Abstract
The propagation of cosmic rays through the heliosphere has been 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 the 1D backward in time stochastic differential equations method. The error dependence on simulation statistics and energy is presented for different combinations of input parameters. The 1% precision criterion in mean value units of intensity standard deviation is defined as a function of solar wind velocity and diffusion coefficient value.
Highlights
The socalled solar modulation process begins when the galactic cosmic rays (GCRs) reach the heliosphere’s boundary, which presents a decrease of GCR intensity inside the heliosphere
Preliminary analysis of statistical error for 1D forward-in-time method we present in article [19]
We present an explanation of how statistical error in the backward stochastic differential equations (SDEs) method appears and show how someone with his own SDE code, could fastly estimate the dependence of statistical error of his own method on a number of injected particles
Summary
The socalled solar modulation process begins when the galactic cosmic rays (GCRs) reach the heliosphere’s boundary, which presents a decrease of GCR intensity inside the heliosphere (mostly for particles with energies less than 30 GeV). This article used the backward-in-time stochastic integration approach for all of the simulations In this approach, quasi-particle objects were injected at the registration boundary inside the heliosphere. We evaluate the solution of the Parker equation using the backward-intime stochastic integration approach. We focus on the estimation of statistical error for 1D backward- in-time stochastic differential equations method. 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].
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
