•
Shape of magnetosphere
•
Size of magnetosphere
•
Pressure distribution on magnetopause
•
Viscous stress
•
Reconnection
Dungey model
Poynting flux versus mechanical energy flux
Importance of the plasma mass density
Interplanetary electric field
Angular dependence
Beta dependence
•
Where does it occur?
•
Frequency response of the magnetosphere
•
Saturation of the auroral and polar regions
•
Substorms at Earth and Jupiter
•
Northward IMF triggering of substorms
•
Summary and Conclusions

Confinement of a Planetary Magnetic Field by a Flowing Magnetized Plasma
Momentum conservation in a stream tube
( ρ u 2 + nkT + B 2 /2 μ o
) S = constant
Consider ratio of first two terms
ρ u 2 /nkT = u 2 /(kT/m i
) = γμ 2 /c s
2 = γ M s
2
Consider ratio of first and third terms
ρ u
2
/(B
2
/2 μ o
) = 0.5 u
2
/( B
2
/ μ o
ρ ) = 0.5M
A
2
Consider ratio of second and third terms m i kT/(B 2 /2 μ o
) = β = (M
A
2 /M
S
2 )/2 γ
In the solar wind the sonic and Alfven Mach numbers are large and the pressure is dominated by the dynamic pressure.
At the magnetopause the dynamic pressure is zero and the static pressure dominates.
The pressure is slightly diminished from the solar wind value because S increases by about 1 0%.
Inside the magnetosphere the pressure is dominated by the magnetic pressure. The strength of this field is (aB o
/L mp
3 ) where a is a shape dependent parameter. Balancing the magnetic pressure against the solar wind dynamic pressure we obtain
L mp
[RE] = 1 07.4 (n sw
u sw
2
)
1 /6 with n sw being the number of proton masses per cm 3 and u sw being the solar wind speed in km/s.

Planar Magnetopause Spherical Magnetopause
Elliptical Magnetopause Empirical Magnetosphere
Shape determines magnetic field enhancement at subsolar point
Planar magnetopause -- double dipole field strength
Spherical magnetopause -- triple
Elliptical magnetopause (T89a) -- 2.4
Empirical magnetopause (T89b) -- 2.4
CR-719

a
Relative Scaling of
Pressure Terms r v 2
= g
M
S nkT r v 2
2
= 2 M
A
2
(B /2 m
0
) nkT
(B /2 m
0
)
= b
Normal Pressure in
Gas Dynamics r v cos 2 a +
P sin 2 a
Standoff Distance
L = 107.4 (n V )
-1/6 Solar Wind Pressure
Dynamic
Static
Magnetic r v 2 nkT
B /2 m
0
Pressure applied by the solar wind to the magnetopause varies with the angle of the normal to the solar wind flow
CR-1516

4
2
8
6
0
0
1100-1300 MLT
2 4 6
Solar Wind Dynamic Pressure [nPa]
8
The pressure of the plasma inside the cusp is directly proportional to the dynamic pressure of the solar wind flow. The straight line is the expected pressure given the orientation of the surface of the cusp to the solar wind flow.
CR-1669

X 2
-1
1
-1
Field Line
Streamline
Foreshock
Boundary
Y
The gas dynamic convected field model carries magnetic field lines as if they were threads in the fluid. The shaded foreshock is where ions reflected from the shock move upstream.
CR.327

Interplanetary
Magnetic Field Tail Current
Polar
Cusp
Plasmasphere
Plasma Mantle
Magnetic Tail Northern Lobe
Plasma Sheet
Ring Current
Solar Wind
Magnetopause Current
Neutral Sheet Current
Field-Aligned Current
Magnetopause
This cutaway model of the magnetosphere illustrates the flows and current systems in the magnetosphere. The field aligned currents couple stresses in the outer magnetosphere with those in the ionosphere.
CR-1266

North
Solar
Wind
Interplanetary Field Northward
N
N
North
Solar
Wind
N
Interplanetary Field Southward
N
When the interplanetary magnetic field is northward (top), Dungey's 1963 model of the magnetosphere predicts reconnection with tail region, flow over the polar cap toward the sun and flow back to the nightside along the flanks.
When the interplanetary magnetic field is southward (bottom), Dungey's 1961 model of the magnetosphere predicts a flow of plasma and the frozen in field over the polar cap and after reconnection in the magnetotail back to the dayside magnetosphere.
CR-777

Sheath
Sources of Viscosity at the Magnetopause
Sphere Sheath Sphere
Diffusive Entry Boundary Oscillation
Impulsive Penetration Kelvin-Helmholtz Instability

