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On the forward-backward-in-time approach for Monte Carlo solution of Parker's transport equation: One-dimensional case
- Source :
- Journal of Geophysical Research: Space Physics. 121:3920-3930
- Publication Year :
- 2016
- Publisher :
- American Geophysical Union (AGU), 2016.
-
Abstract
- The cosmic rays propagation 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, a Monte Carlo approach became widely used in force of its advantages with respect to other numerical methods. In this approach the transport equation is associated to a fully equivalent set of stochastic differential equations (SDE). This set is used to describe the stochastic path of quasi-particle from a source, e.g., the interstellar space, to a specific target, e.g., a detector at Earth. We present a comparison of forward-in-time and backward-in-time methods to solve the cosmic rays transport equation in the heliosphere. The Parker equation and the related set of SDE in the several formulations are treated in this paper. For the sake of clarity, this work is focused on the one-dimensional solutions. Results were compared with an alternative numerical solution, namely, Crank-Nicolson method, specifically developed for the case under study. The methods presented are fully consistent each others for energy greater than 400 MeV. The comparison between stochastic integrations and Crank-Nicolson allows us to estimate the systematic uncertainties of Monte Carlo methods. The forward-in-time stochastic integrations method showed a systematic uncertainty
- Subjects :
- Physics
Work (thermodynamics)
010504 meteorology & atmospheric sciences
Numerical analysis
Monte Carlo method
Space (mathematics)
01 natural sciences
Range (mathematics)
Stochastic differential equation
Geophysics
Space and Planetary Science
0103 physical sciences
Statistical physics
Convection–diffusion equation
010303 astronomy & astrophysics
Heliosphere
0105 earth and related environmental sciences
Subjects
Details
- ISSN :
- 21699380
- Volume :
- 121
- Database :
- OpenAIRE
- Journal :
- Journal of Geophysical Research: Space Physics
- Accession number :
- edsair.doi...........89f702f577fc7eb2ab75c2a5450cf1b1