Сumulants and parameters сalculation of distribution function by Monte Carlo and from the equation for it
Keywords:moments of distribution, energetical ions, solid body, Monte Carlo method
Calculations results of the moments, central moments, cumulants and parameters of the distribution function of a beam of ions implanted in a solid body were analyzed. To analyze the differences between the results of modeling this process by the Monte Carlo method, which is widely used for practically important targets, and the results of the solution of the corresponding integrodifferential equations that describe ions distribution analytically, in the simple case of axial symmetry of the ion beam, when all moments of odd order along the transverse Cartesian coordinate is considered equal to zero due to the symmetry of the problem. It is shown that the same moments obtained by the Monte Carlo method is not exactly equal to zero, but slowly decrease with an increase in the number of ions, as predicted by statistics, and then remain approximately constant. Increasing the number of ions for Monte Carlo simulation reduces the statistical component of this error, but does not affect on the component arising from the application of a simplified model of ion-atom collisions.
Pages of the article in the issue: 112 - 115
Language of the article: Ukrainian
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