Comparing Monte Carlo simulations, mean particle theory estimates, and observations of H ⁺ and O ⁺ outflows at high altitudes and latitudes

Abstract. We conducted a comparative analysis of the results from Monte Carlo simulations, mean particle theory estimates, and available observational data across different regions of Earth's magnetosphere, including the auroral, polar-wind, central-polar-cap, and cusp regions, focusing on the outflow of H+ and O+ ions at high latitudes and altitudes. We present altitude profiles for the mean perpendicular energy W⊥, mean parallel energy W∥, and mean total energy Wtotal. The Monte Carlo simulations were carried out using the Barghouthi model (Barghouthi, 2008), while the mean particle theory estimates were derived from Chang et al. (1986), and the observational data were obtained from Nilsson et al. (2013) and Barghouthi et al. (2016). The results of the comparison across different regions reveal the following findings: (1) Monte Carlo simulations and mean particle theory yield similar results in the auroral regions but show discrepancies in the polar-wind region. This discrepancy is attributed to the dominance of wave–particle interactions, which overshadow the effects of external forces (such as gravity, the polarization electric field, the mirror force, and centrifugal acceleration) in the auroral region and compete with them in the polar-wind region. (2) The use of altitude-dependent diffusion coefficients leads to the generation of high-energy particles, which are not consistent with the corresponding observational data at middle and high altitudes. Therefore, we recommend the use of velocity- and altitude-dependent diffusion coefficients. (3) A comparison with observations in the auroral and polar-wind regions demonstrates excellent agreement in the auroral region and good agreement in the polar-wind region, attributed to the implementation of appropriate velocity- and altitude-dependent diffusion coefficients. (4) In the central-polar-cap and cusp regions, both methods and observations show excellent agreement. (5) Based on these comparisons, we conclude that the electromagnetic wave wavelength in the polar-wind and auroral regions is approximately 8 km, and the velocity- and altitude-dependent diffusion coefficients used in the Monte Carlo simulations and mean particle theory are suitable for application in further studies of these regions.