Statistical error for cosmic rays modulation evaluation by 1D model

Abstract

The propagation of cosmic rays through the heliosphere is solved for more than half a century by stochastic methods based on Ito's lemma. This work presents the estimation of statistical error of solution of Fokker-Planck equation by 1D forward stochastic differential equations method. The error dependence on simulation statistics and energy is presented for different combinations of input parameters. The 1% precision criterium in intensities and 1% criterium in standard deviation are defined as a function of solar wind velocity and diffusion coefficient value.

Statistical Error for Cosmic Rays Modulation Evaluated by SDE Backward in Time Method for 1D Model

“…The situation in the backward-in-time method is more straightforward than the forward-in-time approach [19]. Every simulated quasiparticle is registered in the backwardin-time approach.…”

“…We focus on the estimation of statistical error for 1D backward-in-time stochastic differential equations method. Preliminary analysis of statistical error for 1D forward-in-time method we present in article [19]. Scaling study of the SDE approach application to cosmic ray modulations showing the influence of a different number of injected particles on realistic test problem is presented in [20].…”