S. Elkington, GEM 2003 Transport Transport in the in the Radiation Belts Radiation Belts and the role of and the role of Magnetospheric ULF Waves Magnetospheric ULF Waves Scot R. Elkington Scot R. Elkington LASP, University of LASP, University of Colorado Colorado With many thanks to: D. N. Baker, D. H. Brautigam, A. A. Chan, Y. Fei, J. Green, M. K. Hudson, X. Li, K. L. Perry, E. J. Rigler, and M. J. Wiltberger GEM 2003 Snowmass, CO
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S. Elkington, GEM 2003 Transport in the Radiation Belts and the role of Magnetospheric ULF Waves Scot R. Elkington LASP, University of Colorado With many.
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S. Elkington, GEM 2003
Transport Transport in thein the Radiation Belts Radiation Belts and the role ofand the role of
Magnetospheric ULF WavesMagnetospheric ULF Waves
Scot R. ElkingtonScot R. ElkingtonLASP, University of ColoradoLASP, University of Colorado
With many thanks to: D. N. Baker, D. H. Brautigam, A. A. Chan, Y. Fei, J. Green, M. K. Hudson, X. Li, K. L. Perry, E. J. Rigler,
and M. J. Wiltberger
GEM 2003Snowmass, CO
S. Elkington, GEM 2003
OutlineOutline
Introduction to radiation belts.Introduction to radiation belts. Transport in the radiation belts.Transport in the radiation belts. Radial transport and the role of ULF Radial transport and the role of ULF
waves.waves. Characteristics of ULF waves, MHD Characteristics of ULF waves, MHD
simulationssimulations Boundary conditions on radial transport.Boundary conditions on radial transport. Conclusion.Conclusion.
S. Elkington, GEM 2003
The outer zone radiation The outer zone radiation beltsbelts
MM: perpendicular motion: perpendicular motion KK: parallel motion: parallel motion LL: radial distance of eq-: radial distance of eq-
crossing in a dipole field.crossing in a dipole field.
Associated with each motion is a corresponding adiabatic invariant:•Gyro: M=p2/2m0B•Bounce: K•Drift: L
If the fields guiding the particle change slowly compared to the characteristic motion, the corresponding invariant is conserved.
S. Elkington, GEM 2003
Fluxes in the radiation Fluxes in the radiation beltsbelts
The radiation belts exhibit substantial The radiation belts exhibit substantial variation in time:variation in time: •Storm
commencement: minutes•Storm main phase: hours•Storm recovery: days•Solar rotation: 13-27 days•Season: months•Solar cycle: years
S. Elkington, GEM 2003
Why study the radiation Why study the radiation belts?belts?
Because they’re Because they’re physically physically interesting!interesting!
Relativistic Relativistic electrons have electrons have been associated been associated with spacecraft with spacecraft ‘anomalies’.‘anomalies’.
Want to try to Want to try to describe how describe how radiation evolves radiation evolves in time at a given in time at a given point in space.point in space.
S. Elkington, GEM 2003
Describing the radiation Describing the radiation beltsbelts
),,,,,( zyx pppzyxff
The radiation belts may be completely characterized at a point in time by its distribution function:
Also referred to as the phase space density, f gives the number of particles in a volume (x+dx, y+dy, z+dz), with momenta between (px+dpx, py+dpy, pz+dpz ).The flux in a region of space may be related to the distribution function through
2p
jf
S. Elkington, GEM 2003
The distribution function The distribution function and the adiabatic invariantsand the adiabatic invariantsThe distribution function may equivalently be written in terms of the invariants and corresponding phase:
If the distribution is uniform in phase (e.g. uniform 3 no drift bunching in L), then the phase space density taken at a point may be considered the same at all points corresponding to the same M, K, and L.
),,,,,(
),,,,,(
321 LKMf
pppzyxff zyx
),,( LKMff
S. Elkington, GEM 2003
Transport and Fokker-Transport and Fokker-Planck Planck
Sf
J
fD
Jf
dt
dJ
Jdt
df
jij
ji i
i
i i
,
11
The evolution of the phase space density is given by the Fokker-Planck equation:
Coherent terms(e.g. friction)
Stochastic terms(e.g. diffusion)
Losses
Sources
For example, to quantify a process that leads only to diffusion in L, we would write
f
L
fD
LLL
dt
dfLL
2
2 1
(M. Schulz, AGU Monograph 97, 1996)
S. Elkington, GEM 2003
Transport in M, K: local Transport in M, K: local heatingheating
S. Elkington, GEM 2003
Local heating example:Local heating example:resonant interactions with resonant interactions with
VLF wavesVLF waves
Whistler mode chorus at dawn combined with EMIC interactions heat and isotropize particles.
Leads to transport in M, K, and L.
