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\begin{document}

\title{A universal kinetic equation solver for radiation belts}



\author[1]{Liheng Zheng}%
\author[1]{Lunjin Chen}%
\author[2]{Anthony Arthur Chan}%
\author[3]{Peng Wang}%
\author[4]{Z. Y. Xia}%
\author[5]{Xu Liu}%
\affil[1]{University of Texas at Dallas}%
\affil[2]{Rice University}%
\affil[3]{University of California Los Angeles}%
\affil[4]{Unknown}%
\affil[5]{University of Texas at Dallas, Willian B. Hansen Center for Space Sciences}%


\vspace{-1em}



  
  \date{May 21, 2024}


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\begin{abstract}
Recent proceedings in the radiation belt studies have proposed new
requirements for numerical methods to solve the kinetic equations
involved. In this article, we present a numerical solver that can solve
the general form of radiation belt Fokker-Planck equation and Boltzmann
equation in arbitrarily provided coordinate systems, and with
user-specified boundary geometry and boundary conditions. The solver is
based upon the mathematical theory of stochastic differential equations,
whose computational accuracy and efficiency are greatly enhanced by
specially designed adaptive algorithms and variance reduction technique.
The versatility and robustness of the solver is exhibited in three
example problems. The solver applies to a wide spectrum of radiation
belt modeling problems, including the ones featuring nonlinear
wave-particle interactions.%
\end{abstract}%



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