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

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.