## 1. Introduction

[2] The solar system moves through interstellar space populated by three principal particle species: the thermal electron-ion plasma, neutral atoms, and the galactic cosmic rays (GCR). The latter is a highly nonthermal ionic population. One measure of the relative importance of the species is total energy density of the corresponding “gas.” In the local interstellar medium (LISM), also called the local cloud, these three species have energy densities of approximately 0.38, 0.61, and 0.55 eV cm^{−3}, respectively [*Ip and Axford*, 1985; *Frisch*, 1997]. In addition, the plasma component carries with it an embedded magnetic field with an energy density of the order of 0.1 eV cm^{−3} [*Frisch*, 2000], although the last value is highly uncertain.

[3] From the energy density estimates, GCR appear to be the dominant species in the LISM and are expected to have a profound effect on the plasma flow in and around the heliosphere. The issue is, however, complicated by the fact that these highly energetic particles may be only weakly coupled to the background plasma. Indeed, the lengthscale of the plasma-cosmic ray interaction is the diffusion length κ/*u*, where κ is the cosmic-ray diffusion coefficient and *u* is the average velocity of the scattering centers. The diffusion lengthscale can become very large at particle energies above several GeV so that cosmic rays may not interact with the heliosphere at all. On the other hand, MeV particles are expected to be strongly coupled to the plasma and as a result may change the flow of plasma inside the heliosphere.

[4] Galactic cosmic ray propagation in the heliosphere has traditionally been the domain of the modulation studies for the past three decades. It is beyond the scope of this paper to give even a brief overview of the modulation models in existence; recent reviews are given by *Potgieter* [1998] and *Jokipii and Kota* [2000]. However, despite the detailed treatment of the GCR modulation by the the solar wind, virtually all models lack a self-consistent treatment of the three particle species. In particular, the plasma flow geometry and the magnetic field are typically described by a spherically expanding solar wind and the resulting Parker spiral field, with possible modifications. Many models now correctly include a subsonic post-shock solar wind region, an approach first used by *Kota and Jokipii* [1993]. This approach is especially relevant in view of observations showing that galactic cosmic rays experience modulation in the inner heliosheath [*Webber and Lockwood*, 1997; *McDonald et al.*, 2000]. However, both the external “modulation boundary” and the termination shock (TS) are typically taken to be spherically symmetric. Notable exceptions are works by *Fichtner et al.* [1996], *Haasbroek and Potgieter* [1998], and *Sreenivasan and Fichtner* [2001]. In the first paper, the authors studied GCR modulation inside an ellipsoidal domain, assumed to be produced by the TS elongation along the solar polar axis, with the help of a fluid model. By contrast, *Haasbroek and Potgieter* [1998] solved the momentum-dependent transport equation inside an asymmetric domain designed to simulate the shape of the TS produced by the solar wind interaction with the interstellar flow. *Sreenivasan and Fichtner* [2001] solved a similar problem for anomalous cosmic rays (ACR) using a fully three-dimensional (3-D) model. One of the main results of these two papers is that the cosmic-ray asymmetry with respect to the interstellar wind direction becomes smaller at small heliocentric distances; this result will be discussed below in some detail.

[5] It has been realized for some time that the inner heliosphere is not the only region where cosmic rays and solar wind interact. In particular, gas dynamic and MHD models show that the heliospheric magnetic field is strongly amplified near the nose of the heliopause because of flow deceleration [*Nerney et al.*, 1993; *Washimi and Tanaka*, 1996; *Linde et al.*, 1998]. The amplified magnetic field will inhibit particle diffusion and is likely to stop the lower energy galactic cosmic rays from propagating past the inner heliosheath. Dissatisfaction with the “modulation boundary” approach led to development of global GCR models including not only the solar wind but the LISM interaction region as well [*Izmodenov*, 1997; *Fahr et al.*, 2000; *Myasnikov et al.*, 2000a, 2000b]. However, every global heliospheric model has been based on the fluid GCR description, where a momentum averaged quantity (pressure) is used instead of the phase space density. The deficiency of this approach stems from the necessity of introducing momentum-averaged diffusion coefficients and a cosmic-ray “adiabatic index” as input parameters. This makes the model less consistent because the average diffusion coefficients depend on the cosmic ray gradients themselves.

[6] Energy-dependent cosmic-ray modulation in the heliosheath was first studied by *Grzedzielski et al.* [1993] with a non-self-consistent model. The authors used an incompressible flow assumption and constant magnetic field in the heliosheath. The model of *Florinski and Jokipii* [1999] represented the first attempt to study the GCR-solar wind interaction at a self-consistent two-dimensional level without the assumption of spherical symmetry. While the solar wind flow was computed self-consistently, the model did not extend into the interstellar medium and only contained a limited region beyond the TS. As a result, the model was only applicable in the upwind direction with respect to the heliopause. This paper overcomes some of the difficulties encountered in the earlier study by introducing a two-dimensional, axisymmetric global heliospheric model of galactic cosmic ray propagation in the heliosphere and the surrounding LISM. Since neutral atoms have a profound effect on the shape of the heliospheric boundaries and the solar wind flow [*Baranov and Malama*, 1993; *Pauls et al.*, 1995], we include them in the simulation using a fluid approximation. The model treats cosmic rays as a nonthermal distribution in phase space, rather than a fluid, and uses realistic diffusion coefficients calculated from our understanding of the magnetic field and the turbulence levels in both the heliosphere and the LISM. To relate out approach to the fluid models, we compute the momentum-averaged diffusion parameters from our model and compare them to those used by models based on the hydrodynamic approximation.