B
Magnetopause
J
S d
B
JxB
S
E
V
JxB
J
E
V J
Ionosphere
A slab of magnetic field is pulled backward at high altitudes creating a shear layer on either side of the slab on which field-aligned electric current flows. The regions of current closure across the magnetic field at high and low altitudes are regions in which momentum is added to the plasma (top) and lost from the plasma (bottom) leading to the terms generator and load respectively for the two regions.
CR-973

N p
N p
10
1
0.1
0.01
V p
350
250
150
V z
300
100
-100
-300
B z
30
10
-10
-30
ISEE 1
The importance of the Alfven velocity
Orbit 135 Outbound 8 September 1978
RC BL MP MS MP MS S
GSM
GSM
P 1
60
30
B
8.913 R
E
R 7.997
ISEE 2
N p
N p
10
1
0.1
0.01
V p
350
250
150
MP S MS S
B z
30
10
-10
-30
00:23
R 8.302
29 35 41
Universal Time
47 53
GSM
59
9.195 R
E
The ISEE 1 and 2 spacecraft showed that there were persistent accelerated flows at approximately the Alfven velocity as the magnetopause was crossed when the IMF was southward.
CR-833

B
IMF
L
Df
V sw
Bow Shock
Magnetopause
Only a thin slab of solar wind plasma of width, L, perpendicular to the IMF and the flow, reconnects with the magnetosphere. In steady state the drop in electric potential across the solar wind slab equals the drop in electric potential across the polar cap.
CR-1670

Am
40
-5nT
20
0
0
AE
250
+5nT B z
150
-5nT
50
0 +5nT B z
Many geomagnetic indices change slope at zero when plotted versus B z
IMF (in GSM coordinates). When the IMF is northward, there is little geomagnetic activity.
CR-1675

11
10
9
8
-8 -4 0 4 8
When the IMF is southward the magnetopause is closer to the Earth than when it is northward. However, there is a weak tendency for the magnetopause to shrink for strong positive B z
as well.
CR-1671

80
60
40
20
0
-16
Dusk to Dawn
-8 0
Dawn to Dusk
8 16
The energy injected into the ring current is proportional to the interplanetary electric field VB z
, the amount of reconnecting magnetic flux carried to the magnetopause per unit time.
CR-1672

5
0
0
15
10
30 60 90
Clock Angle (degree)
120 150 180
Magnetic indices can be used as a proxy for the efficiency of reconnection.
Here the efficiency is shown versus the clock angle of the IMF where 0 is northward and 180 o southward. The variation is approximately sin
4
( θ/ 2).
CR-1676

10
5
0
20
15
-5
-10
0 2 4 6
Magnetosonic Mach #
8
For high Mach number the reconnection efficiency drops to zero.
10
CR-1678

15
10
5
0
-5
0 30 60
IMF Cone Angle (degree)
For low cone angles the subsolar reconnection efficiency drops to zero.
90
CR-1679

20
15
10
5
0
0.01
0.1
Upstream Ion Beta
1
For high solar wind beta the reconnection efficiency drops.
10
CR-1677

Where does Reconnection occur?
What does it do there?
(001) (010)
(00-1) (01-1)
Using a realistic field model for the magnetic field inside the magnetosphere and the gas dynamic convected fluid outside, one can find the places on the magnetopause where the fields are nearly antiparallel for different
IMF directions. This is where reconnection is most likely to occur.
CR-1041

Sun
Earth
Interplanetary Coronal Mass Ejections
- "Polar" field of sun predicts leading polarity
- Axial field lies along neutral line on source surface but direction
not predictable (as yet)
- Structures often appear to be force free (but is model unique?)
- Cross section is probably not cylindrical

dDst/dt = F(Ey) -a Dst o
Dst o
= Dst - b(P)
½
+ c
F(Ey) = d (Ey - 0.5)
(1)
(2)
Ey
≥
0.50 mV/m (3)
F(Ey) = 0 Ey < 0.50 mV/m (4) where a = 3.6 x 10
-5
s
-1
, b = 15.8 nT/nPa
½
, c = 20 nT; and d = 1.5 x 10
-3
nT/(mv-m
-1
-s).
•
Equation (1) states that the rate of change of the ring current as represented by the Dst index increases due to an energy coupling function F(Ey), and decreases by a fixed percentage each minute because of loss processes
•
Equation (2) states that the observed Dst index consists of a ring current contribution, Dst o
, and magnetopause current proportional to the square root of the dynamic pressure of the solar wind
•
The parameter, c, accounts for the fact that the Dst baseline has been chosen to be zero for a typical solar wind pressure, not for zero pressure
•
Equation (3) and (4) are the energy coupling functions for southward and northward interplanetary magnetic fields

