The LIS for the different galactic CR species are needed as initial conditions at the ‘heliospheric boundary’, presumably the HP but probably even further out. Computed galactic CR spectra could be different from the LIS. Surprisingly, little is known about most of these galactic spectra at energies below a few GeV because of solar modulation so that the uncertainties, mostly attributed to speculation instead of solid evidence, can be rather large as illustrated by Webber and Higbie (2008, 2009). Adiabatic energy losses in the heliosphere cause the galactic CR spectral shapes for ions and anti-protons below 10 GeV to be properly disguised, progressively with decreasing energy and closer to the Sun. In contrast, the intensity of MeV-electrons is much less modified by adiabatic energy losses and also by gradient and curvature drifts. Unfortunately, from an electron LIS point of view, Jupiter is a dominant source of up to 30 MeV electrons in the inner heliosphere, also completely concealing the electron LIS in the inner heliosphere at these energies. This is not the case for positrons. The spectral shape at Earth for the low energy part of the positron spectrum is likely to be the same as for the positron LIS. There also are indications from the PAMELA observations that the LIS for positrons, and to some extent also electrons, may contain contributions from local galactic sources so that the LIS may not be as isotropic as assumed. With the two Voyager spacecraft at or close to the HP, another milestone in the solar modulation of CRs is foreseeable when the LIS gets observed.
The global features, structure, and geometry of the heliosphere as discussed above are important for modulation studies so that several issues arise, e.g., what is the difference in the distance to the ‘modulation boundary’ in the polar and tail regions? How asymmetrical is the heliosphere in the azimuthal and meridional planes and how does it affect CR modulation? See, e.g., Langner and Potgieter (2005) and Ngobeni and Potgieter (2011). How much does the ‘modulation volume’ vary from solar minimum to maximum activity and how much is the inner heliosheath contributing to this aspect? How much is the TS position oscillating (moving inward and outward) with changing solar activity? Furthermore, what is the role that the vastly extended heliospheric tail region plays? It could also be that the alignment of the HMF and the local interstellar magnetic field at the HP, together with the HCS, create regions of ideal entrance for galactic CRs introducing in the process an asymmetry in galactic CR modulation.
The wavy HCS is a successful and well-established physical entity in global modeling of solar modulation. The tilt angle of the HCS has become the most useful indicator of solar activity from a drift-modulation point of view and is widely used in data interpretation and especially in modeling. However, the calculation of this tilt angle is model dependent and it is not clear how the waviness is preserved when propagating outwards away from the Sun, especially with increasing solar activity (Jiang et al., 2010). The dynamic of the HCS has to be studied in more detail, with the first insightful contributions being made (e.g., Borovikov et al., 2011). It is also unclear whether particle drifts play a significant role in the heliosheath and to what extent drift patterns are different than in the inner heliosphere (Webber et al., 2008).
Improved knowledge about the global solar wind profile and HMF remains crucial for effective modeling. Before the Ulysses mission little was explicitly known about the latitudinal dependence of these entities in the inner heliosphere. Today, the solar wind profile can be specified in detail in models, while for the HMF came the realization that it may not be approximated in the heliospheric polar regions by the HMF that Parker envisaged in the 1960s. This aspect is contributed to interesting development in CR modulation. Nowadays, in numerical models significant modifications, mostly phenomenological, to the Parker field are applied in the polar regions, where a possible replacement is in the form of the Fisk (1996) solar magnetic field. Unfortunately, the Fisk-type fields are too complex to handle straight forwardly in standard numerical codes, but progress is being made (e.g., Burger et al., 2008; Sternal et al., 2011). At present, a conclusion for numerical modeling may be that Parkerian type HMFs are mostly too simple (although the interpretation of HMF observations keep pointing to such underlying simplicity) while Fisk-type fields are too complex to handle numerically (and seem absent in the way that HMF observations are interpreted). The question about the HMF geometry is how significant are the modulation effects of the Fisk-type HMF on CR modulation. To answer this, more study is needed to gain a better understand of the finer details of these complex magnetic fields and the relation to long-term CR modulation, especially how this field changes with solar activity. An aspect that should be kept in mind is that the study of more realistic magnetic fields requires an ever more complex diffusion tensor and description of drifts.
Progress has been made in understanding observations of small latitudinal gradients from Ulysses. In order to do so, Burger et al. (2000) argued that the rigidity dependence of the two components of the diffusion tensor, which are perpendicular to the mean HMF, should be decoupled. This approach was supported by the investigation of MeV electrons (Ferreira et al., 2001). Although the concept of increased polar perpendicular diffusion is well established, no conclusive theoretical work has been published to explain this dependence. Such an investigation may also be crucial in deciding to what extent the ‘standard’ Parker HMF has to be modified.
