Transcript GEM Tutorial 2003 - UCLA - IGPP Space Physics Center

Modeling Geomagnetic Storm Dynamics
by
Vania K. Jordanova
Space Science Center/EOS
Department of Physics
University of New Hampshire, Durham, USA
•
•
•
•
Origin, growth, and recovery of geomagnetic storms
Theoretical approaches for studying inner magnetosphere
dynamics
New insights on geomagnetic storms from kinetic model
simulations using multi-satellite data
Future model developments
Tutorial, GEM Workshop, 6/27/03
1
Solar - Interplanetary - Magnetosphere Coupling
[Gonzalez et al., 1994]
Sources of ring current ions
[Chappell et al., 1987]
• Solar wind
• Ionosphere
max H+: solar min &
quiet conditions
max O+: solar max &
active conditions
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2
Magnetic Field of the Earth
[Hess, 1968]
• The main geomagnetic field can be represented by spherical harmonic series in
which the first term is the simple dipole term [Gauss, 1839]. Temporal variations of
the internal field are modeled by expanding the coefficients in Taylor series in time
[e.g., IGRF model, 1995].
• The Earth's real magnetic field is the sum of several contributions including the
main (internal) field and the external source (magnetospheric) fields
[e.g., Tsyganenko, 1996, 2001].

ms  2 v 2   B2  
   B
Gradient-Curvature velocity: vGC   4  v II 
qB 
2   2 
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3
Large-Scale Magnetospheric Electric Field
•
Volland-Stern semiempirical model
convection potential:
U conv  ARo sin  o 
corotation potential:
U cor   C Ro
Drift velocity:
 

EB
v DE 
,
B2

E  U
Cluster/EDI Data
IMF Bz<0, 1Re=0.2 mV/m
[Matsui et al., 2003]
[Lyons and Williams, 1984]
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4
Cluster/EDI Electric Field Data
• Statistically averaged data at L=4-5,
IMF Bz<0, average Kp=2+,
corotating frame of reference
• Radial and azimuthal components
mapped to equatorial plane
• Strong electric field at MLT=19-22,
not observed during northward IMF
[Matsui et al., 2003]
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5
Diffusive Transport
• Standard model [e.g., Sheldon and Hamilton, 1993]
- magnetic diffusion [Falthammer, 1965]
- electric diffusion [Cornwall, 1971]
f i

 L2
t
L
 D f i

 L2 L



f i
C
 f i  S ij f i


M


• The cross-tail potential is enhanced by a superposition of exponentially decaying impulses
[Chen et al., 1993; 1994]
• Profiles of normalized ring current energy density indicate the impulsive character of enhancements
makes significant contribution in storms with long main phase [Chen et al., 1997]
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Ring Current Loss Processes
Energetic
Neutral
Precipitation
Plasmapause
Ring Current Belt
(1-300 keV)
Density Isocontours
Lower Density Cold
Plasmaspheric Plasma
(Dusk Bulge Region)
Dawn
Ion
Cyclotron
Waves
Charge
Exchange
Conjugate
SAR Arcs
( L~4)
Dusk
Anisotropic
Energetic
Ion Precipitation
( L~8 )
( L~6 )
Isotropic Energetic Ion
Precipitation
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Coulomb
Collisions
Between
Ring Currents
and
Thermals
(Shaded Area)
Wave Scattering
of Ring Current Ions
[Kozyra & Nagy, 1991]
7
Theoretical Approaches
• Single particle motion - describes the motion of a particle under the influence of
external electric and magnetic fields
- trajectory tracing studies [e.g., Takahashi & Iyemori, 1989; Ebihara & Ejiri, 2000]
- mapping of distribution function [e.g., Kistler et al., 1989; Chen et al. 1993]
• Magnetohydrodynamics and Multi-Fluid theory - the plasma is treated as
conducting fluids with macroscopic variables, allow self-consistent coupling
of the magnetosphere and ionosphere
- Rice convection model [e.g., Harel et al., 1981; Wolf et al., 1981; 1997]
• Kinetic theory - adopts a statistical approach and looks at the development of
the distribution function for a system of particles
[e.g., Fok et al., 1993; Sheldon & Hamilton, 1993; Jordanova et al., 1994]
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Kinetic Model of the Ring Current - Atmosphere Interactions (RAM)
dFt
dt
 F 
 F 
 F 
  t
  t
  t
 t  chexch
 t  Coul
 t  wpi
collis
where Ft 
dNt
dV
 o  cos o
1
and h o  
2 Ro
 F 
  t
 t  atm
and dV  8 2mt3 Ro2 E  o h o dRo ddEd o
s m'

