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This paper summarizes the results obtained by the team “Heliosheath Processes and the Structure of the Heliopause: Modeling Energetic Particles, Cosmic Rays, and Magnetic Fields” supported by the International Space Science Institute (ISSI) in Bern, Switzerland. We focus on the physical processes occurring in the outer heliosphere, especially at its boundary called the heliopause, and in the local interstellar medium. The importance of magnetic field, charge exchange between neutral atoms and ions, and solar cycle on the heliopause topology and observed heliocentric distances to different heliospheric discontinuities are discussed. It is shown that time-dependent, data-driven boundary conditions are necessary to describe the heliospheric asymmetries detected by the Voyager spacecraft. We also discuss the structure of the heliopause, especially due to its instability and magnetic reconnection. It is demonstrated that the Rayleigh–Taylor instability of the nose of the heliopause creates consecutive layers of the interstellar and heliospheric plasma which are magnetically connected to different sources. This may be a possible explanation of abrupt changes in the galactic and anomalous cosmic ray fluxes observed by Voyager 1 when it was crossing the heliopause structure for a period of about one month in the summer of 2012. This paper also discusses the plausibility of fitting simulation results to a number of observational data sets obtained by in situ and remote measurements. The distribution of magnetic field in the vicinity of the heliopause is discussed in the context of Voyager measurements. It is argued that a classical heliospheric current sheet formed due to the Sun’s rotation is not observed by in situ measurements and should not be expected to exist in numerical simulations extending to the boundary of the heliosphere. Furthermore, we discuss the transport of energetic particles in the inner and outer heliosheath, concentrating on the anisotropic spatial diffusion diffusion tensor and the pitch-angle dependence of perpendicular diffusion and demonstrate that the latter can explain the observed pitch-angle anisotropies of both the anomalous and galactic cosmic rays in the outer heliosheath.

First, simulations of the wind-filled halos of starburst galaxies are performed in the framework of single-fluid magnetohydrodynamics, suitably extended to also track the self-consistent evolution of additional turbulence-related quantities. These quantities comprise the turbulent energy density, the cross-helicity, and the turbulent length scale. After a brief discussion of these extended equations and the employed numerical approach, we present selected simulation results, both for non-magnetized benchmark runs as well as for tests using the full system of equations. The dominant and unexpected feature of the former is a macroscopic flow instability near the rotational axis that prevents the outflow from reaching a steady state. Methods to determine the cause and nature of this instability are presented, followed by a preliminary analysis of the resulting turbulent properties. Second, the above framework is extended further to account for a non-constant energy difference (or residual energy), a quantity not conserved in the absence of dissipation, in addition to the Elsasser energies and by allowing each of these quantities its own characteristic correlation length scale. This setting is then applied to the outer heliosphere beyond the termination shock, where the solar wind expands both sub-Alfveńically and nonradially. The resulting solutions of this six-equation model are illustrated and studied in some detail.

We present a review of Anomalous Cosmic Rays (ACRs), including the history of their discovery and recent insights into their acceleration and transport in the heliosphere. We focus on a few selected topics including a discussion of mechanisms of their acceleration, escape from the heliosphere, their effects on the dynamics of the heliosheath, transport in the inner heliosphere, and their solar cycle dependence. A discussion concerning their name is also presented towards the end of the review. We note that much is known about ACRs and perhaps the term Anomalous Cosmic Ray is not particularly descriptive to a non specialist. We suggest that the more-general term: “Heliospheric Energetic Particles”, which is more descriptive, for which ACRs and other energetic particle species of heliospheric origin are subsets, might be more appropriate.

In the absence of efficient collisions, deviations from thermal equilibrium of plasma particle distributions are controlled by the self-generated instabilities. The whistler instability is a notorious example, usually responsible for the regulation of electron temperature anisotropy A=T⊥/T∥>1\\(A = T_{\\perp }/T_{\\parallel }> 1\\) (with ⊥,∥\\(\\perp , \\parallel \\) respective to the magnetic field direction) observed in space plasmas, e.g., solar wind and planetary magnetospheres. Suprathermal electrons present in these environments change the plasma dispersion and stability properties, with expected consequences on the kinetic instabilities and the resulting fluctuations, which, in turn, scatter the electrons and reduce their anisotropy. In order to capture these mutual effects we use a quasilinear kinetic approach and PIC simulations, which provide a comprehensive characterization of the whistler instability under the influence of suprathermal electrons. Analysis is performed for a large variety of plasma conditions, ranging from low-beta plasmas encountered in outer corona or planetary magnetospheres to a high-beta solar wind characteristic to large heliospheric distances. Enhanced by the suprathermal electrons, whistler fluctuations stimulate the relaxation of temperature anisotropy, and this influence of suprathermals increases with plasma beta parameter.

The Sun moves through the local interstellar medium, continuously emitting ionized, supersonic solar wind plasma and carving out a cavity in interstellar space called the heliosphere. The recently launched Interstellar Boundary Explorer (IBEX) spacecraft has completed its first all-sky maps of the interstellar interaction at the edge of the heliosphere by imaging energetic neutral atoms (ENAs) emanating from this region. We found a bright ribbon of ENA emission, unpredicted by prior models or theories, that may be ordered by the local interstellar magnetic field interacting with the heliosphere. This ribbon is superposed on globally distributed flux variations ordered by both the solar wind structure and the direction of motion through the interstellar medium. Our results indicate that the external galactic environment strongly imprints the heliosphere.

