently, numerical modulation models for the solar modulation of cosmic rays have
been based primarily on finite difference approaches; however, models based on the solution
of an appropriate set of stochastic differential equations have become increasingly
popular. This study utilises such a spatially three-dimensional and time-stationary model,
based on that of Strauss et al. (2011b). The remarkable numerical stability and powerful
illustrative capabilities of this model are utilised extensively and in a distinctly comparative
fashion to enable new insights into the processes of modulation. The model is
refined to provide for both the Smith-Bieber (Smith and Bieber, 1991) and Jokipii-Kota
(Jokipii and Kota, 1989) modifcations to the Parker heliospheric magnetic field (Parker,
1958) and the implications for modulation are investigated. During this investigation
it is conclusively illustrated that the Parker field is most conducive to drift dominated
modulation, while the Jokipii-Kota and Smith-Bieber modifcations are seen to induce
successively larger contributions from diffusive processes. A further refinement to the
model is the incorporation of a different profile for the heliospheric current sheet. This
profile is defined by its latitudinal extent given by Kota and Jokipii (1983), as opposed
to the profile given by Jokipii and Thomas (1981). An extensive investigation into current
sheet related matters is launched, illustrating the difference between these current
sheet geometries, the associated drift velocity fields and the effect on modulation. At
high levels of solar activity, such that the current sheet enters deep enough into the polar
regions, the profile of Kota and Jokipii (1983) is found to significantly reduce the effective
inward (outward) drifts of positively (negatively) charged particles during A > 0 polarity
cycles. The analogous effect is true for A < 0 polarity cycles and the overall effect is of
such an extent that the A > 0 and A < 0 solutions are found to coincide at the highest
levels of solar activity to form a closed loop. This is a result that has never before been
achieved without having to scale down the drift coefficient to zero at solar maximum,
as was done by e.g. Ndiitwani et al. (2005). Furthermore, it is found that the drift
velocity fields associated with these two current sheet profiles lead to significant differences
in modulation even at such low levels of solar activity where no difference in the
geometries of these profiles are yet in evidence. The model is finally applied to reproduce
four observed galactic proton spectra, selected from PAMELA measurements (Adriani
et al., 2013) during the atypical solar minimum of 2006 to 2009; a new proton local interstellar
spectrum was employed. The results are found to be in accordance with that
found by other authors and in particular Vos (2011), i.e. the diffusion was required to
consistently increase from 2006 to 2009 and, in addition, the rigidity dependence below ~
3 GV was required to change over this time so that the spectra became increasingly softer. / MSc (Space Physics), North-West University, Potchefstroom Campus, 2015
| Identifer | oai:union.ndltd.org:NWUBOLOKA1/oai:dspace.nwu.ac.za:10394/15516 |
| Date | January 2015 |
| Creators | Raath, Jan Louis |
| Source Sets | North-West University |
| Language | English |
| Detected Language | English |
| Type | Thesis |
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