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Radiation belt particles: radial transport, acceleration and loss
Radiation belt electron flux and energy enhancements result from radial transport
with conservation of the first adiabatic invariant, proportional to energy (or momentum in
the relativistic limit) and inversely proportional to magnetic field strength. There are two
classes of such transport and acceleration on MHD time scales, impulsive and diffusive.
An extreme example of impulsive acceleration occurred on March 24, 1991, due to a high
speed interplanetary shock produced by a Coronal Mass Ejection (CME). The
magnetopause was compressed inside the orbit of geosynchronous spacecraft, producing
new electron and proton radiation belts with energies > 10 MeV in the normally depleted
slot region (see Figure 1b). Radial transport and energization of electrons occurred on a
particle drift time scale of minutes, due to the induction electric field launched by rapid
magnetopause compression. Figure 2 shows ‘before’ and ‘after’ shock arrival snapshots
of electron flux vs. energy (x-axis) and L (y-axis) from guiding center test particle
calculations which advance trajectories using electric and magnetic fields produced by a
global MHD simulation of magnetosphere interaction with the solar wind (Elkington et
al., 2002). The new > 10 MeV electron (and proton, see Hudson et al., 1997) belts
produced inside geosynchronous orbit on the time scale of interplanetary shock passage
persisted for years, as observed by the low altitude SAMPEX satellite in polar orbit,
viewing radiation belt particle precipitation into the atmosphere.
The more typical response of the highly variable outer zone electron flux to solar
wind variation occurs over a time scale of hours to days and weeks (Reeves et al., 1998).
Increase in flux at higher energies has been observed to be correlated with increased solar
wind velocity and southward interplanetary magnetic field. The former may drive the
growth of velocity-shear instability along the boundary between the magnetosphere and
solar wind, the magnetopause. Low frequency, long wavelength perturbations of the
magnetopause boundary can transfer energy to modes in the same frequency and
wavelength range within the magnetosphere, called Ultra Low Frequency or ULF
oscillations, with periods up to tens of minutes. Enhancement in wave power at these
frequencies has been seen both with ground-based and space-borne magnetic field
measurements to be correlated with relativistic electron flux enhancements (Baker et al.,
1998).
Near solar maximum, large geomagnetic storms are often initiated by solar
Coronal Mass Ejections. CME-driven interplanetary shocks compress the magnetopause,
causing what is called a storm sudden commencement (SSC). Even without an SSC, an
extended period of southward IMF Bz will give rise to geomagnetic storm activity
through enhanced reconnection on the dayside driving substorm activity on the nightside
and overall enhanced convection. The average horizontal component of the earth's
magnetic field at four near-equatorial locations used to compute the Dst index first shows
an increase in the case of a shock-induced SSC, but over a longer period of hours
decreases due to enhanced magnetospheric convection and build up of the ring current.
Plasma is transported radially inward from the plasma sheet (Figure 1a) due both to
steady enhanced convection and substorm dipolarization to a stronger magnetic field
region where the radial gradient in the magnetic field causes a westward drift of energetic
(tens - hundred keV) ions and eastward drift of electrons making up the ring current. As
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much as 30% of the enhanced energy input to the magnetosphere during a geomagnetic
storm resides in the ring current, which produces a magnetic field at the surface of the
earth of opposite sign to the dipole field, giving rise to the Dst signature plotted in Figure
3 with the 30-day averaged flux of 2-6 MeV electrons (bottom) and 19-27.4 MeV protons
(top) along with the average sunspot number plotted over a decade of SAMPEX
measurements (Li et al., 2001). Both electrons and protons of keV-MeV energies drift
azimuthally around the earth on closed drift shells, conserving the magnetic flux through
the cross sectional area of their drift paths. When such drifting particles experience a
variation in magnetic (or convection electric) field strength at a frequency comparable to
their drift period, the magnetic flux invariant is no longer conserved, and particles will
diffuse radially from one drift shell to another.
Radial diffusion due to fluctuating fields on the drift time scale has a long history
of explaining transport and energization of trapped MeV electrons on time scales of days
to years. However, recent storm analysis using multi-spacecraft measurements has shown
that electron flux can increase by many orders of magnitude on the time scale of hours,
slower than the acceleration over a drift period (minutes) seen for the March 24, 1991
storm (Li et al., GRL, 1993), but much too fast for standard radial diffusion models. It
has been shown, using fields from LFM MHD simulations of storm events, with solar
wind input measured at WIND or ACE coupled to a guiding center test particle code, that
ULF waves with periods corresponding to the longitudinal drift period of MeV electrons
(minutes) give rise to enhanced radial diffusion (Elkington et al., 2002; 2003; 2004;
Hudson et al., 2001), exceeding previous estimates which incorporate simplifying
assumptions for spatial and temporal variations and azimuthal symmetry (Falthammar,
1965).
Satellite measurements of particle velocity distributions suggest that additional
localized heating due to waves with frequencies comparable to the electron gyrofrequency
is also taking place (Braughtigam and Albert, 2002). Such waves are generated
spontaneously by increased electron flux levels and perpendicular velocity space
anisotropy which results from radial transport. The short time scale over which electrons
are seen to precipitate into the atmosphere by the SAMPEX satellite, after increased
fluxes are first seen closer to the equatorial plane, suggests that particles diffuse in
velocity space, trading perpendicular and parallel energy on a time scale comparable to
that of radial transport (as fast as a few hours). For relativistic electrons the same resonant
interaction with waves at a multiple of the gyrofrequency can cause local diffusion in
energy as well (Summers and Ma, 2000; Roth et al., 1999; Summers et al., 2004).
