Radiation belt particle diffusion, drift and advection via cyclotron interactions

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 ‘standard diffusion equation’ 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.

In general, advection coefficients are in fact a combination of both ‘drift coefficients’ 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].

In this paper [2] we present a new theory that incorporates and builds upon the ‘weak turbulence/quasilinear results’ of [3,4] and demonstrates the breaking of the ‘Landau-Lichtenberg-Liebermann condition’ for the case of high wave amplitudes, or equivalently small timescales.

We therefore obtain:
(i) the standard quasilinear results for small wave amplitudes and long timescales;
(ii) and non-zero advection coefficients - as well as diffusion coefficients - that are valid for short timescales (high wave amplitudes).

These limiting timescales are determined by the electromagnetic wave amplitude. This also demonstrates that one can use what may be considered ‘quasilinear methods’ to obtain interesting new results for ‘nonlinear/high-amplitude’ waves in radiation belt modelling. We verify the results using high-performance test-particle experiments.

References

[1] A.J. Lichtenberg, and M.A. Lieberman, “Regular and Chaotic Dynamics”, 2nd Ed., Springer, 1991

[2] O. Allanson et al (in prep)

[3] D.S. Lemons, PoP, 19, 012306, 2012

[4] O. Allanson, T. Elsden, C. Watt, and T. Neukirch, Frontiers Aston. Space Sci., 8:805699, 2022