Speaker
Description
The numerical modeling of energetic particle transport in turbulent astrophysical plasmas, governed by
Fokker-Planck equations, is a cornerstone of modern space physics. Methods based on Stochastic Differential
Equations (SDEs) have gained popularity over traditional finite-difference schemes due to their unconditional
stability and suitability for parallel computing. The accuracy and computational cost of these simulations depend
critically on the choice of numerical integration scheme. While the Euler-Maruyama method remains most common,
higher-order methods like Milstein and Stochastic Runge-Kutta (SRK) promise greater accuracy. This study presents
a comparative analysis of these three SDE solvers in the context of Galactic Cosmic Ray (GCR) modulation in the
heliosphere, evaluating their relative performance to inform best practices for large-scale simulations. We simulated
GCR proton transport under identical conditions, assessing results against multiple benchmarks: modulated GCR
intensity compared with the Local Interstellar Spectrum and in-situ data from IMP-8 and PAMELA; statistical
distributions of pseudo-particle exit positions; visualization of characteristic trajectory paths; and quantitative
accuracy assessment using Euler-Maruyama as the baseline. All simulations used an identical number of
pseudo-particles for each scheme. Our findings indicate that all three solvers produce highly consistent results. The
computed energy spectra showed good agreement with experimental data, while exit position distributions and
trajectory analyses revealed no statistically significant differences between schemes. Percentage deviations remained
minimal across the parameter space studied. However, computational runtime varied considerably, with SRK
exhibiting the highest cost. These results suggest that for GCR modulation problems with the particle statistics
employed, higher-order schemes may not yield appreciably different physical results, validating the continued use of
the computationally efficient Euler-Maruyama method.
| Apply for student award at which level: | MSc |
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| Consent on use of personal information: Abstract Submission | Yes, I ACCEPT |