A comparison study between observations and simulation results of Barghouthi model for O⁺ and H⁺ outflows in the polar wind

Abstract. To advance our understanding of the effect of wave-particle interactions on ion outflows in the polar wind region and the resulting ion heating and escape from low altitudes to higher altitudes, we carried out a comparison between polar wind simulations obtained using Barghouthi model with corresponding observations obtained from different satellites. The Barghouthi model describes O⁺ and H⁺ outflows in the polar wind region in the range 1.7 R_E to 13.7 R_E, including the effects of gravity, polarization electrostatic field, diverging geomagnetic field lines, and wave-particle interactions. Wave-particle interactions were included into the model by using a particle diffusion equation, which depends on diffusion coefficients determined from estimates of the typical electric field spectral density at relevant altitudes and frequencies. We provide a formula for the velocity diffusion coefficient that depends on altitude and velocity, in which the velocity part depends on the perpendicular wavelength of the electromagnetic turbulence λ_⊥. Because of the shortage of information about λ_⊥, it was included into the model as a parameter. We produce different simulations (i.e. ion velocity distributions, ions density, ion drift velocity, ion parallel and perpendicular temperatures) for O⁺ and H⁺ ions, and for different λ_⊥. We discuss the simulations in terms of wave-particle interactions, perpendicular adiabatic cooling, parallel adiabatic cooling, mirror force, and ion potential energy. The main findings of the simulations are as follows: (1) O⁺ ions are highly energized at all altitudes in the simulation tube due to wave-particle interactions that heat the ions in the perpendicular direction, and part of this gained energy transfer to the parallel direction by mirror force, resulting in accelerating O⁺ ions along geomagnetic field lines from lower altitudes to higher altitudes. (2) The effect of wave-particle interactions is negligible for H⁺ ions at altitudes below ~7 R_E, while it is important for altitudes above 7 R_E. For O⁺ wave particle interaction is very significant at all altitudes. (3) For certain λ_⊥ and at points, altitudes, where the ion gyroradius is equal to or less than λ_⊥, the effect of wave-particle interactions is independent of the velocity and it depends only on the altitude part of the velocity diffusion coefficient; however, the effect of wave-particle interactions reduce above that point, called saturation point, and the heating process turns to be self-limiting heating. (4) The most interesting result is the appearance of O⁺ conics and toroids at low altitudes and continue to appear at high altitudes; however, they appear at very high altitudes for H⁺ ions. We compare quantitatively and qualitatively between the simulation results and the corresponding observations. As a result of many comparisons, we find that the best agreement occurs when λ_⊥ equals to 8 km. The quantitative comparisons show that many characteristics of the observations are very close to the simulation results, and the qualitative comparisons between the simulation results for ion outflows and the observations produce very similar behaviors. To our knowledge, most of the comparisons between observations (ion velocity distribution, density, drift velocity, parallel and perpendicular temperatures, anisotropy, etc.) and simulations obtained from different models produce few agreements and fail to explain many observations (see Yau et al., 2007; Lemaire et al., 2007; Tam et al., 2007; Su et al., 1998; Engwall et al., 2009). This paper presents many close agreements between observations and simulations obtained by Barghouthi model, for O⁺ and H⁺ ions at different altitudes i.e. from 1.7 R_E to 13.7 R_E.