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Radial diffusion and MHD particle simulations of relativistic electron transport by ULF waves in the September 1998 storm
Author  Fei, Yue; Chan, Anthony; Elkington, Scot; Wiltberger, Michael; 
Keywords  Radial Transport 
Abstract  In an MHD particle simulation of the September 1998 magnetic storm the evolution of the radiation belt electron radial flux profile appears to be diffusive, and diffusion caused by ULF waves has been invoked as the probable mechanism. In order to separate adiabatic and nonadiabatic effects and to investigate the radial diffusion mechanism during this storm, in this work we solve a radial diffusion equation with ULF wave diffusion coefficients and a timedependent outer boundary condition, and the results are compared with the phase space density of the MHD particle simulation. The diffusion coefficients include contributions from both symmetric resonance modes (ω ≈ mωd, where ω is the wave frequency, m is the azimuthal wave number, and ωd is the bounceaveraged drift frequency) and asymmetric resonance modes (ω ≈ (m \textpm 1)ωd). ULF wave power spectral densities are obtained from a Fourier analysis of the electric and magnetic fields of the MHD simulation and are used in calculating the radial diffusion coefficients. The asymmetric diffusion coefficients are proportional to the magnetic field asymmetry, which is also calculated from the MHD field. The resulting diffusion coefficients vary with the radial coordinate L (the Roederer Lvalue) and with time during different phases of the storm. The last closed drift shell defines the location of the outer boundary. Both the location of the outer boundary and the value of the phase space density at the outer boundary are timevarying. The diffusion calculation simulates a 42hour period during the 24\textendash26 September 1998 magnetic storm, starting just before the storm sudden commencement and ending in the late recovery phase. The differential flux calculated in the MHD particle simulation is converted to phase space density. Phase space densities in both simulations (diffusion and MHD particle) are functions of Roederer Lvalue for fixed first and second adiabatic invariants. The Roederer Lvalue is calculated using drift shell tracing in the MHD magnetic field, and particles have zero second invariant. The radial diffusion calculation reproduces the main features of the MHD particle simulation quite well. The symmetric resonance modes dominate the radial diffusion, especially in the inner and middle L region, while the asymmetric resonances are more important in the outer region. Using both symmetric and asymmetric terms gives a better result than using only one or the other and is better than using a simple power law diffusion coefficient. We find that it is important to specify the value of the phase space density on the outer boundary dynamically in order to get better agreement between the radial diffusion simulation and the MHD particle simulation. 
Year of Publication  2006 
Journal  Journal of Geophysical Research 
Volume  111 
Number of Pages  
Section  
Date Published  12/2006 
ISBN  
URL  http://onlinelibrary.wiley.com/doi/10.1029/2005JA011211/abstract 
DOI  10.1029/2005JA011211 