Monte Carlo Methods and Appl., Vol. 9, No. 3, pp. 201 – 216 (2003) c  VSP 2003 Monte Carlo Simulation of Boltzmann Equation in Space Plasma at High Latitudes Imad A. Barghouthi ∗ , Naji A. Qatanani † and Fathi M. Allan ‡ Abstract — The Monte Carlo method was shown to be a very powerful technique in solving the Boltzmann equation by particle simulation. Its simple concept, straightfor- ward 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 meth- ods. 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 veloc- ity 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. Keywords: Monte Carlo simulation, Boltzmann equation, Milne problem, Coulomb collision, Space Plasma. Mathematical reviews index: 65C05,76P05 1 Introduction Computer simulation is an essential tool in studying the space plasma physics. Simulation allows us to develop and test models, to evaluate approximate theo- ries of space plasma, and to obtain detailed information about the ion velocity distribution function and its moments (i.e. density, drift velocity, temperature, heat flux, ...) at different altitudes. The plasma medium, such as the polar wind, ionosphere, magnetosphere, and plasmasphere, consists of ions, electrons and neutral atoms. The motion of these species under the effect of geomagnetic field, gravitational field, polarization electric field and the interactions between them is very difficult to understand. However, Monte Carlo simulation can offer detailed information describing the motion of the plasma constituents and some of the interactions between plasma species. In dealing with plasma it is conve- nient to describe each species in the plasma by a separate velocity distribution * Department of Physics, P.O.Box 20002, Al-Quds University, Jerusalem, Palestine † Department of Mathematics, P.O.Box 20002, Al-Quds University, Jerusalem, Palestine ‡ Department of Mechanical Engineering, MIT, 77 Mass. Ave. Cambridge MA 02139.