0 50 100
−100
−50 0 50 100
Radial distance (AU)
Radial distance (AU)
α = 10o A > 0
200 MeV
−2
−1.5
−1
−0.5 0 0.5 1 1.5 2
0 50 100
−100
−50 0 50 100
Radial distance (AU)
Radial distance (AU)
α = 10o A < 0
200 MeV
−2
−1.5
−1
−0.5 0 0.5 1 1.5 2
Figure 5.18: Contour plots for 200 MeV electron intensity ratios, illustrating the factor by which solu- tions with full drift efficiency is larger (or smaller) than corresponding solutions without drifts in the meridional plane of the heliosphere for A>0 (left) and A<0 (right). The colour bars follow a log- arithmic scale (e.g. 1.5≡ 101.5). The dashed white halfcircle indicates the TS position at 94 AU, the dash-dotted lines indicate the polar extent of the HCS forα= 10◦, and the dashed black line shows the trajectory alongθ= 55◦at which the corresponding ratios in Figures 5.16 and 5.17 are shown. The Sun is located at the origin.
at high latitudes facilitates particle transport through those regions, while the low-diffusion barrier in the heliosheath may hinder transport - this is touched on in the discussion on drift patterns in Section 5.2. It should also be noted that the drift features discussed above, although indicative of basic trends also predicted by 3-D models [e.g.Strauss et al., 2012], are presented within the context of the 2-D model utilised in this study. While CR modulation studies con- ducted using 2-D models with drift capabilities usually scale down the drift efficiency based on scattering assumptions (see Section 3.4), full drift efficiency (κD,0 = 1.0) is assumed for the illustrations in this section. See also the work ofNndanganeni[2012, 2015]. Recently,Ngobeni [2015] andNgobeni and Potgieter[2015], also using a 2-D model, questioned if drifts could be large in the outer heliosphere - an issue that requires further investigation with full 3-D models.
introduces and details the various major processes involved in the transport and modulation of galactic electrons that may also later influence their re-acceleration.
Section 5.2 highlights the attributes of electrons and conveys how these are accounted for in the model; the model configuration for the study of electron transport is summarised and solutions are presented as reference for subsequent sections. These solutions also convey the standard features of the modulation of galactic electrons as also reported in earlier studies. As a first step in modelling galactic electrons, various possibilities for an input spectrum is considered in Section 5.3. The reference input spectrum specified at the HP (subsequently referred to as the HPS) is discussed, and its features, especially at very low energies (E .5 MeV), are surveyed.
Several possible modifications to the very-low-energy HPS are suggested and evaluated by ap- plication in subsequent sections. Section 5.4 investigates the rigidity dependence of electron diffusion. A number of variations of the rigidity profiles for diffusion coefficients (and their associated MFPs) in different energy regions are discussed; these scenarios, along with some of the input spectra introduced in the previous section, will surface again in Chapter 6 to have their influence on the features of re-accelerated electrons gauged. The most probable configu- ration consists of a low-energy (E .5 MeV) up-turn in MFPs attributed to dissipation-range turbulence effects, followed by a rigidity-independent segment at intermediate energies up to a few hundred MeV, from where MFPs increase again at higher energies.
It follows as general conclusions from Section 5.4 that sufficiently small diffusion cedes domi- nance to the effects of other processes such as adiabatic energy changes, while very large diffu- sion negates modulation altogether. Furthermore, MFPs that decrease with increasing rigidity are shown to soften distributions from the form of the input spectrum in that energy region, while harder spectra are obtained when MFPs increase with rigidity. This observation is im- portant with regards to the acceleration of these electron distributions; see Chapter 6. Section 5.5 reveals the value of MFPs also affect electron drifts: If diffusion is impaired, drift effects and their contribution to intensities are enhanced, while drift effects are subdued for the smaller in- tensity gradients brought about by enhanced diffusion. Also, pertaining to more global trans- port, the levels of diffusion largely dictate the extent to which drifts may affect the spatial distributions of electrons.
These general modulation features of galactic electrons are revisited in the next chapter, where the interaction between the transport processes reviewed here and DSA will be drawn into focus.
Diffusive Shock Acceleration of Electrons at the Termination Shock
6.1 Introduction
Galactic electrons, after having travelled through interstellar space and the heliosheath, may be accelerated upon their arrival at the TS. These locally accelerated electrons are henceforth referred to as re-accelerated electrons and it is aimed in this chapter to survey their features. The insights of the previous two chapters are hence combined, firstly to study how the acceleration of electrons at the TS is influenced by major modulating processes in the heliosphere, and also to ascertain the dependence of the DSA mechanism on the spectral properties of incident electrons. It is furthermore aimed to illustrate the contribution of re-accelerated electrons to global intensities and how this affects other processes accounted for in the TPE. A particular emphasis is placed on spectral features in this chapter, since DSA is characterised by changes in energy distributions.
As an introduction, the spectral features arising from the acceleration of strategically specified electron source functions are presented to convey the imprint of DSA on energy distributions more directly. Thereafter, the standard features of re-accelerated galactic electrons emerging under the reference model configuration are reviewed, followed by in-depth discussions of their spectral properties in subsequent sections. Due to the distinct nature of electrons and their modulation at different energies, the influence of input spectra and diffusion properties on acceleration are considered separately at low and high energies, with the effects of drifts also regarded at the latter. The spatial distributions of re-accelerated electrons are also discussed.