Four-fluid model and numerical simulations of magnetic structures in the heliosheath

Abstract

The first part of this paper extends the three-fluid model of Avinash & Zank for magnetic structures in the heliosheath to a four-fluid model consisting of electrons, pick-up ions (PUIs), solar wind ions (SWIs), and neutral hydrogen. The PUIs are generated by neutrals via charge exchange with SWI. Since the kinetic pressure of PUI is nearly three to four times the pressure of SWI, these are more suited to mediate small-scale structures in the heliosheath such as magnetic holes (MH)/humps etc. The constant energy exchange between these two fluids drives them nonadiabatic. The PUIs are isothermal (γ = 1) while SWIs are nonadiabatic with an index γ ≈ 1.25. The four-fluid model captures these effects via a modified equation of state for PUI and SWI. The phase space of time-independent solutions in terms of the Mach numbers of PUI and SWI is constructed to delineate the parameter space which allows structure formation in the heliosheath. The second part of the paper examines the stability of the time-independent solutions computed in the first part by evolving them via a full system of Hall-MHD equations. The simulation results show that these solutions are not quite stable. As the structure propagates it develops growing oscillations in the wings. Concomitantly, there are changes in the amplitude and width of the structure. This instability could be due to local changes in the velocity of the structure and reflects an exchange between the kinetic and magnetic parts of the total energy. Our results about the presence of growing oscillations in the wings of solitary wave solutions are consistent with the recent analysis of MHs in the heliosheth by Burlaga et al. Their analysis also shows evidence for the presence of oscillations and instabilities in the wings of MHs in the heliosheath.