0
-40
10
0
-10
0
AU
AL
-2000
What geomagnetic activity responds to what solar wind input?
AE roughly the same for weak IEF
oscillating IEF
strong IEF
Ring current responds to strong IEF
20
Wind Time Delay 21m
10
40
-100
-200
20 22
September 24
0 2
Universal Time
4 6
September 25, 1998
8

-160
0
-160
0
-160
0
-160
0
-160
122
0
-160
0
-160
0
-160
0
-160
0
-160
0
127 132 137
Universal Time
142
28 Sep 78
25 Oct 78
21 Nov 78
18 Dec 78
14 Jan 79
10 Feb 79
09 Mar 79
05 Apr 79
02 May 79
147
29 May 79
The Burton formula is not perfect but does well in predicting Dst over a wide range of solar wind parameters.
CR-1680

1200
800
400
0
200
100
0
-5
September 24-25, 1998
0 5
1200
800
400
10
0
200
150
100
50
15
0
-10
Vx x Bz (mV/m)
0
May 2-5, 1998
10 20
When the interplanetary electric field increases the potential drop does not follow it linearly if the IEF is large; neither does the Joule heating.
CR-1478

600
400
200
0
120
80
40
0
-10
January 9-11, 1997 October 18-20, 1995
600
400
200
0
120
80
40
10
0
-10 0 0
Another pair of examples of the non-linearity of the polar ionosphere currents and the potential drop.
10
CR-1477

Substorm Model (ca 1973)
Solar
Wind
F
Day
F
PS
F
Lobe
M
C
R
Thin Exp
An early model of the driving of substorms by a southward turning of the interplanetary magnetic field. A delay of the onset of tail reconnection allows the magnetic flux in the tail to be built up.
CR-793

20
0
-20
-40
60
40
Current Sheet
-60
60 40 20 0 -20 -40
Distance Along Jupiter-Sun Line [Jovian Radii]
-60
Noon midnight meridian view of the Jovian magnetosphere.
CR.697

-8
16
0
Outward
Inward
8
0
South
North
4
0
With Rotation
Opposite Rotation
16
8
0
1200
A
1230
Universal Time
1300
June 17, 1997
CR.545
In the near tail of Jupiter sporadic reconnection occurs across the magnetodisk current sheet. The large overshoot in magnetic pressure suggests this process at Jupiter is much stronger than in the terrestrial magnetotail.

Solar
Wind
M
F
Day
F
NPS
F
Lobe
F
PM
F
DPS
R
D
R
N
S P N L
M
R
D
R
N
C
R
Thin Exp
0
0
Time
A recent model of substorms in the magnetotail that takes note of the existence of two neutral points. This allows two substorm onsets corresponding to the first initiation of reconnection of the near-Earth neutral point and to the time of which this reconnection region manages to reach the open field lines of the lobe. It also explains the triggering of substorms by northward IMF turning.
Figure 16
CR-1509

•
The solar wind dynamic and static pressures determine the zeroth order size and shape of the magnetosphere
•
Reconnection both opens the field lines between the solar wind and the magnetosphere and applies tangential stress that transfers magnetic flux and stores magnetic energy
•
The energy to power geomagnetic activity is derived from the mechanical energy flux of the solar wind not the Poynting flux. The
Poynting flux is the agent for transfer first to plasma accelerated at the subsolar magnetopause and also to transfer energy into the tail
•
The shock changes the plasma conditions at the subsolar magnetopause. Thus the cone angle of the IMF and the Mach number of the flow are important in determining the reconnection rate
•
The magnetosphere is a good half-wave rectifier of the IEF
•
Magnetospheric convection seems not to respond to temporal scales shorter than 20 minutes
•
The AE index maximizes at about 2000 nT. Other quantities such as the potential drop and the Joule dissipation also tend to saturate but may just have a long response time
•
ICMEs are very geoeffective because they have large IEFs, long time constants and low beta
•
The explosive phase of substorms can be explained both at Earth and
Jupiter by the reconnection point reaching a low density region where the Alfven velocity is large
•
Northward triggering of substorms can be explained in terms of the modulation of the rate of reconnection at the near Earth neutral point by the supply of plasma from the distant neutral point