Further work is needed to quantify the rate at which ULF waves affect radial
transport and electron cyclotron waves provide additional energization, along with
quantifying scattering loss into the atmosphere due to whistler mode chorus on the dawn
side and electromagnetic ion cyclotron waves at dusk, where the ring current source
population intersects the plasmaphere buldge. The importance of developing predictive
capability based on measured solar wind input, quantifying the balance between source
and loss processes, has been identified as one of the major goals of NASA’s Living With
a Star program, because of the threat that trapped relativistic electrons pose to satellites
and astronauts.
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Model Description
A numerical model has been developed which follows the evolution of energetic particle
distributions from Lorentz or guiding center, test particle trajectories in time dependent
fields obtained from the Lyon-Feder Mobarry (LFM) global MHD code (Lyon et al.,
2004). Thus, the full kinetic effects of particle interactions with MHD fields is included.
Since the total energy density of MeV electrons (and ions) in the magnetosphere is very
small compared to the thermal population, these particles may be considered noninteracting, justifying a test particle approach. This approach has been used extensively,
both to isolate and understand the physical processes affecting radiation belt populations,
and to model the global dynamics of the Earth's radiation belts under a variety of
magnetospheric conditions (c.f. Hudson et al, 1997,1998; Elkington et al., 2002,2004;
Kress et al. 2004,2005).
Currently, we calculate energetic electron fluxes in the magnetosphere either by launching
electrons from the plasmasheet or using an initial source population such as AE8 evolved
in time. The latter has been renormalized to fit measured flux levels and spectra for
specific storms (Hudson et al., 2001).
Energetic electron trajectories are computed by solving the relativistic Lorentz equation
using an adaptive 4th order Rung-Kutta integrator. The step size is adjusted at each time
step to be ~1% of the instantaneous gyro period of the particle. Linear interpolations in
space and time from gridded MHD fields are used to obtain the fields at the instantaneous
particle position. In our previous near-earth radiation belt studies, magnetospheric model
fields were first interpolated from the MHD code's distorted spherical grid onto a 3D
Cartesian grid where particle trajectories are computed, with the spatial resolution over
the entire Cartesian grid corresponding to the highest (innermost) MHD grid resolution.
For the proposed work, the code will be generalized to interpolate field quantities to
particle positions on a general grid structure, utilizing the metric for that grid to
interpolate field quantities to particle positions.
Outstanding questions to be addressed by a coupled model:
1. What is the relative influence of solar wind velocity and interplanetary
magnetic field in controlling relativistic electron acceleration? What are the
distinctions and commonality of the two classes of electron flux enhancements, those
produced by CMEs around solar maximum and those due to high speed solar wind
streams which predominate during the declining phase of the solar cycle, see Figure 3?
2. What role does location of the plasmapause play in determining the
location of the MeV electron phase space density peak and it maximum value. A
coupled MHD-test particle model which includes a dynamic plasmasphere and a
parametrized loss rate describing pitch angle scattering by whistler mode and EMIC
waves will address this question.
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3. What role does the prior state of the magnetosphere play? e.g. plasmasheet
source population density? Are multiple Dst-minimum storms more geoeffective for
electrons than isolated storms? This question is tied to the fact that solar active regions
often produce multiple storms, such as the 2003 Halloween storm, in a short time period
each of which affects the evolution of its predecessor.
4. How probable are extreme radiation belt flux enhancements? such as that
which occurred on March 24, 1991, which produced new MeV electron and trapped solar
proton belts on a drift time scale of minutes?
References
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Figure 1a. A schematic of the magnetosphere, showing major particle populations and current
systems.
Figure 1b. Schematic of major radiation belt components, the outer zone electrons
(purple), inner zone – primarily protons (blue), with slot region between, and trapped
anomalous cosmic rays (yellow). Highly idealized structure contrasts with timedependence evident in Figure 2.
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Figure 2. The unexpected creation of new electron (and proton, not shown) radiation belts
during the March 24, 1991 geomagnetic storm, simulated using an AE-8 source population
(insert) to initialize guiding center test particle trajectory calculations in fields obtained from
global MHD simulations with the Lyon-Feddar-Mobarry 3D MHD code driven by model
upstream solar wind parameters. In this case no measurements were available in the solar wind as
available from WIND and ACE for the Cycle 23 solar maximum (Source: Elkington et al.,
JASTP, 64(5-6): pp.607-615). See Hudson et al., 1997 for corresponding MHD simulation results
for protons.
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Figure 3. Thirty-day averaged MeV proton (top) and electron (bottom) fluxes from July 1992 to
January 2001, as measured by the SAMPEX satellite in low-altitude polar orbit. Solar cycle
variation is evident, with electron fluxes greater during the declining phase of the solar cycle,
penetrating to lowest L-value (equatorial radial distance) during large storms characterized by
negative Dst geomagnetic activity index. The latter penetration has been correlated with
plasmapause location (Baker et al., Nature, 2004). Inner zone proton fluxes maximize at solar
minimum (1996), when cosmic rays have greater access to the inner heliosphere. Source: Li et
al., 2001.