Bibliography

Global MHD test particle simulations of >10 MeV radiation belt electrons during storm sudden commencement

[1] Prior to 2003, there are two known cases where ultrarelativistic (≳10 MeV) electrons appeared in the Earth\textquoterights inner zone radiation belts in association with high speed interplanetary shocks: the 24 March 1991 and the less well studied 21 February 1994 storms. During the March 1991 event electrons were injected well into the inner zone on a timescale of minutes, producing a new stably trapped radiation belt population that persisted for \~10 years. More recently, at the end of solar cycle 23, a number of violent geomagnetic disturbances resulted in large variations in ultrarelativistic electrons in the inner zone, indicating that these events are less rare than previously thought. Here we present results from a numerical study of shock-induced transport and energization of outer zone electrons in the 1\textendash7 MeV range, resulting in a newly formed 10\textendash20 MeV electron belt near L \~ 3. Test particle trajectories are followed in time-dependent fields from an MHD magnetospheric model simulation of the 29 October 2003 storm sudden commencement (SSC) driven by solar wind parameters measured at ACE. The newly formed belt is predominantly equatorially mirroring. This result is in part due to an SSC electric field pulse that is strongly peaked in the equatorial plane, preferentially accelerating equatorially mirroring particles. The timescale for subsequent pitch angle diffusion of the new belt, calculated using quasi-linear bounce-averaged diffusion coefficients, is in agreement with the observed delay in the appearance of peak fluxes at SAMPEX in low Earth orbit. We also present techniques for modeling radiation belt dynamics using test particle trajectories in MHD fields. Simulations are performed using code developed by the Center for Integrated Space Weather Modeling.

Kress, B.; Hudson, M.; Looper, M.; Albert, J.; Lyon, J.; Goodrich, C.;

Published by: Journal of Geophysical Research      Published on: 09/2007

YEAR: 2007     DOI: 10.1029/2006JA012218

Shock-Induced Transport. Slot Refilling and Formation of New Belts.

Incorporating spectral characteristics of Pc5 waves into three-dimensional radiation belt modeling and the diffusion of relativistic electrons

The influence of ultralow frequency (ULF) waves in the Pc5 frequency range on radiation belt electrons in a compressed dipole magnetic field is examined. This is the first analysis in three dimensions utilizing model ULF wave electric and magnetic fields on the guiding center trajectories of relativistic electrons. A model is developed, describing magnetic and electric fields associated with poloidal mode Pc5 ULF waves. The frequency and L dependence of the ULF wave power are included in this model by incorporating published ground-based magnetometer data. It is demonstrated here that realistic spectral characteristics play a significant role in the rate of diffusion of relativistic electrons via drift resonance with poloidal mode ULF waves. Radial diffusion rates including bounce motion show a weak pitch angle dependence for αeq >= 50\textdegree (λ <= 20\textdegree) for a power spectral density which is L-independent. The data-based model for greater power at higher L values yields stronger diffusion at αeq = 90\textdegree. The L6 dependence of the diffusion coefficient which is obtained for a power spectral density which is L-independent is amplified by power spectral density which increases with L. During geomagnetic storms when ULF wave power is increased, ULF waves are a significant driver of increased fluxes of relativistic electrons inside geosynchronous orbit. Diffusion timescales obtained here, when frequency and L dependence comparable to observations of ULF wave power are included, support this conclusion.

Perry, K.; Hudson, M.; Elkington, S.;

Published by: Journal of Geophysical Research      Published on: 03/2005

YEAR: 2005     DOI: 10.1029/2004JA010760

Radial Transport

MHD/particle simulations of radiation belt dynamics

Particle fluxes in the outer radiation belts can show substantial variation in time, over scales ranging from a few minutes, such as during the sudden commencement phase of geomagnetic storms, to the years-long variations associated with the progression of the solar cycle. As the energetic particles comprising these belts can pose a hazard to human activity in space, considerable effort has gone into understanding both the source of these particles and the physics governing their dynamical behavior. Computationally tracking individual test particles in a model magnetosphere represents a very direct, physically-based approach to modeling storm-time radiation belt dynamics. Using global magnetohydrodynamic models of the Earth\textendashSun system coupled with test particle simulations of the radiation belts, we show through two examples that such simulations are capable of capturing the outer zone radiation belt configuration at a variety of time scales and through all phases of a geomagnetic storm. Such simulations provide a physically-based method of investigating the dynamics of the outer radiation zone, and hold promise as a viable method of providing global nowcasts of the radiation environment during geomagnetically active periods.

ELKINGTON, S; Hudson, M.; Wiltberger, M.J; Lyon, J.;

Published by: Journal of Atmospheric and Solar-Terrestrial Physics      Published on: 04/2002

YEAR: 2002     DOI: 10.1016/S1364-6826(02)00018-4

Shock-Induced Transport. Slot Refilling and Formation of New Belts.

Acceleration of relativistic electrons via drift-resonant interaction with toroidal-mode Pc-5 ULF oscillations

There has been increasing evidence that Pc-5 ULF oscillations play a fundamental role in the dynamics of outer zone electrons. In this work we examine the adiabatic response of electrons to toroidal-mode Pc-5 field line resonances using a simplified magnetic field model. We find that electrons can be adiabatically accelerated through a drift-resonant interaction with the waves, and present expressions describing the resonance condition and half-width for resonant interaction. The presence of magnetospheric convection electric fields is seen to increase the rate of resonant energization, and allow bulk acceleration of radiation belt electrons. Conditions leading to the greatest rate of acceleration in the proposed mechanism, a nonaxisymmetric magnetic field, superimposed toroidal oscillations, and strong convection electric fields, are likely to prevail during storms associated with high solar wind speeds.

