ner_tags: O B-CelestialObjectRegion O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObjectRegion O O O B-CelestialObjectRegion O O O O O O O B-CelestialObjectRegion O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation O B-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O B-CelestialObjectRegion O O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObjectRegion O O O O O O O O O O O O B-CelestialObject O O O O B-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObjectRegion O O B-CelestialObjectRegion B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject O O O O O B-Model I-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model I-Model O O O B-Citation I-Citation I-Citation I-Citation O B-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O
tokens: perpendicular HTS and find that the PUIs and thermal gas are more heated and energized at the parallel than the perpendicular shock. We also model a quasi-parallel HTS and a quasi-perpendicular HTS to consider the case of an oblique HTS. In the last section, we summarize our results about the structure of collisionless oblique shock waves when mediated by energetic particles. 2. Model In this section, we present a brief review of the formulation of the PUI or SEP-mediated plasma model presented by Zank et al. ( 2014 , 2016 ), Zank ( 2016 ), and Mostafavi et al. ( 2017b ). The heliosphere comprises thermal solar wind, suprathermal energetic particles such as PUIs or SEPs, and neutral atoms (beyond an ionization cavity of about 6–10 au). The charge exchange mean free path in the IHS is approximately 2500 au and greater than 200 au in the supersonic solar wind beyond 10 au (Zank 2015 ). Thus, the charge exchange mean free paths are very large, and we can ignore the coupling between neutral atoms and solar wind protons when studying the structure of shocks. Using appropriate parameters for the supersonic solar wind beyond 10 au, the IHS, and the VLISM, Zank et al. ( 2014 ) estimated the equilibration timescales of PUIs and thermal plasma in these regions. They showed that the PUIs are not equilibrated with the background thermal plasma. Zank et al. ( 2016 ) showed that SEPs with energies greater than 5 keV cannot equilibrate in the inner heliosphere. Therefore, energetic particles such as PUIs, SEPs, and ACRs are a distinct component in the plasma system. The plasma flow is described by a multi-component model comprising thermal solar wind ions and electrons with Maxwellian distributions, and an energetic ion component (PUIs, SEPs, or ACRs). The multi-component model is too complicated for most problems, but it can be reduced to a single-fluid-like model by making some assumptions (see details in Zank et al. 2014 ). The collisionless diffusion or heat flux tensor and pressure tensor for the energetic particles may be expressed, respectively, as where η ≃ P p τ s is the viscosity coefficient and τ s is PUI-scattering timescale. P p is the PUI scalar pressure and Π p a stress tensor. The assumption is that the magnetic field is along the x -axis. K ∥ and K ⊥ are diffusion coefficients parallel and perpendicular to the magnetic field. The reduced single-fluid-like model equations, together with the Maxwell equations, are given by (Zank et al. 2014 , 2016 ) where μ 0 is the permeability of free space and J is the current density. B and E denote the magnetic and electric fields, P p the PUI pressure, P g the thermal gas (sum of electrons and protons) pressure, U the bulk flow velocity, and ρ the total density. We denote all quantities pertaining to PUIs and thermal gas with the subscripts p and g , respectively. γ p/g denotes the adiabatic index for PUIs/thermal gas. The viscosity and heat flux dissipation terms introduce distinct length scales into