The Physics of Space Plasmas
Magnetic Storms
William J. Burke
31October 2012
University of Massachusetts, Lowell
Magnetic Storms
Lecture 7
• Historical background:
- Dessler-Parker-Sckopke
- Burton-Russell-McPherron relationships
• Electric fields in the inner magnetosphere: penetration, shielding and
over-shielding.
- Single particle approach: the Volland-Stern model
- Fluid/multi-fluid approach: The Rice Convection model
- Two crises: (1) too much shielding (June 1991 storm), and
(2) electric field saturation (Bastille Day Storm)
- Tsyganenko: Magnetic inflation and contributors to Dst
- Siscoe-Hill and revised Volland-Stern models
• Love and Gannon: Dst movies
• Transmission line analogy
Magnetic Storms
Magnetic Storms: a brief history:
• Alexander von Humboldt coined the term “magnetic storm” after
watching aurorae and magnetic deflection over Berlin in Dec.21, 1806.
• Richard Carrington: witnesses white light flare August 28, 1859
followed by magnetic storm on the next day: aurorae over Havana.
• Kristin Birkeland: After 1902-1903 campaign distinguished between
polar elementary storms (substorms) and equatorial perturbations.
• Sydney Chapman: phases of magnetic storms
• Alex Dessler & Gene Parker: (1959) ERC  H at the Earth’s surface.
• Masahisa Sugiura: Dst stations and hourly index to calibrate storms
• Burton et al. (1975): Predict Dst from solar wind/IMF
Magnetic Storms
Stormtime E-fields in Inner Magnetosphere:
• E-fields are the only force that can accelerate charged particles
• In general:
F  mx
F  x  mx  x 
m d 2 d
x  K
2 dt
dt
• Consider a charge particle with an equatorial pitch angle of 90 in the
presence of a dawn-to-dusk electric field E = - .
Since VG 
dK
 qE  V  qE  (VEB  VG )  qE  VG  q  VG
dt

qB
2
( B B)
dK
( B B)
( E  B)
 qE VG   E 


B  VE  B
2
2
dt
B
B
Magnetic Storms
The Volland-Stern single-particle model:
• Here we use a version of the V-S model formulated by Ejiri, JGR, 83, 4798, 1978.
• Consider the electric potential (R, f) in the magnetospheric equatorial plane as a
superposition of a co-rotation and “externally imposed” potentials
B0 RE3
( R, f )  C ( R)   M ( R, f )  
 CRg Sinf
R
• The corotation potential B0RE2  91 kV . C is a constant determined by boundary
conditions and g is a fitting parameter whose physical meaning is addressed below.
• We will use both cylindrical (R , f) and Cartesian (XGSM, Y GSM) coordinates.
 Rˆ   Cosf Sinf   Xˆ 
 
 
 fˆ    Sinf Cosf   Yˆ 
 
 
 Xˆ  Cosf
 
 Yˆ   Sinf
 
 Sinf   Rˆ 
 
Cosf   fˆ 
•Assume that E is in the dawn-dusk (+ YGSM) direction
  ˆ1  
E  ( R, f )   rˆ
f
( R, f )

R f 
 R
Magnetic Storms
The Volland-Stern single-particle model:
B0 RE3
E(R,f )  E C (R)  E M (R,f )  
rˆ  CRg 1 g Sinf rˆ  Cosffˆ 
2
R
At some point RS = RE LS along the dusk meridian (f = p/2) the inward pointing
EC exactly cancels the outward directed EM allowing us to calculate C
B0 RE3
B0 RE3
C

g 1
g RS
g ( RE LS )g 1
g 1




B0 R
1 R
1    Sinf 
( R, f )  
R  g  RS 


3
E
B0 RE3
E(R,f )  
R2
g 1
   R g 1


 R
1
ˆ
 1    Sinf  rˆ    Cosff 
   RS 

 g  RS 


g 1

91kV  1  L 
1    Sinf 
( L, f )  
L  g  LS 


Magnetic Storms
The Volland-Stern single-particle model:
g 1
g 1



1 L 
 mV  1    L 
ˆ
E(L,f )  15 
 2 1    Sinf  rˆ    Cosff 

 m  L    LS 
 g  LS 


At the stagnation point LS the potential is
p
91  1 
( LS , )   kV 1  
2
LS
 g
Since the last closed equipotential touches LS => calculate locus of this potential
91kV
( LA , f )  
LS
 LA 
 