Summers et al. (JGR 103, 20487, 1998) proposed that resonant interactions with VLF waves could heat particles:
S. Elkington, GEM 2003
Transport in Transport in LL: radial : radial transporttransport
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Energization and ULF Energization and ULF waveswaves
ffDD~mHz … ULF waves!~mHz … ULF waves! Only need consider Only need consider
resonant frequencies resonant frequencies in analysis:in analysis:
Evqdt
dWD
)cos(0 tmEE
Electron moving in a dipole magnetic field with slowly-varying dawn-dusk potential electric field
S. Elkington, GEM 2003
……and to radial transportand to radial transport
3/10
W
MBL
Nonrelativistically, and in a dipole,
or
0
3
0
2
2 B
WL
Bm
pM
so changing energy (W) while conserving M willnecessarily lead to transport in L.
S. Elkington, GEM 2003
Observed associations Observed associations between ULF waves and between ULF waves and radiation belt activity?radiation belt activity?
•Baker et al., GRL 25, 2975, 1998 •Rostoker, GRL 25, 3701, 1998•Mathie & Mann, GRL 27, 3621, 2000•O’brien et al., JGR, 2003, in press.
Start series of particles Start series of particles at one at one L.L.
Let them evolve in a Let them evolve in a compressed dipole compressed dipole under the influence of a under the influence of a constant constant P(L,P(L,).).
Watch spread of Watch spread of LL in in time.time.
Calculate DCalculate DLLLL=<dL=<dL22>/2>/2 Invert to calculate DInvert to calculate D00..
Constant solar wind Constant solar wind velocity 600 km/s.velocity 600 km/s.
Density perturbations Density perturbations in solar wind at 3 mhZ.in solar wind at 3 mhZ.
Spectral analysis in Spectral analysis in magnetosphere shows magnetosphere shows strong peak at 3 mHz, strong peak at 3 mHz, but also peaks at 5, 7, but also peaks at 5, 7, and 10 mHz.and 10 mHz.
S. Elkington, GEM 2003
Parametric studies, const Parametric studies, const solar windsolar wind
Constant solar wind Constant solar wind velocity 600 km/s.velocity 600 km/s.
Nothing else!Nothing else!
Indicates that 5, 7 Indicates that 5, 7 mHz features are due mHz features are due to K-H waves on the to K-H waves on the flanks.flanks.
Limited local time: Limited local time: propagating waves dusk propagating waves dusk and counterpropagating and counterpropagating waves dusk still lead to waves dusk still lead to energization. energization.
S. Elkington, GEM 2003
Mode structure in ULF Mode structure in ULF simulationssimulations
Diffusion coefficients: depend on Diffusion coefficients: depend on P(mP(mDD),), etc., so etc., so must know the power in must know the power in each specific mode numbereach specific mode number..
Main
P
hase
Reco
very
P
hase
S. Elkington, GEM 2003
Energization through radial Energization through radial transport: a plasma sheet transport: a plasma sheet
source?source? Simplistic considerations put Simplistic considerations put rr00~20 ~20
RREE for for MM corresponding to a corresponding to a 1 MeV1 MeV geosynchronous electrongeosynchronous electron
Conversely, Conversely, W for rW for r00=6.6R=6.6REE is 50 keV. is 50 keV. So is transport/acceleration a viable So is transport/acceleration a viable
mechanism at all? mechanism at all?
N. Tsyganenkohttp://nssdc.gsfc.nasa.gov/space/model/magnetos/data-based/modeling.html
S. Elkington, GEM 2003
Plasmasheet access to Plasmasheet access to inner magnetosphere: inner magnetosphere:
observationsobservations
Korth et al. [Korth et al. [JGR 104JGR 104, 25047, 1997] found good , 25047, 1997] found good agreement with theory for keV electrons.agreement with theory for keV electrons.
MeV electrons?MeV electrons?
S. Elkington, GEM 2003
MHD/particle simulations MHD/particle simulations of energetic electron of energetic electron
trappingtrapping
60 keV test electrons, 60 keV test electrons, constant constant MM. .
Started 20 RStarted 20 REE downtail, 15s intervals.downtail, 15s intervals.
Evolves naturally Evolves naturally under MHD under MHD E E and and BB fields.fields.
Removed from Removed from simulation at simulation at magnetopause.magnetopause.
Color coded by energy.Color coded by energy.
S. Elkington, GEM 2003
Conclusions/SummaryConclusions/SummaryOur understanding of radial transport in the Our understanding of radial transport in the
radiation belts is better, but still will require radiation belts is better, but still will require considerable effort.considerable effort.
Transport equations: DLL proportionalities, Transport equations: DLL proportionalities, energy dependence.energy dependence.
ULF waves:ULF waves: Power spectrum and occurrence characteristics of ULF Power spectrum and occurrence characteristics of ULF
waves.waves. Mode structure of magnetospheric waves.Mode structure of magnetospheric waves. How is power coupled from solar wind to inner How is power coupled from solar wind to inner
magnetosphere?magnetosphere? Boundary conditions: the plasma sheet?Boundary conditions: the plasma sheet?
Determine plasmasheet access.Determine plasmasheet access. Distribution in plasmasheet.Distribution in plasmasheet.