sm
ds
1  B s  B m
[Jordanova et al., 1994; 1997]
Ro - radial distance in the equatorial plane from 2 to 6.5 RE
 - azimuthal angle from 0 to 360, E - kinetic energy from 100 eV to 400 keV
o - equatorial pitch angle from 0 to 90
- bounce-averaging (between mirror points)
•
•
Initial conditions: POLAR, CLUSTER and EQUATOR-S data
Boundary conditions: LANL/MPA and SOPA data
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Model: Drift of Ring Current Particles
dFt
dt

 

E E 
1
Ft
1 
 2
t
Ro R0
E
 2 dR0


  d
 Ro
Ft  

Ft  
dt


   dt

dE
1

Ft  
dt
 h o   o  o
Initial E=0.2 keV at L=10


d o
 h o   o
Ft 
dt


Initial E=0.4 keV at L=10
The 90 deg pitch angle particle tracings. Asteriks are
plotted at 1 hour steps within 20 hours [Ejiri, 1978]
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Model: Ring Current Loss Processes
Charge exchange with Hydrogen from geocorona
 Ft 
 t


  t c he xc h
t
2E
n H Ft
mt
(A)
(A+)
- cross section for charge exchange with H
nH
- bounce-averaged exospheric Hydrogen density
[Schulz and Blake, 1990]
Loss of particles to the atmosphere due to the emptying of
the loss cone (twice per bounce period B) [Lyons, 1973]
Ft 
Ft

 t at m
 at m
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, where
 at m
 B 2, inside the loss cone
 
, outside the loss cone
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Model: Ring Current Loss Processes
Coulomb collisions with thermal plasma:
- Fokker-Planck equation considering energy degradation & pitch angle scattering
- plasmaspheric density model for e-, H+, He+, O+ species [Rasmussen et al., 1993]
Plasma waves scattering: quasi-linear theory
[Kennel and Engelmann, 1966; Lyons and Williams, 1984]
Ft 
Ft 
1
 
1  
 Ft 

E DEE


 Doo h o  o


h o  o  o 
 o 
E 
E E 
 t  wpi
where
D o o
and DEE - quasi-linear
diffusion coefficients including heavy ion
components [Jordanova et al., 1996]
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Plasmasphere Model
Equatorial plasmaspheric electron density
Ion composition: 77% H+, 20% He+, 3% O+
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EMIC Waves Observations
EMIC waves recorded using DE1 magnetometer
within 30° MLAT during the 10-year mission
lifetime [Erlandson and Ukhorskiy, 2001]
Freja data, April 2-8, 1993 storm, Dst=-170 nT, Kp=8• Wave amplitudes decreased with storm evolution
• Waves below O+ gyrofrequency observed near Dst
minimum [Braysy et al., 1998]
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Self-consistent Wave-Particle Interactions Model
(1) Solve the hot plasma dispersion relation for
EMIC waves:

  nt , E II , At 
Vg
where nt, EII, At are calculated with our kinetic
model for H+, He+, and O+ ions
(2) Integrate the local growth rate along wave
paths and obtain the wave gain G(dB)
a) Use a semiempirical model to relate G to the
wave amplitude Bw:
for
G  Gmax
Bsat  10 nT


