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\begin{document}

\title{ULF Wave Transport of Relativistic Electrons in the Van Allen Belts:
Criteria for Transition to Radial Diffusion}



\author[1]{Zhi-Gu Li}%
\author[2]{Ian Mann}%
\author[2]{Louis Godwin Ozeke}%
\author[2]{Leonid Olifer}%
\author[3]{Alexander William Degeling}%
\affil[1]{West Virginia University}%
\affil[2]{University of Alberta}%
\affil[3]{Shandong University}%


\vspace{-1em}



  
  \date{May 25, 2024}


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\begin{abstract}
Relativistic electrons in the radiation belts can be transported as a
result of wave-particle interactions (WPI) with ultra-low frequency
(ULF) waves. Such WPI are often assumed to be diffusive, parametric
models for the radial diffusion coefficient often being used to assess
the rates of radial transport. However, these WPI transition from
initially coherent interactions to the diffusive regime over a finite
time, this time depending on the ULF wave power spectral density, and
local resonance conditions. Further, in the real system on the
timescales of a single storm, interactions with finite discrete modes
may be more realistic. Here, we use a particle-tracing model to simulate
the dynamics of outer radiation belt electrons in the presence of a
finite number of discrete frequency modes. We characterize the point of
the onset of diffusion as a transition from separate discrete
interactions in terms of wave parameters by using the ``two-thirds''
overlap criterion (Lichtenberg \& Lieberman, 1992), a comparison between
the distance between, and the widths of, the electron's primary resonant
islands in phase space. Further, we find the particle decorrelation time
in our model system with typical parameters to be on the timescale of
hours, which only afterwards can the system be modeled by
one-dimensional radial diffusion. Direct comparison of particle
transport rates in our model with previous analytic diffusion
coefficient formulations show good agreement at times beyond the
decorrelation time. These results are critical for determining the time
periods and conditions under which ULF wave radial diffusion theory can
be applied.%
\end{abstract}%



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\textbf{Hosted file}

\verb`Rev.Submit_ZGL.docx`  available at \url{https://authorea.com/users/671785/articles/717481-ulf-wave-transport-of-relativistic-electrons-in-the-van-allen-belts-criteria-for-transition-to-radial-diffusion}

\textbf{Hosted file}

\verb`ZGL_Supporting_Info.docx`  available at \url{https://authorea.com/users/671785/articles/717481-ulf-wave-transport-of-relativistic-electrons-in-the-van-allen-belts-criteria-for-transition-to-radial-diffusion}

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