Comparison of Monte Carlo simulations and polynomial expansions of auroral non-Maxwellian distributions. I - The 3-D representation. II - The 1-D representation

Physics

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Auroras, Computerized Simulation, Monte Carlo Method, Polynomials, Series Expansion, Three Dimensional Models, Convergence, Earth Ionosphere, Electric Fields, Ion Distribution, Maxwell-Boltzmann Density Function, Molecular Ions, Nitrogen, Oxygen, Velocity Distribution

Scientific paper

Auroral ion distributions under the influence of large electric fields were obtained using the Monte Carlo approach and were compared to limited order polynomial expansion, for both the three-dimensional velocity space and one-dimensioanal ion distribution. It is shown that Monte Carlo simulations can provide velocity moments to high orders with a high degree of accuracy. These results are used in Grad's (1949) expansions providing analytical expressions of ion distribution. It is shown that the convergence of a polynomial expansion is dependent on the weighting function and on the particular domain in the three-dimensional velocity space. The results of one-dimensioal representation show the role played by the correction in form of polynomial expansion about a weighting function.

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