1
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
2
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
2
Tutorial, GEM Workshop, 6/27/03
3
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.
• Gradient-Curvature velocity

3
Tutorial, GEM Workshop, 6/27/03
4
Large-Scale Magnetospheric Electric Field

• Volland-Stern semiempirical model
• convection potential
• corotation potential
• Drift velocity

Cluster/EDI Data IMF Bzlt0, 1Re0.2 mV/m Matsui
et al., 2003
Lyons and Williams, 1984
Tutorial, GEM Workshop, 6/27/03
4
5
Cluster/EDI Electric Field Data

• Statistically averaged data at L4-5, IMF Bzlt0,
  average Kp2, corotating frame of reference
• Radial and azimuthal components mapped to
  equatorial plane
• Strong electric field at MLT19-22, not
  observed during northward IMF

Matsui et al., 2003
Tutorial, GEM Workshop, 6/27/03
5
6
Diffusive Transport

• Standard model e.g., Sheldon and Hamilton,
  1993
• - magnetic diffusion Falthammer, 1965
• - electric diffusion Cornwall, 1971

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
6
Tutorial, GEM Workshop, 6/27/03
7
Ring Current Loss Processes
Energetic
Ring Current Belt (1-300 keV) Density Isocontours

Neutral
Plasmapause
Precipitation
Lower Density Cold
Plasmaspheric Plasma
(Dusk Bulge Region)
Dawn
Ion
Cyclotron
Charge
Waves
Exchange
Coulomb
Conjugate
Collisions
SAR Arcs
Between
Ring Currents
( L4)
and
Dusk
Thermals
Anisotropic
(Shaded Area)
Energetic
Ion Precipitation
( L6 )
( L8 )
Wave Scattering
of Ring Current Ions
Isotropic Energetic Ion
Kozyra Nagy, 1991
Precipitation
Tutorial, GEM Workshop, 6/27/03
7
8
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

Tutorial, GEM Workshop, 6/27/03
8
9
Kinetic Model of the Ring Current - Atmosphere
Interactions (RAM)
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

Tutorial, GEM Workshop, 6/27/03
9
10
Model Drift of Ring Current Particles
Initial E0.2 keV at L10
Initial E0.4 keV at L10 The 90 deg pitch
angle particle tracings. Asteriks are
plotted at 1 hour
steps within 20 hours Ejiri, 1978

Tutorial, GEM Workshop, 6/27/03
10
11
Model Ring Current Loss Processes
Charge exchange with Hydrogen from geocorona
(A)
(A)
- cross section for charge exchange with H -
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
, where
Tutorial, GEM Workshop, 6/27/03
11
12
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
- quasi-linear diffusion
coefficients including heavy ion components
Jordanova et al., 1996
Tutorial, GEM Workshop, 6/27/03
12
13
Plasmasphere Model
Equatorial plasmaspheric electron density Ion
composition 77 H, 20 He, 3 O
Tutorial, GEM Workshop, 6/27/03
13
14
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,
  Kp8-
• Wave amplitudes decreased with storm evolution
• Waves below O gyrofrequency observed near Dst
  minimum Braysy et al., 1998

Tutorial, GEM Workshop, 6/27/03
14
15
Self-consistent Wave-Particle Interactions Model
(1) Solve the hot plasma dispersion relation for
EMIC waves
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
b) Or, use the analytical solution of the wave
equation to relate G to the wave amplitude
BwBoexp(G), where
Bo is a background noise level
Jordanova et al., 2001
Tutorial, GEM Workshop, 6/27/03
15
16
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
Tutorial, GEM Workshop, 6/27/03
16
17
WIND Data Geomagnetic IndicesJanuary 9-11,
1997

• An interplanetary shock arrived at Wind at
  hour25
• It is driven by a magnetic cloud which extends
  from hour29 to hour51
• Triggered a moderate geomagnetic storm with
  Dst -83 nT Kp6

Tutorial, GEM Workshop, 6/27/03
17
18
Convection Electric Field Comparison with
POLAR/EFI Data

• Enhanced electric fields are measured below L5
  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
  (L5-8) 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
Tutorial, GEM Workshop, 6/27/03
18
19
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

Tutorial, GEM Workshop, 6/27/03
19
20
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
Tutorial, GEM Workshop, 6/27/03
20
21
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
Tutorial, GEM Workshop, 6/27/03
21
22
Model Results Dst Index, Jan 10, 1997

• Comparison of
• Kp-dependent Volland-Stern model
• Empirical MACEP model
• gt MACEP model predicts larger electric field,
  which results in larger injection rate and
  stronger ring current buildup

Tutorial, GEM Workshop, 6/27/03
22
23
Modeled Distributions and POLAR Data Jan 10,
0930 UT
Tutorial, GEM Workshop, 6/27/03
23
24
Ion Pitch Angle Distributions POLAR/IPS

• Data are from the southern pass at MLT6 and
  E20 keV on Jan 9 (left), 10 (middle) and
  11 (right)
• Empty loss cones, indicating no pitch angle
  diffusion are observed at these locations

24
Tutorial, GEM Workshop, 6/27/03
25
Ion Pitch Angle Distributions POLAR/IPS

• Data are from the southern pass at MLT18 and
  E20 keV at hour8.5 (middle) and at hour25.5
  (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

Tutorial, GEM Workshop, 6/27/03
25
26
EMIC Waves ExcitationJanuary 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

Tutorial, GEM Workshop, 6/27/03
26
27
Model Results Precipitating Proton Flux
Hour 25
Hour 9

• 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

27
Tutorial, GEM Workshop, 6/27/03
28
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 Kp9- occurs

Tutorial, GEM Workshop, 6/27/03
28
29
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

Tutorial, GEM Workshop, 6/27/03
29
30
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
30
Tutorial, GEM Workshop, 6/27/03
31
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
Tutorial, GEM Workshop, 6/27/03
31
32
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
32
Tutorial, GEM Workshop, 6/27/03
33
IMAGE/HENA Data, courtesy of Mona Kessel, NASA
Tutorial, GEM Workshop, 6/27/03
33
34
RAM Simulations, movie prepared at NASA, Nov 2000
Tutorial, GEM Workshop, 6/27/03
34
35
Relativistic Electron Kinetic Model

• g - relativistic factor, mo - rest mass, p -
  relativistic momentum of particle
• - radial diffusion coefficients

Tutorial, GEM Workshop, 6/27/03
35
36
Relativistic Electron Transport and Loss

• Radial diffusion coefficients Brautigam and
  Albert, 2000
• magnetic field fluctuation

electric field fluctuation

• Wave-particle interactions (WPI)
• within plasmasphere Lyons, Thorne, and
  Kennel, 1972
• n5 cyclotron and Landau resonance
• hiss and lightning whistler (10 pT -
  Abel and Thorne, 1998 Albert, 1999
• outside plasmasphere
• EgtEo empirical scattering rate Chen
  and Schulz, 2001
• EltEo strong diffusion scattering rate
  Schulz, 1974

• Boundary conditions LANL/MPA and SOPA data

36
Tutorial, GEM Workshop, 6/27/03
37
RAM Electron Results Test simulations
37
Tutorial, GEM Workshop, 6/27/03
38
Model Results and NOAA Data October 21-25, 2001
Miyoshi et al., 2003
38
Tutorial, GEM Workshop, 6/27/03
39
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

Tutorial, GEM Workshop, 6/27/03
39
40
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

Tutorial, GEM Workshop, 6/27/03
40