Cosmic Rays Propagation with HelMod: Difference between forward-in-time and backward-in-time approaches

TL;DR

This paper compares forward-in-time and backward-in-time Monte Carlo methods for modeling cosmic ray propagation within the heliosphere, demonstrating their differences are below 5%, thus establishing their systematic uncertainty.

Contribution

It introduces and compares both forward and backward Monte Carlo approaches within the HelMod framework for cosmic ray transport modeling.

Findings

Difference between approaches is below 5%.

Both methods are systematically consistent within this margin.

Provides implementation details for HelMod Monte Carlo algorithms.

Abstract

The cosmic rays modulation inside the heliosphere is well described by a transport equation introduced by Parker in 1965. To solve this equation several approaches were followed in the past. Recently the Monte Carlo approach becomes widely used in force of his advantages with respect to other numerical methods. In the Monte Carlo approach, the transport equation is associated to a fully equivalent set of Stochastic Differential Equations. This set is used to describe the stochastic path of a quasi-particle from a source, e.g., the interstellar medium, to a specific target, e.g., a detector at Earth. In this work, we present both the Forward-in-Time and Backward-in-Time Monte Carlo solutions. We present an implementation of both algorithms in the framework of HelMod Code showing that the difference between the two approach is below 5\% that can be quoted as the systematic uncertain of the Method itself.