Double‐hump H⁺ velocity distribution in the polar wind

Abstract

The polar wind is an ambipolar plasma outflow from the terrestrial ionosphere at high latitudes. As the ions drift upward along geomagnetic flux tubes, they move from collision‐dominated (ion barosphere) to collisionless (ion exosphere) regions. A transition layer is embedded between these two regions where the ion characteristics change rapidly. A Monte Carlo simulation was used to study the steady‐state flow of H+ ions through a background of O+ ions. The simulation domain covered the collision‐dominated, transition, and collisionless regions. The model properly accounted for the divergence of magnetic field lines, the gravitational force, the electrostatic field, and H+‐O+ collisions. The H+ velocity distribution, f(H+), was found to be very close to Maxwellian at low altitudes (deep in the barosphere). As the ions drifted to higher altitudes, f(H+) formed an upward tail. In the transition layer, the upward tail evolved into a second peak with a kidney bean shape, and hence, f(H+) developed a double‐humped shape. The second peak grew with altitude and eventually became dominant as the ions reached the exosphere. This behavior is due to the interplay between the electrostatic force and the velocity‐dependent Coulomb collisions. Moreover, the H+ heat flux, q(H+), was found to change rapidly with altitude in the transition layer from a positive maximum to a negative minimum. This remarkable feature of q(H+) is closely related to the coincident formation of the double‐humped structure of f(H+). The double‐hump distribution might destabilize the plasma or, at least, cause enhanced thermal fluctuations. The double‐hump f(H+), and the associated wave turbulence, have several consequences with regard to our understanding of the polar wind and similar space physics problems. The plasma turbulence can significantly alter the behavior of the plasma in and above the transition region and, therefore, should be considered in future polar wind models. The wave turbulence can serve as a signature for the formation of the double‐hump f(H+). Also, more sophisticated (than the existing bi‐Maxwellian 16‐moment) generalized transport equations might be needed to properly handle problems such as the one considered here.

A collisional kinetic model of the polar wind

“…In our study, regularity conditions are imposed on the velocity distribution function to obtain a fast convergence toward a stable stationary numerical solution of the Fokker-Planck equation. Results of these both kinetic models are in good agreen/ent with those of the Monte Carlo simulations [Barghouthi et al, 1990;Barakat et al, 1995].…”

Effects of Wave-Particle Interactions on Double-Hump Distributions of the H + Polar Wind

“…The model and the algorithm used in this problem are similar to those described in and Barakat et al (1995) except that effects of WPI are here included. We consider the steady state of a plasma composed of H + , O + and e − .…”

“…collisionless region). The aim of the present work is to analyze the effects of WPI on double-hump H + ion distributions in the polar wind, in other words to include the effect of WPI into the Monte Carlo model of Barakat et al (1995), which included the effects of gravity, electric field, diverging geomagnetic field and Coulomb collisions.…”

“…Generalized transport models (Demars and Schunk, 1987) are in principle applicable in the barosphere, the transition region and the exosphere but only with proper choice of base function and correction term. and Barakat et al (1995) used Monte Carlo simulation to study the flow of H + ions in the polar wind in the three regions. Taking into account the effects of gravity, electrostatic field, diverging geomagnetic field and H + −O + Coulomb collisions represented by Fokker-Planck expression, they found double-hump H + velocity distribution functions in the transition region when the velocity distribution is assumed to be a Maxwellian distribution function at the lower boundary.…”

O<sup>+</sup> and H<sup>+</sup> ion heat fluxes at high altitudes and high latitudes

“…These observations are characteristic of any plasma flow where collisions are not dominated. Different theoretical studies have discussed the ion outflows in the polar wind and auroral regions either by using kinetic models (e.g., Lemaire and Scherer, 1973, and for more details see the review by Tam et al, 2007), transport theory approach (e.g., Schunk and Watkins, 1982;Demars and Schunk, 1989, 1992Khazanov et al, 1984; or the Monte Carlo method (e.g., Barakat and Schunk, 1983;Barghouthi et al, 1993Barghouthi et al, , 2001Barakat et al, 1995). These models have investigated the ion outflows either in the collision-dominated region or collisionless regions or in both regions.…”