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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

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modeling geomagnetic storm dynamics
Modeling Geomagnetic Storm Dynamics


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


solar interplanetary magnetosphere coupling
Sources of ring current ionsSolar - Interplanetary - Magnetosphere Coupling

[Gonzalez et al., 1994]

[Chappell et al., 1987]

• Solar wind

• Ionosphere

max H+: solar min &

quiet conditions

max O+: solar max &

active conditions

Tutorial, GEM Workshop, 6/27/03


magnetic field of the earth
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:

Tutorial, GEM Workshop, 6/27/03


large scale magnetospheric electric field
Large-Scale Magnetospheric Electric Field
  • Volland-Stern semiempirical model
  • convection potential:
  • corotation potential:
  • Drift velocity:

Cluster/EDI Data

IMF Bz<0, 1Re=0.2 mV/m

[Matsui et al., 2003]

[Lyons and Williams, 1984]

Tutorial, GEM Workshop, 6/27/03


cluster edi electric field data
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]

Tutorial, GEM Workshop, 6/27/03


diffusive transport
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]

Tutorial, GEM Workshop, 6/27/03


ring current loss processes
Ring Current Loss Processes


Ring Current Belt

(1-300 keV)

Density Isocontours




Lower Density Cold

Plasmaspheric Plasma

(Dusk Bulge Region)










SAR Arcs


Ring Currents

( L~4)





(Shaded Area)


Ion Precipitation

( L~8 )

( L~6 )

Wave Scattering

of Ring Current Ions

Isotropic Energetic Ion

[Kozyra & Nagy, 1991]


Tutorial, GEM Workshop, 6/27/03


theoretical approaches
Theoretical Approaches
  • • Single particlemotion - 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


kinetic model of the ring current atmosphere interactions ram
Kinetic Model of the Ring Current - Atmosphere Interactions (RAM)
  • •Initial conditions: POLAR, CLUSTER and EQUATOR-S data
  • •Boundary conditions: LANL/MPA and SOPA data

[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)

Tutorial, GEM Workshop, 6/27/03


model drift of ring current particles
Model: Drift of Ring Current Particles

Initial E=0.2 keV at L=10Initial 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]

Tutorial, GEM Workshop, 6/27/03


model ring current loss processes
Model: Ring Current Loss Processes

Charge exchange with Hydrogen from geocorona



- 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


model ring current loss processes12
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


plasmasphere model
Plasmasphere Model

Equatorial plasmaspheric electron density

Ion composition: 77% H+, 20% He+, 3% O+

Tutorial, GEM Workshop, 6/27/03


emic waves observations
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-
  • •Waveamplitudesdecreased with storm evolution
  • •Wavesbelow O+ gyrofrequencyobserved near Dst minimum [Braysy et al., 1998]

Tutorial, GEM Workshop, 6/27/03


self consistent wave particle interactions model
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: Bw=Boexp(G), where Bo is a background noise level

[Jordanova et al., 2001]

Tutorial, GEM Workshop, 6/27/03


image mission imaging the inner magnetosphere
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


wind data geomagnetic indices january 9 11 1997
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

Tutorial, GEM Workshop, 6/27/03


convection electric field comparison with polar efi data
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]

Tutorial, GEM Workshop, 6/27/03


effects of inner magnetospheric convection january 10 11 1997
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
  • •MACEPmodel is more complex and exhibits variable east-west symmetry and spatial irregularities

Tutorial, GEM Workshop, 6/27/03


ring current asymmetry main phase
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


ring current asymmetry recovery phase
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


model results dst index jan 10 1997
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

Tutorial, GEM Workshop, 6/27/03


ion pitch angle distributions polar ips
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

Tutorial, GEM Workshop, 6/27/03


ion pitch angle distributions polar ips25
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

Tutorial, GEM Workshop, 6/27/03


emic waves excitation january 10 1997
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 whenMACEPmodel is used

Tutorial, GEM Workshop, 6/27/03


model results precipitating proton flux

Hour 9

Model Results: Precipitating Proton Flux

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


Tutorial, GEM Workshop, 6/27/03

effects of plasma sheet variability march 30 april 3 2001
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

Tutorial, GEM Workshop, 6/27/03


lanl boundary conditions march april 2001
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


effects of time dependent plasma sheet source population march 30 april 3 2001
Effects of Time-Dependent Plasma Sheet Source Population: March 30 - April 3, 2001
  • • Enhancement in the convection electric fieldalone 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]


Tutorial, GEM Workshop, 6/27/03

emic waves excitation july 13 18 2000
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


proton ring current energy losses
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]


Tutorial, GEM Workshop, 6/27/03

image hena data courtesy of mona kessel nasa
IMAGE/HENA Data, courtesy of Mona Kessel, NASA

Tutorial, GEM Workshop, 6/27/03


ram simulations movie prepared at nasa nov 2000
RAM Simulations, movie prepared at NASA, Nov 2000

Tutorial, GEM Workshop, 6/27/03


relativistic electron kinetic model
Relativistic Electron Kinetic Model
  • g - relativistic factor, mo - rest mass, p - relativistic momentum of particle
  • - radial diffusion coefficients

Tutorial, GEM Workshop, 6/27/03


relativistic electron transport and loss
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]
  • 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

Tutorial, GEM Workshop, 6/27/03


ram electron results test simulations
RAM Electron Results: Test simulations

Tutorial, GEM Workshop, 6/27/03


model results and noaa data october 21 25 2001
Model Results and NOAA Data: October 21-25, 2001

[Miyoshi et al., 2003]

Tutorial, GEM Workshop, 6/27/03


  • Thering currentis a very dynamic region that couples the magnetosphere and the ionosphere during geomagnetic storms
  • New resultsemerging from recent simulation studies were discussed:
  • • the predominant role of theconvection electric fieldfor ring current dynamics & Dst index
  • • the importance of the stormtime plasma sheet enhancement and dropoutfor ring current buildup and decay
  • • the formation of anasymmetricring current during the main and early recovery storm phases
  • • it was shown that charge exchangeis the dominant internal ring current loss process
  • • wave-particle interactionscontribute 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, moreoverO+is the dominant ring current specie during great storms
  • • study effects of diffusive transport and substorm-induced electric fieldson 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


  • 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