tokens: indices of the thermal plasma/PUIs. The collisional thermal plasma stress tensor and PUI stress tensor in a 1D form may be expressed as , where η g is the thermal collisional viscosity coefficient and η I is the collisionless PUI viscosity coefficient associated with magnetic fluctuations (Jokipii Williams 1992 ; Zank et al. 2014 ). A 1D steady-state model in which all physical quantities depend on the x Cartesian coordinate is used and U = ( U x , 0, 0) and B = (0, 0, B z ). The 1D form of Equations ( 10 )–( 12 ) in normalized form is where is the thermal gas Mach number of the flow, , L ≡ K g / U 1 , is distance normalized to the diffusion length scale, and is the Schmidt number of the thermal plasma/PUI. The inverse compression ratio is y = U x / U x 1 and , , and . The inverse Alfvén Mach number squared of the flow far upstream is . Based on the thermal collisional term scales derived above from the expressions in Zank ( 2014 ), the dominant collisional terms in a collisional magnetized plasma can be estimated. The small mass of electrons compared to protons means they do not contribute significantly to either the thermal heat conduction or thermal viscosity. Proton–electron collisions are negligible since the mean free path is very large compared to that of proton–proton collisions. The dominant collisional terms derive from proton–proton collisions. The diffusion coefficient associated with proton–proton collisions, K pp , upstream of the observed VLISM shock is about 10 15 m 2 s −1 , and the thermal viscosity is 2.5 × 10 −8 kg m −1 s −1 , giving a thermal Schmidt number of about 0.25. Energetic PUIs outside the heliosphere are generated by secondary charge exchange, and their number density is very small in the VLISM ( n p ≈ 5 × 10 −5 cm −3 ; Zirnstein et al. 2014 ), therefore they contribute a very small pressure compared to the thermal plasma ( P I1 / P g 1 ≈ 0.05). A characteristic value for the PUI heat conduction, K I , in the VLISM is ∼10 14 m 2 s −1 . The pitch-angle scattering timescale in the VLISM is taken to be , giving 5.17 × 10 2 s, which gives a value for the PUI viscosity, η I , as ∼3.57 × 10 −13 kg m −1 s −1 , making the PUI Schmidt number about 10 −3 . The PUI Schmidt number is much smaller than that of the thermal gas (), thus PUIs and the dissipation associated with them cannot mediate the VLISM shock, as shown by Mostafavi et al. ( 2017a , 2017b ). Consequently, we can neglect PUI dissipation terms in favor of the corresponding thermal gas terms. Unlike the HTS, PUIs will therefore behave adiabatically, is constant through a broad VLISM shock, and the thermal gas will be heated preferentially. Recall that PUIs were predicted (Zank et al. 1996 ) and observed (Richardson et al. 2008 ) to be heated preferentially at the HTS, with the thermal plasma component remaining relatively unheated. The physical processes determining the structure of the HTS and the VLISM shocks are therefore different. We use the 1D form of the
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