Elkington, Scot; Hudson, M.; Chan, Anthony;

Published by: Geophysical Research Letters      Published on: 11/1999

YEAR: 1999     DOI: 10.1029/1999GL003659

Radial Transport

Simulation of Radiation Belt Dynamics Driven by Solar Wind Variations

The rapid rise of relativistic electron fluxes inside geosynchronous orbit during the January 10-11, 1997, CME-driven magnetic cloud event has been simulated using a relativistic guiding center test particle code driven by out-put from a 3D global MHD simulation of the event. A comparison can be made of this event class, characterized by a moderate solar wind speed (< 600 km/s), and those commonly observed at the last solar maximum with a higher solar wind speed and shock accelerated solar energetic proton component. Relativistic electron flux increase occurred over several hours for the January event, during a period of prolonged southward IMF Bz more rapidly than the 1-2 day delay typical of flux increases driven by solar wind high speed stream interactions. Simulations of the January event captured the flux

Hudson, M.; Elkington, S.; Lyon, J.; Goodrich, C.; Rosenberg, T.;

Published by:       Published on:

YEAR: 1999     DOI: 10.1029/GM10910.1029/GM109p0171

Simulation of the prompt energization and transport of radiation belt particles during the March 24, 1991 SSC

We model the rapid (\~ 1 min) formation of a new electron radiation belt at L ≃ 2.5 that resulted from the Storm Sudden Commencement (SSC) of March 24, 1991 as observed by the CRRES satellite. Guided by the observed electric and magnetic fields, we represent the time-dependent magnetospheric electric field during the SSC by an asymmetric bipolar pulse that is associated with the compression and relaxation of the Earth\textquoterights magnetic field. We follow the electrons using a relativistic guiding center code. The test-particle simulations show that electrons with energies of a few MeV at L > 6 were energized up to 40 MeV and transported to L ≃ 2.5 during a fraction of their drift period. The energization process conserves the first adiabatic invariant and is enhanced due to resonance of the electron drift motion with the time-varying electric field. Our simulation results, with an initial W-8 energy flux spectra, reproduce the observed electron drift echoes and show that the interplanetary shock impacted the magnetosphere between 1500 and 1800 MLT.

Li, Xinlin; Roth, I.; Temerin, M.; Wygant, J.; Hudson, M.; Blake, J.;

Published by: Geophysical Research Letters      Published on: 11/1993

YEAR: 1993     DOI: 10.1029/93GL02701

Shock-Induced Transport. Slot Refilling and Formation of New Belts.

Radial Diffusion of Outer-Zone Electrons: An Empirical Approach to Third-Invariant Violation

The near-equatorial fluxes of outer-zone electrons (E>0.5 Mev and E>1.9 Mev) measured by an instrument on the satellite Explorer 15 following the geomagnetic storm of December 17\textendash18, 1962, are used to determine the electron radial diffusion coefficients and electron lifetimes as functions of L for selected values of the conserved first invariant \textmu. For each value of \textmu, the diffusion coefficient is assumed to be time-independent and representable in the form D = DnLn. The diffusion coefficients and lifetimes are then simultaneously obtained by requiring that the L-dependent reciprocal electron lifetime, as determined from the Fokker-Planck equation, deviate minimally from a constant in time. Applied to the data, these few assumptions yield a value of D that is smaller by approximately a factor of 10 than the value recently found by Newkirk and Walt in a separate analysis of 1.6-Mev electron data obtained during the same time period on another satellite. The electron lifetimes are found to be strong functions of L, with 4- to 6-day lifetimes observed at the higher L values (4.6\textendash4.8).

Lanzerotti, L.; Maclennan, C.; Schulz, Michael;

Published by: Journal of Geophysical Research      Published on: 10/1970

YEAR: 1970     DOI: 10.1029/JA075i028p05351

Radial Transport

Diffusion of Equatorial Particles in the Outer Radiation Zone

Expansions and contractions of the permanently compressed magnetosphere lead to the diffusion of equatorially trapped particles across drift shells. A general technique for obtaining the electric fields induced by these expansions and contractions is described and applied to the Mead geomagnetic field model. The resulting electric drifts are calculated and are superimposed upon the gradient drift executed by a particle that conserves its first (μ) and second (J = 0) adiabatic invariants. The noon-midnight asymmetry of the unperturbed drift trajectory (resulting from gradient drift alone) is approximated by means of a simple model. In this model the angular drift frequency is found to be the geometric mean of a particle\textquoterights angular drift velocities at noon and midnight. The radial diffusion coefficient D = (\textonehalf) (ΔL)\texttwosuperior/time is calculated as a function of the McIlwain parameter L and in terms of the spectral density of fluctuations in the stand-off distance of the magnetosphere boundary. Because the unperturbed drift trajectories are asymmetric, drift-resonant diffusion of particles is produced by spectral components at all harmonics of the drift frequency, although the first (fundamental) harmonic is the major contributor.

Schulz, Michael; Eviatar, Aharon;

Published by: Journal of Geophysical Research      Published on: 05/1969

YEAR: 1969     DOI: 10.1029/JA074i009p02182

Radial Transport