The Interstellar Boundary Explorer (IBEX) is a small explorer mission that launched on 19 October 2008 with the sole, focused science objective to discover the global interaction between the solar wind and the interstellar medium . IBEX is designed to achieve this objective by answering four fundamental science questions: (1) What is the global strength and structure of the termination shock, (2) How are energetic protons accelerated at the termination shock, (3) What are the global properties of the solar wind flow beyond the termination shock and in the heliotail, and (4) How does the interstellar flow interact with the heliosphere beyond the heliopause? The answers to these questions rely on energy-resolved images of energetic neutral atoms (ENAs), which originate beyond the termination shock, in the inner heliosheath. To make these exploratory ENA observations IBEX carries two ultra-high sensitivity ENA cameras on a simple spinning spacecraft. IBEX’s very high apogee Earth orbit was achieved using a new and significantly enhanced method for launching small satellites; this orbit allows viewing of the outer heliosphere from beyond the Earth’s relatively bright magnetospheric ENA emissions. The combination of full-sky imaging and energy spectral measurements of ENAs over the range from ∼10 eV to 6 keV provides the critical information to allow us to achieve our science objective and understand this global interaction for the first time. The IBEX mission was developed to provide the first global views of the Sun’s interstellar boundaries, unveiling the physics of the heliosphere’s interstellar interaction, providing a deeper understanding of the heliosphere and thereby astrospheres throughout the galaxy, and creating the opportunity to make even greater unanticipated discoveries.

Simulations of energetic neutral atom (ENA) maps predict flux magnitudes that are, in some cases, similar to those observed by the Interstellar Boundary Explorer (IBEX) spacecraft, but they miss the ribbon. Our model of the heliosphere indicates that the local interstellar medium (LISM) magnetic field (BLISM) is transverse to the line of sight (LOS) along the ribbon, suggesting that the ribbon may carry its imprint. The force-per-unit area on the heliopause from field line draping and the LISM ram pressure is comparable with the ribbon pressure if the LOS approximately 30 to 60 astronomical units and BLISM approximately 2.5 microgauss. Although various models have advantages in accounting for some of the observations, no model can explain all the dominant features, which probably requires a substantial change in our understanding of the processes that shape our heliosphere.

Cosmogenic Isotopes are produced in the Earth's atmosphere due to the interaction of galactic cosmic rays with nuclei of atmospheric atoms. Among others, the 10Be concentration in ice cores depends on the galactic cosmic ray flux outside of the Earth's magnetosphere and provides therefore a unique tool to investigate the solar modulation over very long time periods. In this study we investigate the importance of different local interstellar proton spectra often used in literature obtained outside of the Earth's magnetosphere. In order to parameterize the heliospheric modulation we apply the force‐field solution using individual local interstellar proton spectrum (LIS) model dependent ϕ values. Thus among atmospheric and magnetospheric processes, the 10Be concentration depends on an interplay of the different LIS and their modulation parameters. Since 10Be measurements do not provide any spectral resolution, PAMELA data have been used for a comparison with the calculated spectra and to provide the model dependent modulation parameters during the solar minimum in July 2006. Within the limitation of the force‐field solution and the freedom in parameter space, all LIS lead to a reasonable agreement with the data. Taking the LIS dependency of the modulation parameter into account, we derive linear equations to convert the individual ϕ between the different LIS. The conversions used here are then applied to a long‐term reconstruction of ϕ derived from a record of the cosmogenic radionuclide 10Be. By using the derived LIS conversions, we show that the occasionally observed negative ϕ values in the reconstruction of Steinhilber et al. (2008) vanish if another LIS model is used. In order to estimate other processes which alter this conclusion, the influence of the palaeo‐magnetic field has been included. Thus, if all inner‐heliospheric effects on the 10Be flux would be known, this investigation would have the potential to rule out certain LIS.

To present the main influence of anomalous diffusion on the energetic particle propagation, the fractional derivative model of transport is developed by deriving the fractional modified Telegraph and Rayleigh equations. Analytical solutions of the fractional modified Telegraph and the fractional Rayleigh equations, which are defined in terms of Caputo fractional derivatives, are obtained by using the Laplace transform and the Mittag-Leffler function method. The solutions of these fractional equations are given in terms of special functions like Fox's H, Mittag-Leffler, Hermite and Hyper-geometric functions. The predicted travelling pulse solutions are discussed in each case for different values of fractional order.

In the last few years it has been demonstrated, both by data analysis and by numerical simulations, that the transport of energetic particles in the presence of magnetic turbulence can be superdiffusive rather than normal diffusive (Gaussian). The term ‘superdiffusive’ refers to the mean square displacement of particle positions growing superlinearly with time, as compared to the normal linear growth. The so-called anomalous transport, which in general comprises both subdiffusion and superdiffusion, has gained growing attention during the last two decades in many fields including laboratory plasma physics, and recently in astrophysics and space physics. Here we show a number of examples, both from laboratory and from astrophysical plasmas, where superdiffusive transport has been identified, with a focus on what could be the main influence of superdiffusion on fundamental processes like diffusive shock acceleration and heliospheric energetic particle propagation. For laboratory plasmas, superdiffusion appears to be due to the presence of electrostatic turbulence which creates long-range correlations and convoluted structures in perpendicular transport: this corresponds to a similar phenomenon in the propagation of solar energetic particles (SEPs) which leads to SEP dropouts. For the propagation of energetic particles accelerated at interplanetary shocks in the solar wind, parallel superdiffusion seems to be prevailing; this is based on a pitch-angle scattering process different from that envisaged by quasi-linear theory, and this emphasizes the importance of nonlinear interactions and trapping effects. In the case of supernova remnant shocks, parallel superdiffusion is possible at quasi-parallel shocks, as occurring in the interplanetary space, and perpendicular superdiffusion is possible at quasi-perpendicular shocks, as corresponding to Richardson diffusion: therefore, cosmic ray acceleration at supernova remnant shocks should be formulated in terms of superdiffusion. The possible relations among anomalous transport in laboratory, heliospheric, and astrophysical plasmas will be indicated.