Monte Carlo Study of the transition region in the polar wind: An improved collision model

Abstract

A Monte Carlo simulation was used to study the steady state flow of the polar wind protons through a background of O+ ions. The simulation region included a collision‐dominated region (barosphere), a collisionless region (exosphere), and the transition layer embedded between these two regions. Special attention was given to using an accurate collision model, i.e., the Fokker‐Planck expression was used to represent H+ ‐ O+ collisions. The model also included the effects of gravity, the polarization electric field, and the divergence of the geomagnetic field. For each simulation, 105 particles were monitored, and the collected data were used to calculate the H+ velocity distribution function fnof;H+, density, drift velocity, parallel and perpendicular temperatures, and heat fluxes for parallel and perpendicular energies at different altitudes. The transition region plays a pivotal role in the behavior of the H+ flow. First, the shape of the distribution function is very close to a slowly drifting Maxwellian in the barosphere, while a “kidney bean” shape prevails in the exosphere. In the transition region, the shape of fnof;H+ changes in a complicated and rapid manner from Maxwellian to kidney bean. Second, the flow changes from subsonic (in the barosphere) to supersonic (in the exosphere) within the transition region. Third, the H+ parallel and perpendicular temperatures increase with altitude in the barosphere due to frictional heating, while they decrease with altitude in the exosphere due to adiabatic cooling. Both temperatures reach their maximum values in the transition region. Fourth, the heat fluxes of the parallel and perpendicular energies are positive and increase with altitude in the barosphere, and they change rapidly from their maximum (positive) values to their minimum (negative) values within the transition region. The results of this simulation were compared with those found in previous work in which a simple (Maxwell‐molecule) collision model was adopted. It was found that the choice of the collision model can alter the results significantly. The effect of the body forces was also investigated. It was found that they can also alter the results significantly. Both the body forces and collision model have a large effect on the heat flux, while they have only a small quantitative effect on the lower‐order moments (density, drift velocity, and temperature).