Bw  Bsat 10G Gmax  Gmin for Gmin  G  Gmax

G  Gmin
 0.1 nT (neglect) for
b) Or, use the analytical solution of the wave
equation to relate G to the wave amplitude:
Bw=Boexp(G),
where Bo is a background noise level
Tutorial, GEM Workshop, 6/27/03
[Jordanova et al., 2001]
15
IMAGE Mission: Imaging the inner magnetosphere
•
Simultaneous global images of the plasmasphere and the ring current during the storm
main phase (Dst= -133 nT) on May 24, 2000 [Burch et al., 2001]
EUV image of the plasmasphere at 0633
UT from above the north pole
•
Superimposed HENA image of 39-60 keV fluxes
showing significant ion precipitation near dusk
The low altitude ENA fluxes peak near dusk and overlap the plasmapause [Burch et al., 2001]
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WIND Data &
Geomagnetic Indices:
January 9-11, 1997
• An interplanetary shock arrived at
Wind at hour~25
• It is driven by a magnetic cloud
which extends from hour~29 to
hour~51
• Triggered a moderate geomagnetic
storm with Dst= -83 nT & Kp=6
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Convection Electric Field: Comparison with POLAR/EFI Data
• Enhanced electric fields are
measured below L=5 during the main
phase of the storm on the duskside
(MLT18)
• Such electric fields appear about
an hour or more before a strong ring
current forms
• Much smaller electric fields at
larger L shells (L=5-8) and on the
dawnside (MLT6)
• Good agreement with the MACEP
model we developed on the basis of
the ionospheric AMIE [Richmond,
1992] model and a penetration
electric field [Ridley and Liemohn,
2002]
[Boonsiriseth et al., 2001]
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Effects of Inner
Magnetospheric Convection:
January 10-11, 1997
Electric potential in the equatorial plane:
• Both models predict strongest fields
during the main phase of the storm
• Volland-Stern model is symmetric
about dawn/dusk by definition
• MACEP model is more complex and
exhibits variable east-west symmetry
and spatial irregularities
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Ring Current Asymmetry:
Main Phase
•
Initial ring current injection at high L
shells on the duskside
•
A very asymmetric ring current
distribution during the main phase of
the storm due to freshly injected
particles on open drift paths
•
The total energy density peaks near
midnight using MACEP, near dusk
using Volland-Stern
•
Ring current ions penetrate to lower L
shells and gain larger energy in
MACEP than in Volland-Stern
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Ring Current Asymmetry:
Recovery Phase
•
•
Energy density peaks near dusk in both
MACEP and Volland-Stern models
during early recovery phase
The trapped population evolves into a
symmetric ring current during late
recovery phase
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Model Results:
Dst Index, Jan 10, 1997
Comparison of:
• Kp-dependent Volland-Stern model
• Empirical MACEP model
=> MACEP model predicts larger
electric field, which results in
larger injection rate and
stronger ring current buildup
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Modeled Distributions and POLAR Data: Jan 10, 09:30 UT
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Ion Pitch Angle
Distributions:
POLAR/IPS
•
Data are from the southern
pass at MLT~6 and
E=20
keV on Jan 9 (left), 10
(middle) and 11 (right)
•
Empty loss cones, indicating
no pitch angle diffusion are
observed at these locations
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Ion Pitch Angle
Distributions:
POLAR/IPS
•
Data are from the
southern pass at
MLT~18 and E=20 keV
at hour~8.5 (middle)
and at hour~25.5 (right)
•
Isotropic pitch angle
distributions, indicating
strong diffusion
scattering are observed
at large L shells near
Dst minimum
•
Partially filled loss
cones, indicating
moderate diffusion are
observed during the
recovery phase
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EMIC Waves Excitation:
January 10, 1997
•
We calculated the wave growth
of EMIC waves from the He+
band (between O+ and He+
gyrofrequency)
•
Comparable wave growth is
predicted by both models
during the early main phase
•
Intense waves are excited near
Dst minimum and during the
recovery phase only when
MACEP model is used
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Model Results: Precipitating Proton Flux
Hour 9
Hour 25
•
•
Precipitating H+ fluxes are significantly enhanced by wave-particle interactions
Their temporal and spatial evolution is in good agreement with POLAR/IPS data at low L shells
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Tutorial, GEM Workshop, 6/27/03
Effects of Plasma Sheet
Variability:
March 30 - April 3, 2001
• An interplanetary (IP) shock is
detected by ACE at ~0030 UT
on March 31
• A great geomagnetic storm
Dst= -360 nT (SYM-H= -435 nT)
and Kp=9- occurs
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LANL Boundary
conditions:
March - April, 2001
•
Enhanced fluxes are observed in
both energy channels of the MPA
instrument for ~10 hours after the
IP shock
•
The magnitude of the ion fluxes
gradually decreases after that
• The MPA plasma sheet ion density
shows a similar trend
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Effects of Time-Dependent Plasma Sheet Source Population:
March 30 - April 3, 2001
•
•
•
Enhancement in the convection electric field alone is not sufficient to reproduce the Dst index
The ring current (RC) increases significantly when the stormtime enhancement of plasma sheet
density is considered
The drop of plasma sheet density during early recovery phase is important for the fast RC decay
[Jordanova et al., GRL, 2003]
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EMIC Waves Excitation:
July 13-18, 2000
•
Intense EMIC waves from the
O+ band are excited near Dst
minimum
•
The wave gain of the O+ band
exceeds the magnitude of
the He+ band
•
EMIC waves from the O+ band
are excited at larger L shells
than the He+ band waves
[Jordanova et al., Solar Physics, 2001]
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Proton Ring Current Energy Losses
• Proton precipitation losses increase by more than an order of magnitude when WPI are considered
• Losses due to charge exchange are, however, predominant
[Jordanova, Space Sci. Rev., 2003]
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IMAGE/HENA Data, courtesy of Mona Kessel, NASA
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RAM Simulations, movie prepared at NASA, Nov 2000
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Relativistic Electron Kinetic Model
Ft
1 
 2
t
Ro R0
 2 dR0

