Origin, growth, and recovery of geomagnetic storms Theoretical approaches for studying inner...

• 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

by

Vania K. Jordanova

Space Science Center/EOS

Department of Physics

University of New Hampshire, Durham, USA

Modeling Geomagnetic Storm Dynamics

Tutorial, GEM Workshop, 6/27/03 1

Solar - Interplanetary - Magnetosphere Coupling

Sources of ring current ions

[Gonzalez et al., 1994]

• Solar wind

• Ionosphere

[Chappell et al., 1987]

max O+: solar max & active conditions

max H+: solar min & quiet conditions

2Tutorial, GEM Workshop, 6/27/03

• 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:

Magnetic Field of the Earth

B2

B

2

vv

Bv

222II4

q

msGC


[Hess, 1968]

Large-Scale Magnetospheric Electric Field

[Lyons and Williams, 1984]

• Volland-Stern semiempirical model convection potential:

corotation potential:

Drift velocity:

ooconv sinARU

ocor RCU

UDE

E ,B

BEv

2


Cluster/EDI DataIMF Bz<0, 1Re=0.2 mV/m [Matsui et al., 2003]

• 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

Cluster/EDI Electric Field Data

[Matsui et al., 2003]


• 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]

Diffusive Transport

iijiiii fSf

M

fC

L

f

L

D

LL

t

f

22

• 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]


Ring Current Belt(1-300 keV)Density Isocontours

Dawn

Dusk

ConjugateSAR Arcs

EnergeticNeutralPrecipitation

AnisotropicEnergeticIon Precipitation

CoulombCollisionsBetweenRing CurrentsandThermals(Shaded Area)

Lower Density ColdPlasmaspheric Plasma(Dusk Bulge Region)

( L~6 )( L~8 )Wave Scattering of Ring Current Ions

Plasmapause

( L~4)

Isotropic Energetic IonPrecipitation

Ion Cyclotron Waves Charge

Exchange

[Kozyra & Nagy, 1991]

Ring Current Loss Processes


• 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]

Theoretical Approaches


'm

m

s

s moooo

ooooott

t

atm

t

wpi

t

collisCoul

t

exchch

tt

BsB

ds

Rh cos

dEdddRhERmdV dV

dNF

t

F

t

F

t

F

t

F

dt

dF

12

1

28 23

and

andwhere

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)

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]


to

ooooo

t

ttoo

tt

Fdt

dh

hF

dt

dEE

EE

Fdt

dF

dt

dRR

RRt

F

dt

dF

11

1 02

02

Model: Drift of Ring Current Particles

Initial E=0.2 keV at L=10 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]


Charge exchange with Hydrogen from geocorona

Ft

t

chexch

t2 Em t

nH Ft

- cross section for charge exchange with H

- bounce-averaged exospheric Hydrogen density [Schulz and Blake, 1990]

t

nH

Loss of particles to the atmosphere due to the emptying of

the loss cone (twice per bounce period B) [Lyons, 1973]

Ft

t

atm

Ft

atm

atm B 2 , inside the loss cone

, outside the loss cone

, where

(A+)(A)

Model: Ring Current Loss Processes


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]

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]

E

FDE

EE

FhD

ht

F tEE

o

too

ooowpi

t

oo

11

EEDDoo

and where


Plasmasphere Model

Equatorial plasmaspheric electron density

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


EMIC Waves Observations

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]

EMIC waves recorded using DE1 magnetometer within 30° MLAT during the 10-year missionlifetime [Erlandson and Ukhorskiy, 2001]


Self-consistent Wave-Particle Interactions Model

tIItg

A,E,n

V

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:

min

maxmin

max

w

(neglect) nT 1.0

10

nT 10

for

for

for

minmax

GG

GGGB

GGB

B GGGsat

sat

[Jordanova et al., 2001]

(1) Solve the hot plasma dispersion relation for EMIC waves:

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


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]

• The low altitude ENA fluxes peak near dusk and overlap the plasmapause [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


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


• Enhanced electric fields are measured below L=5 during the main phase of the storm on the duskside (MLT18)

• 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 (MLT6)

• 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]

Convection Electric Field: Comparison with POLAR/EFI Data

[Boonsiriseth et al., 2001]


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


• 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

Ring Current Asymmetry: Main Phase


• 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

• Energy density peaks near dusk in both MACEP and Volland-Stern models during early recovery phase

Ring Current Asymmetry: Recovery Phase


• The trapped population evolves into a symmetric ring current during late recovery phase

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


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


• 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

Ion Pitch Angle Distributions:

POLAR/IPS


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


• 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

EMIC Waves Excitation:January 10, 1997


Model Results: Precipitating Proton Flux

• 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

Hour 25Hour 9

Tutorial, GEM Workshop, 6/27/0327

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


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


• 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

Effects of Time-Dependent Plasma Sheet Source Population: March 30 - April 3, 2001

Tutorial, GEM Workshop, 6/27/0330[Jordanova et al., GRL, 2003]

• 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

EMIC Waves Excitation: July 13-18, 2000


[Jordanova et al., Solar Physics, 2001]

• Proton precipitation losses increase by more than an order of magnitude when WPI are considered

• Losses due to charge exchange are, however, predominant

Proton Ring Current Energy Losses

Tutorial, GEM Workshop, 6/27/0332[Jordanova, Space Sci. Rev., 2003]

IMAGE/HENA Data, courtesy of Mona Kessel, NASA


RAM Simulations, movie prepared at NASA, Nov 2000


- relativistic factor, mo - rest mass, p - relativistic momentum of particle

- radial diffusion coefficients

Relativistic Electron Kinetic Model

220

2

02

02

1 and 1

where

1

11

cm

Eγ

R

FD

RRR

t

F

t

F

t

F

t

F

t

F

Fdt

dh

h

Fdt

dEp

EpF

dt

dF

dt

dRR

RRt

F

oo

tRR

oo

rd

t

atm

t

wpi

t

cc

t

rd

t

to

ooooo

tttoo

t

oo


ooRRD

36

Relativistic Electron Transport and Loss

Tutorial, GEM Workshop, 6/27/03

Radial diffusion coefficients [Brautigam and Albert, 2000]

• magnetic field fluctuation

62

2

0

60 )2/(1

25.0),,( LT

T

B

KpcELDLMKpD

D

rmsEELL

• electric field fluctuation

100),( LDLKpD MM

LL 325.9506.00 10 KpMD

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

RAM Electron Results: Test simulations


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

38[Miyoshi et al., 2003]Tutorial, GEM Workshop, 6/27/03

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

Conclusions


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

Acknowledgments


Origin, growth, and recovery of geomagnetic storms Theoretical approaches for studying inner...

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