Three-dimensional models to describe the propagation and modulation of Jovian electrons in the inner heliosphere were applied by Fichtner et al. (2000), Ferreira et al. (2001), and Moeketsi et al. (2005). They studied the radial and latitudinal transport of these particles in detail and estimated upper and lower limits for the ratio of the parallel and perpendicular diffusion coefficients, which in numerical model is a crucial modulation parameter. This needs to be investigated further. They also disentangled the galactic and Jovian contributions to these electron observations, a process that improved understanding and the interpretation of Ulysses data (see also Strauss et al., 2013a). They found that Jovian electrons dominate the inner equatorial regions up to 10 – 20 AU but it is unlikely that they can dominate the low-energy galactic electrons to heliolatitudes higher than 30° off the equatorial plane. This is determined however by how large polar perpendicular diffusion is made and needs further study. Recently, Potgieter and Nndanganeni (2013a) offered computations of what can be considered lower and upper limits for galactic electrons at Earth at energies below a 100 MeV.
The acceleration and propagation of CRs and the ACRs at the TS and beyond are presently highly controversial and need further studies. The standing paradigm of the ACRs being accelerated at the TS was severely questioned when the Voyager spacecraft crossed the TS and observed unexpected results. The spectrum of ACRs did not unfold to an anticipated power-law, and the ACR fluxes simply continued to increase as the two Voyagers moved away from the TS. Magnetic reconnection (Drake et al., 2010; Lazarian and Opher, 2009) and different forms of stochastic acceleration (Fisk and Gloeckler, 2009; Strauss et al., 2010a) have been invoked as causing this phenomena, or it could simply be due to the so-called bluntness of the TS (e.g., McComas and Schwadron, 2006; Kóta and Jokipii, 2008). The answer to this unresolved question and the full grasp of where and how ACRs are accelerated should have important impacts on the transport and reacceleration of CRs in the heliosphere and elsewhere in the interstellar medium. Other interesting aspects of CRs beyond the TS were discussed by Potgieter (2008).
In the field of the long-term (11-years and longer) CR modulation in the heliosphere, several issues need further investigation and research: (1) Despite the apparent success of the compound numerical model described above the amount of merging taking place beyond 20 AU needs to be studied with MHD models, especially the relation between interplanetary CMEs and GMIRs, and how these large barriers may modify the TS, the inner heliosheath and perhaps also the HP. (2) The full rigidity dependence of the compound model is as yet not well described because the underlying effects of turbulence on the diffusion coefficients is poorly observed and understood. (3) A major issue with time-dependent modeling, apart from global dynamic features such as the wavy HCS, is what to use for the time dependence of all the diffusion coefficients in Equation (5), on top of the already complex issue of what their steady-state energy (rigidity) and spatial dependence are in the inner heliosphere (e.g., Manuel et al., 2011a,b). It has now also become vital to understand the diffusion tensor beyond the TS. Equation (5) is probably more complex for this region and needs to be extended to include processes (perhaps even completely new ones) that are otherwise considered to be negligible. (4) Fundamentally, from first principles, it is not yet well understood how gradient and curvature drifts reduce with solar activity. This aspect needs now also to be investigated for the region beyond the TS. For example, what happens to the wavy HCS in the heliosheath and how will the strong latitudinal and azimuthal components of the solar wind velocity and the associated HMF influence particle drifts and CR modulation in the heliosheath? The question arises if the modulation in this region is really fundamentally different from the rest of the heliosphere? (5) Another important question is how the heliospheric modulation volume varies with time on the scale of thousands to millions of years? The Sun encounters different interstellar environments during its passage through the galaxy, and hence the outer structure and size of heliosphere should change over such periods.
Other interesting aspects that will hopefully be addressed in future are: (1) The solar modulation of many CR species and their isotopes has not been properly modeled. The first obstacle, and therefore prime objective, will be to establish LIS for these isotopes. (2) The anisotropy of CRs at various energies as caused inside the heliosphere, also related to what a very extensive heliotail may contribute, is another specialized topic. In this context, see the review by Kóta (2012). (3) At what rigidity is the modulation of CRs beginning? This is important for the interpretation of observations of CRs, also for anisotropy studies. In modulation modeling it is simply assumed to begin at 30 GeV. (4) The extended solar cycle 23/24 minimum provides an opportunity to investigate conditions that were different than before, perhaps similar to those in the early 1900s. This may reveal a 100 – 120 year cycle in CR modulation. (5) Over the last decade, there has been noteworthy progress in obtaining, analyzing and interpreting Be10 and other isotopes produced by CRs in the atmosphere, which reveals a history of CRs going back to millions of years (e.g., Wieler et al., 2011). This certainly contributes to the growing interest in the topic of space climate (see Scherer et al., 2006, and reference therein).
Mewaldt (2012) noted from an experimental point of view that there are presently a dozen spacecraft measuring galactic CRs and ACRs over energies from below 1 MeV to 1 TeV and in situ from 1 to 122 AU (see his Figure 1 for current missions). These space missions are supplemented by ground-based detectors such as NMs and by balloon-flight instruments. He concluded that the challenge during the next decade will be to maintain enough of these missions and facilities to support the Voyagers’ approach and passage through the HP into interstellar space, and to record in detail the evolving story of how CRs in the heliosphere respond to the Sun’s new direction in solar activity.