 LS 
 1
91kV
1



 g
LA


g 1
LA (f ) 
Sinf 
 1  L g 1

1   A  Sinf 
 g  LS 

LA
(g  1)  g  0
LS
LS

2
 f  3p / 2  
1

Cos


 
g
2


• LA(f) gives shape of zero-energy
Alfvén boundary (ZEAB)
• Still don’t know what g means
or how to relate EM to the
interplanetary medium.
Magnetic Storms
The Volland-Stern single-particle model:
At the magnetopause on the dawn (LY, 3p/2) and dusk (LY, p/2) the potentials are
approximately PC/2 and - PC/2, respectively.
LY  1.5 LX
g 1
 (kV )
p
91kV  L Y 
 M ( LY , )  

   PC
B02
9.6
2
g LY  LSg 
2
LX  6

0 PSW 6 PSW (nPa)
1

 g 1
182
6 P (nPa)
L

14.4
/
LSg  LY 
Y
SW

g
L

(
kV
)
 Y PC

g
91kV  PC (kV )  L 
 ( L, f )  

  Sinf
L
2
 LY 
E(L,f )  
91(kV ) ˆ  PC (kV )  L 
R
 
2
RE L
2 RE LY  LY 
Average E across magnetosphere
g 1
g Sinf Rˆ  Cosffˆ 


1
Yˆ
Magnetic Storms
Rice Convection Model: (Harel et al., JGR 1981)
Vasyliunas (1969, 1970)
 B  p 
j 

2
B


 j  0
 p  B 
  j|| 
1
1

      j    
2
s  B 
B
B
B


Bi
ds
ˆ
j|| 
(p  Be )  
2 Be
B
Magnetic Storms
Main Phase Electric fields and particles measured by CRRES
Magnetic Storms
Magnetic Storms
Electric field and particle boundaries sampled by DMSP F8 and CRRES
Magnetic Storms
Magnetosphere simulation at 22:00 UT on 6 April 2000
Tsyganenko, N. A., H. J. Singer, and J. C. Kasper, Storm-time distortion of the inner
magnetosphere: How severe can it get? J. Geophys. Res., 108 (A5), 1209, 2003.
Magnetic Storms
Magnetosphere simulation at 08:00 UT on 31 March 2001
Magnetic Storms
Magnetic Storms
Model validation with F13 & F15
B
Z
Y
Siscoe et al. (2002), Hill model of transpolar saturation:
Comparisons with MHD simulations, JGR 107, A6, 1025.
B
Ober et al. (2003) , Testing the Hill model of transpolar
potential saturation, JGR, 108, (A12),
Magnetic Storms
MRC: ISM Simulations with IMF BZ = -2 and -20 nT
S = 1600 PSW 0.33 (nPa) / S
PC = I S / (I + S )
Ober et
I = 0 + LG V BT Sin2 (q/2)
Magnetic Storms
Love, J. J., and J. L. Gannon (2010), Movie‐maps of low‐latitude magnetic storm
disturbance, Space Weather, 8, S06001, doi:10.1029/2009SW000518.
Magnetic Storms
November 2003 storm
Magnetic Storms
Magnetic Storms
Magnetic Storms
Magnetic Storms
Electric field Scaling:
• Kelley et al. (2003), Penetration of the solar wind electric field into the
magnetosphere/ionosphere system, GRL., 30(4), 1158. compared electric
measured with the Jicamarca ISR fields with the Y component of IEF (VBZ).
• Found the electric field in the equatorial ionosphere is one 15th of the electric
field in the solar wind
• It seemed useful to compare eVS with IEFY
Magnetic Storms
Magnetic Storms
Huang, C. Y. and W. J. Burke (2004) Transient sheets of field aligned currents
observed by DMSP during the main phase of a magnetic superstorm, JGR, 109,
A06303.
Magnetic Storms
“Measured” Poynting Flux
Transmission line model
EY  EYi  EYr  EYr  REYi
R
S A  SP
S A  SP
S|| 
S A  1/ 0VAR
BZ  BZi  BZr
EY   BZ
0
EYi
RE
E
 VAS   Yr   Yi
 BZi
 BZr
 BZr
 BZr   R BZi
 BZ  BZi   BZr
EY

EYi  EYr

1 1 R
1 S P VAR


0 S P
VAS 1  R VAS S A VAS

EY  BZ
0
(1  R2 )  S||i (1  R2 )  S||i  S||r
Aurorae and High-Latitude Electrodynamics
Nopper and Carovillano, GRL 699, 1978
Region 1 = 106 A
Region 2 = 0 A
Region 1 = 106 A
Region 2 = 3105 A
Wolf, R. A., Effects of Ionospheric Conductivity on Convective Flow of Plasma
in the Magnetosphere, JGR, 75, 4677, 1970.