 1  

  d
dE
 Ro
Ft  

Ft  
 p
Ft  
dt
dt
 p E 


   dt

h o   o  o


d o
 h o   o
Ft  
dt


1
 Ft 


 t  rd
 F 
 F 
  t 
  t 
 t  cc
 t  wpi
 F 
  t 
 t  atm
where
 Ft 



t

 rd
 Ro2

R0
 1
Ft
 2 D Ro Ro
Ro
 Ro



and
γ  1
E
mo c 2
 - relativistic factor, mo - rest mass, p - relativistic momentum of particle
DRo Ro
- radial diffusion coefficients
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Relativistic Electron Transport and Loss
 Radial diffusion coefficients [Brautigam and Albert, 2000]
• magnetic field fluctuation
M
DLL
(Kp, L)  D0M L10
D0M  100.506 Kp9.325
• electric field fluctuation
 cE Kp  

D ( Kp, M , L)  D L  0.25 rms
B0


E
LL
E
0
6
2

 6
T
L

2 
1  ( D T / 2) 
 Wave-particle interactions (WPI)
• within plasmasphere [Lyons, Thorne, and Kennel, 1972]
n=±5 cyclotron and Landau resonance
hiss and lightning whistler (10 pT - [Abel and Thorne, 1998; Albert, 1999]
• outside plasmasphere –
E>Eo : empirical scattering rate [Chen and Schulz, 2001]
E<Eo : strong diffusion scattering rate [Schulz, 1974]
 Boundary conditions: LANL/MPA and SOPA data
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RAM Electron Results: Test simulations
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Model Results and NOAA Data: October 21-25, 2001
Tutorial, GEM Workshop, 6/27/03
[Miyoshi et al., 2003]
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Conclusions
The ring current is a very dynamic region that couples the magnetosphere and the ionosphere during
geomagnetic storms
New results emerging from recent simulation studies were discussed:
• the predominant role of the convection electric field for ring current dynamics & Dst index
• the importance of the stormtime plasma sheet enhancement and dropout for ring current buildup
and decay
• the formation of an asymmetric ring current during the main and early recovery storm phases
• it was shown that charge exchange is the dominant internal ring current loss process
• wave-particle interactions contribute significantly to ion precipitation, however, their effect on the
total energy balance of the ring current H+ population is small (~10% reduction)
Future studies
• determine the effect of WPI on the heavy ion components, moreover O+ is the dominant ring current
specie during great storms
• study effects of diffusive transport and substorm-induced electric fields on ring current dynamics
• determine the role of a more realistic magnetic field model
• development of a relativistic electron model
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Acknowledgments
Many thanks are due to:
Yoshizumi Miyoshi, Tohoku University, Japan, & UNH, Durham, USA
R. Thorne, A. Boonsiriseth, Y. Dotan, Department of Atmospheric Sciences,
UCLA, CA
M. Thomsen, J. Borovsky, and G. Reeves, Los Alamos Nat Laboratory, NM
J. Fennell and J. Roeder, Aerospace Corporation, Los Angeles, CA
H. Matsui, C. Farrugia, L. Kistler, M. Popecki, C. Mouikis, J. Quinn, R. Torbert,
Space Science Center/EOS, University of New Hampshire, Durham, NH
This research has been supported in part by NASA under grants NAG5-13512,
NAG5-12006 and NSF under grant ATM 0101095
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