An-Najah Staff

The Monte Carlo method was shown to be a very powerful technique in solving the Boltzmann equation by particle simulation. Its simple concept, straightforward algorithm, and its adaptability to include new features (such as, gravity, electric field, geomagnetic field, and different collision models) make it useful tool in space plasma physics, and a powerful test of results obtained with other mathematical methods. We have used Monte Carlo method to solve Boltzmann equation, which describes the motion of a minor ion in a background of ions under the effect of external forces and Coulomb collisions with background ions. We have computed the minor ion velocity distribution function, drift velocity, density, temperatures and heat fluxes. As an application, Monte Carlo simulation method has been adapted to determine the O ⁺ velocity distribution function, O ⁺ density, O ⁺ drift velocity, O ⁺ temperatures, and O ⁺ heat fluxes for Coulomb Milne problem.

Altitude profiles for O+ ion velocity distribution functions, O+ parallel and perpendicular temperatures, O+ temperature anisotropy, O+–O+ and O+–O collision frequencies and O+ temperature partition coefficients β|| and β⊥ are obtained in the auroral ionosphere (150 km–500 km). A Monte Carlo simulation was used to investigate the behavior of O+ ions that are E×B drifting through a background of neutrals O, with the effects of O+–O resonant charge exchange and polarization interactions as well as O+–O+ Coulomb collisions. We have found, for low altitudes, the effect of O+–O+ Coulomb collisions is negligible and, as electric field increases, O+–O collision rate increases, therefore non-Maxwellian features of fO+ appeared and becomes pronounced at large electric fields, O+ temperature increases, νO+–O increases, νO+–O+ decreases, O+ temperature partition coefficients β|| decreases and β⊥ increases. As altitude increases, the effect of O+–O+ Coulomb collision becomes significant, and for constant electric field, the non-Maxwellian features of O+ distributions are reduced, T⊥O+ decreases, T|| O+ increases, O+ temperature anisotropy decreases, νO+–O decreases, νO+–O+ increases with altitude and reaches its maximum at 300 km and then decreases, β|| increases and β⊥ decreases. However, as E increases, the O+–O collision frequency increases, while O+–O+ collision frequency decreases, β|| decreases, β⊥ increases, νO+–O increases, νO+–O+ decreases. Monte Carlo simulation of the effect of O+–O+ Coulomb collision on the O+ temperature partition coefficients β|| and β⊥, which has not been taken into account so far, is to increase β|| and decreases β⊥. We believe that the Monte Carlo calculations presented here provided the best description to date of auroral F-region O+ velocity distributions, O+ temperature and O+ temperature partition coefficients β|| and β⊥ in the presence of the electric field, primarily because of the self consistent handling of O+–O+ and O+–O collisions.