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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

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Modeling geomagnetic storm dynamics l.jpg

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 l.jpg

Sources of ring current ions

Solar - 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 l.jpg

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 l.jpg

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 l.jpg

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 l.jpg

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 l.jpg

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 l.jpg

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 l.jpg

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 l.jpg

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 l.jpg

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 l.jpg

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 l.jpg

Plasmasphere Model

Equatorial plasmaspheric electron density

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

Tutorial, GEM Workshop, 6/27/03


Emic waves observations l.jpg

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 l.jpg

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 l.jpg

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 l.jpg

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 l.jpg

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 l.jpg

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 l.jpg

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 l.jpg

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 l.jpg

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


Modeled distributions and polar data jan 10 09 30 ut l.jpg

Modeled Distributions and POLAR Data: Jan 10, 09:30 UT

Tutorial, GEM Workshop, 6/27/03


Ion pitch angle distributions polar ips l.jpg

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 l.jpg

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 l.jpg

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 l.jpg

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 l.jpg

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 l.jpg

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 l.jpg

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 l.jpg

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 l.jpg

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 l.jpg

IMAGE/HENA Data, courtesy of Mona Kessel, NASA

Tutorial, GEM Workshop, 6/27/03


Ram simulations movie prepared at nasa nov 2000 l.jpg

RAM Simulations, movie prepared at NASA, Nov 2000

Tutorial, GEM Workshop, 6/27/03


Relativistic electron kinetic model l.jpg

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 l.jpg

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 l.jpg

RAM Electron Results: Test simulations

Tutorial, GEM Workshop, 6/27/03


Model results and noaa data october 21 25 2001 l.jpg

Model Results and NOAA Data: October 21-25, 2001

[Miyoshi et al., 2003]

Tutorial, GEM Workshop, 6/27/03


Conclusions l.jpg


  • 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


Acknowledgments l.jpg


  • 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


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