Radiation belt particle diffusion, drift and advection via cyclotron interactions

<p>There is a growing body of observational, theoretical and experimental evidence to indicate that a proper description of radiation belt charged particle transport will require new mathematical models, i.e. new partial differential equations. One leading candidate is to extend the &#8216;standard diffusion equation&#8217; to a more general Fokker-Planck equation in order to include advection coefficients. Ideally, these advection (first-order transport) coefficients should be parameterized by plasma and VLF/ELF electromagnetic wave parameters in a similar manner to that used for the diffusion coefficients. To the authors' knowledge, this goal has not yet been achieved - at least not to obtain an equation that can be/has been implemented into operational global scale numerical models.</p><p>In general, advection coefficients are in fact a combination of both &#8216;drift coefficients&#8217; and derivatives of the diffusion coefficients. In the standard quasilinear formalism, this combination produces advection coefficients that are identically zero because of specific constraints imposed via the Hamiltonian structure, with a derivation often attributed to Landau/Lichtenberg & Lieberman [1].</p><p>In this paper [2] we present a new theory that incorporates and builds upon the &#8216;weak turbulence/quasilinear results&#8217; of [3,4] and demonstrates the breaking of the &#8216;Landau-Lichtenberg-Liebermann condition&#8217; for the case of high wave amplitudes, or equivalently small timescales.</p><p>We therefore obtain:<br>(i) the standard quasilinear results for small wave amplitudes and long timescales;<br>(ii) and non-zero advection coefficients - as well as diffusion coefficients - that are valid for short timescales (high wave amplitudes).</p><p>These limiting timescales are determined by the electromagnetic wave amplitude. This also demonstrates that one can use what may be considered &#8216;quasilinear methods&#8217; to obtain interesting new results for &#8216;nonlinear/high-amplitude&#8217; waves in radiation belt modelling. We verify the results using high-performance test-particle experiments.</p><p>References</p><p>[1] A.J. Lichtenberg, and M.A. Lieberman, &#8220;Regular and Chaotic Dynamics&#8221;, 2nd Ed., Springer, 1991</p><p>[2] O. Allanson et al (in prep)</p><p>[3] D.S. Lemons, PoP, 19, 012306, 2012</p><p>[4] O. Allanson, T. Elsden, C. Watt, and T. Neukirch, Frontiers Aston. Space Sci., 8:805699, 2022</p>