ULF Wave Modelling With A
Motive: Effects on Energetic
Paritcles
Mary Hudson, Scot Elkington, Brian Kress,
Kara Perry, John Lyon, Mike Wiltberger
ULF Wave-Relativistic Electron
Correlation
Rostoker et al., GRL, 1998
Toroidal and Polodial Modes
Hughes, Solar Wind Sources of Magnetospheric ULF
Waves, AGU, 1994
CRRES Poloidal and Toriodal ULF Wave B Components
CRRES 18 degree inclination, 6.3 RE apogee,
July 90 – Oct 91
Hudson et al., Annales. Geophys., 2004
CRRES Occurrence Rates of
Poloidal and Toroidal ULF Waves
Hudson et al., Annales Geophys., 2004
AMPTE CCE Occurrence Rates Of
Toroidal Mode
9 RE apogee
Takahashi et
al., JGR,
2002
AMPTE IRM Occurrence Rates Of
Poloidal/Compressional Mode
Anderson et al., JGR 1990
Groundbased Magnetometer ULF Wave Studies
Mathie & Mann
2000 JGR
Mathie & Mann JGR 2000
Pc5 Correlation with Solar Wind
Speed and Relativistic Electrons
Mann et
al., JASTP,
2004
Convective Growth of
Magnetopause K-H Waves
Miura, JGR, 1992
Direct Coupling of Solar Wind ULF Waves
Kepko et al., GRL, 2002
Transmitting ULF Wave Power Into
Magnetosphere via Fast Mode
Structure of Externally Driven FLRs
Linear dipole
MHD simulation
δv ~
δE/B_0
Proehl et al., JGR
2002
Parallel Mode Structure
Poloidal mL=1/3
Global LFM-MHD Simulations
of Magnetosphere

Solar wind
measurements made
by satellite at L1, or
CME-solar wind
coupled MHD codes

Ideal MHD equations
are solved on a
computational grid to
simulate the response
of the magnetosphere
Goodrich et al. ‘98
L dependence of Ephi power
0.558-15 mHz
Elkington, S. R., M. Wiltberger, A. A. Chan, and D. N. Baker, J. Atmos. Solar Terr.
Phys., 66, 1371, 2004.
Azimuthal Distribution of P(Ephi)
Azimuthal Distribution of P(Ephi)
Azimuthal Mode Number from MHD
Simulations and Ground Magnetometers
Sept 98 storm MHD (Ephi) wave
power in 0.14-15 mHz, low m modes
Mathie & Mann,
JGR, 2000
Frequency Dependence
Bloom, R. M. and H. J. Singer, JGR, 100, 14943, 1995.
Convective Growth of
Magnetopause K-H Waves
K-H Shear-Driven Instability
Direct Coupling of Solar Wind ULF Waves
Kepko et al., GRL, 2002
3 MHz Solar Wind Pulsations
SW Density Driven Pulsations
Test Particle Simulations of
Radiation Belts


2D: Drift motion of electrons
and ions in the equatorial
plane is followed using timevarying electric and magnetic
fields from global MHD
simulation
3D: Bounce and drift motion
of guiding center electrons in
MHD fields; gyro, bounce and
drift motion of Solar Energetic
Particles (el, protons, Fe)
Solar Energetic Particle (SEP) cutoffs
calculated using MHD fields
MHD Fields Injection of RadBelt
Electrons
Radiation Belt Electron Energization
Processes Conserving First Invariant
Particles can be
energized by:
1)Convection: steady,
or substorm and
storm-enhanced
2)Diffusion*:
convection E
fluctuations, ULF wave
δE and δB δE
enhance diffusion
3) Drift time scale
injection (Mar 91)
*
a)Falthammar, JGR, 1965;
b)Elkington et al., JGR, 2003
Diffusion Rates vs. L
Radial diffusion
rates in model
ULF wave fields
D_LL ~
LN
Falthammar, 1965 N=6, 10
Elkington et al., 2003 N=11
Selesnick et al., 97, 2000 N=12
Perry et al., JGR, 2005, N=6, 18
Braughtigam & Albert, 2000, N=6, 10
Perry includes δEφ, δBr, δB//,
freq and L-dependent Power
MHD-Driven Phase Space Density
AE8 Max-Initialized, Sept 98 Storm
Fei et al., 2005
Drift Time Scale Injection from SSC’s
Blake et al., 2005
EF in equatorial plane from MHD simulation of March 24, 1991
CME-interplanetary shock compression of magnetopause.
E x B transport of ring of radiation belt electrons inward
by inductive EF due to magnetopause compression dBz/dt.
MHD-Guiding Center Simulation
Elkington et al., JASTP, 2002; 2004
Equatorial Plane Proton MHD Guiding Center Simulation
March 24, 91 event
Hudson et al., JGR, 1997
Average Count Rate of 10-20 MeV
Electrons Mirroring at SAMPEX
Solar Proton Trapping Nov 01
New belt example: 24 Nov 2001
Mazur et al.,
SHINE mtg, 2004
Clear trapping of solar particles - no
other source of heavy ions possible
Solar Energetic Particle Access
Summary of ‘ULF Wave’ Effects on
Energetic Particles



Electrons interact diffusively with ULF
waves with f ~ electron drift period while
conserving first invariant
Large amplitude distortion of
magnetopause launches magnetosonic
impulse outside range of linear ULF wave
models, drift time scale injection of MeV
electrons and protons (electrons unusual)
Solar energetic particles trapped on drift
time scale, stay trapped as long as 1st
invariant conserved (Young et al., 2002)
Higher Frequency Wave Mode
Effects

Other, 1st invariant
violating processes
responsible for
energy/momentum
diffusion and pitch
angle diffusion at
fixed L (VLF/ELF)
Summers and Ma,
JGR, 2000
Externally and Internally Excited Pc5 (mHz) ULF Waves: low and high
m
Field Line Resonance
Dawn-Dusk Assymmetry in Toroidal
Mode ULF Wave Power
Sharper dawn-side radial
gradient affects ionospheric
screening (Glassmeir &
Duskside B-compression affects K-H instability Stellmacher, JGR, 2000)
threshold velocity shear (Lee et al., JGR, 1981)
Perry et al.,
JGR, 2005
Compressed (solid) vs. dipole (dashed) diffusion coefficients