For low ion densities, the interaction among ions is usually neglected and only the interaction with the host gas is taken into account. In the simulation we follow the evolution of a certain number of ions that collide with the background gas. Here we will briefly describe the technique. Gases was made by Wannier Wannier ( 1953). The first attempt to apply an MC simulation for ions in Due to stochastic nature of the MC method, an average over many uncorrelated measurements is necessary. After the system has relaxed, it is quite simple task to directly sample all ion properties in a simulation. Since the initial conditions for ions are arbitrary, the system should evolve for some time until the stationary regime is achieved, when the distribution function of ions becomes time independent. Instead of solving the BE an alternative route in determining the ion distribution function and their transport parameters (e.g. the mean energy, the drift velocity, the diffusion coefficients) is by an MC simulation where one simulates real physical processes and follows the temporal evolution of ions. Since realistic cross sections are almost always complicated functions of the relative velocity ion-neutral gas, direct solution of the BE is often quite complicated, apart from some model cross sections. The collision integral of the BE is a functional that depends on the distribution functions of both, ions and the background gas and also depends on the total cross section for their collisions. In ( I.1) we assumed that the neutral gas is homogeneous and that its distribution function does not significantly change due to collisions with ions. Having verified our algorithm, we were able to produce calculations for Ar + bold_F start_POSTSUBSCRIPT italic_e end_POSTSUBSCRIPT. The results we obtained are in excellent agreement with the existing ones obtained by complementary methods. The range of energies where it is necessary to apply the technique has been defined. The developed techniques described here are required for Monte Carlo simulations of ion transport and for hybrid models of non-equilibrium plasmas. We address the cases when the background gas is monocomponent and when it is a mixture of different gases. Also, we have derived exact analytical formulas for piecewise calculation of the collision frequency integrals. We found the conditional probability distribution of gas velocities that correspond to an ion of specific velocity which collides with a gas particle. A special attention has been paid to properly treat the thermal motion of the host gas particles and their influence on ions, which is very important at low electric fields, when the mean ion energy is comparable to the thermal energy of the host gas. We consider the limit of low ion densities when the distribution function of the background gas remains unchanged due to collision with ions. We have developed a Monte Carlo simulation for ion transport in hot background gases, which is an alternative way of solving the corresponding Boltzmann equation that determines the distribution function of ions.
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