1. ESS 154/200C Lecture 14 Solar Wind Magnetosphere Coupling II; The Inner Magnetosphere I

2. Date Day Topic Instructor Due
ESS 200C Space Plasma Physics ESS 154 Solar Terrestrial Physics M/W/F 10:00 – 11:15 AM Geology Instructors: C.T. Russell (Tel. x-53188; Office: Slichter 6869) R.J. Strangeway (Tel. x-66247; Office: Slichter 6869)
Date Day Topic Instructor Due
1/4 M A Brief History of Solar Terrestrial Physics CTR
1/6 W Upper Atmosphere / Ionosphere CTR
1/8 F The Sun: Core to Chromosphere CTR
1/11 M The Corona, Solar Cycle, Solar Activity
Coronal Mass Ejections, and Flares CTR PS1
1/13 W The Solar Wind and Heliosphere, Part 1 CTR
1/15 F The Solar Wind and Heliosphere, Part 2 CTR
1/20 W Physics of Plasmas RJS PS2
1/22 F MHD including Waves RJS
1/25 M Solar Wind Interactions: Magnetized Planets YM PS3
1/27 W Solar Wind Interactions: Unmagnetized Planets YM
1/29 F Collisionless Shocks CTR
2/1 M Mid-Term PS4
2/3 W Solar Wind Magnetosphere Coupling I CTR
2/5 F Solar Wind Magnetosphere Coupling II;
The Inner Magnetosphere I CTR
2/8 M The Inner Magnetosphere II CTR PS5
2/10 W Planetary Magnetospheres CTR
2/12 F The Auroral Ionosphere RJS
2/17 W Waves in Plasmas 1 RJS PS6
2/19 F Waves in Plasmas 2 RJS
2/26 F Review CTR/RJS PS7
2/29 M Final

3. The Energy in the Magnetospheric Plasma: The Dst Index
One of the earliest geomagnetic disturbances discovered was the geomagnetic storm.
Often it begins with a sudden compression of the magnetic field on the surface of the Earth and is followed by a reduction of the magnetic field strength worldwide at low latitudes as recorded by stations such as those shown on the map.
This depression is known as a ring current build up and occurs when energy enters the magnetosphere from the solar wind.

4. Predicting the Ring Current Strength
We can predict the disturbances on the ground if we have measurements in the solar wind near the Earth.
The initial rise in the field strength is due to the increase in solar wind dynamic pressure.
The drop in the horizontal component of the Earth occurs when there is a strong steady interplanetary electric field that produces strong coupling with the Earth’s magnetic field.

5. Empirical Prediction of Dst Index
The rate of change of the energy in the ring current Dst0 is proportional to the energy added less the decay of that energy that is a fixed fraction of that energy.
(9.1)
To determine the energy content of the magnetosphere, we must correct Dst for the solar wind dynamic pressure compression of the magnetosphere plus an adjustment of the baseline.
(9.2)
The energy input is proportional to the convected southward magnetic field VBs above a threshold of 0.5 mVm and zero otherwise.
F(E) = 0 Ey <0.50 mV/m (9.3)
F(E) = d(Ey-0.5) Ey>0.50 mV/m
where d equals -1.5 x 10-3 nT (mV.m-1)-1.s-1
E = -VBz.10-3mV.m-1
P = 1.67x10-15 npV2 Nm-2
where np is measured in cm-3 and V in km.s-1
This simple algorithm predicts Dst quite well. Other more complicated approaches exist as well.

6. The Physical Interpretation of Dst Index
We can understand the Dst index as a measure of the energy content of the magnetospheric plasma by noting that the drift speed of magnetospheric particles is given by
(9.4)
Here ∇B is the gradient in the Earth’s field at the orbit of the particle and B its strength there and W┴ the perpendicular energy of the particle. If the particle is L RE from the center of the Earth, this drift produces at magnetic field at the center of the Earth of
(9.5)
The particle has a gyromotional current that produces a northward field at the center of the Earth of 
(9.6)

7. The Physical Interpretation of Dst Index, cont.
Summing these two contributions, we get
(9.7)
The total magnetic energy of the Earth’s dipole above the surface of the Earth is 
(9.8)
The ratio of the magnetic field due to the ring current to the magnetic field strength at the surface of the Earth is 
(9.9)
However, this field is predicted for the center of the Earth and the Earth’s conductivity shields the field from the interior. Accounting for this shielding, we find that
(9.10)
Thus a -100 nT Dst index corresponds to a ring current energy of 2.8 x 1015 J.

8. Geomagnetic Tail Particle Drift
There are two types of particle drifts across the tail in the dawn to dusk direction.
In the north, the magnetic field is toward the Earth and in the south away from the Earth as the diagram on the right shows.
In the tail lobes where the field is uniform, the particles gyrate and do not drift.
In the region where the field is weakening as the center of the tail is approached, proton drift to dawn and electrons drift to dusk in both the north and the south.
If the particles encounter the field reversal at the center of the current sheet, they can enter serpentine orbits that drift the opposite way with protons drifting from dawn to dusk and electrons from dusk to dawn.
It is this serpentine current that is in the sense to complete the solenoidal current around each of the tail lobes.

9. Harris Current Sheet
A Harris current sheet is a simple, self-consistent analytic model of a current sheet like that in the Earth’s tail. The x-direction is sunward. The z-direction is roughly to the north ecliptic pole. The magnetic field is a function of z.
(9.11)
The plasma pressure is
(9.12)
The total pressure becomes
(9.13)
 Ampere’s law gives the current in the tail in the y-direction
(9.14)
The plasma pressure gradient is balanced by the J x B force
(9.15)
(9.16)

10. Particle Motion in Tail
Near X-point
Alfven (1968) pointed out that there was a very simple self-consistent model of a magnetotail in which an electric field Ey from dawn to dusk in the tail caused cold plasma to drift to the current sheet from both sides.
Once in the current sheet the particles drifted in the current sheet in serpentine orbits and provide the current needed to reverse the field across the center of the tail.
Since there is no normal component of the magnetic field across the current sheet, this approximates conditions near the x-point.
Closer to the Earth there is a normal component. Particles that drift across the tail pick up energy. They can get ejected from the current sheet and become energized magnetospheric particles.
Closer than X-point

11. The AE Index
Stations used for the AL and AU indices
A substorm recorded in the AU and AL indices
Magnetic activity in the auroral zone can be quite independent of the ring current and not registered by the Dst index.
The field aligned currents are hard to detect from the ground. In fact a straight wire flowing into a conducting plate produces no magnetic field on the far side of the plate.
The currents flowing in the auroral ionosphere do produce significant magnetic fields on the surface of the Earth. Generally these fields are equatorward (negative) on the dawn side and poleward (positive) on the dusk side.
Three indices have been created using the dawn and dusk surface fields produced by the auroral currents.
AU – the maximum value of the auroral fields at many stations
AL – the minimum value of the auroral fields at many stations
AE – the maximum value minus the minimum value

12. Phenomenological Model of Substorm
The OGO 5 spacecraft carried out a systematic study of the Earth’s tail with comprehensive particles, plasma and magnetic field data.
The availability of solar wind magnetic field data allowed the cause of the substorm-associated changes in the tail to be determined.
Three phases of the substorm are seen in space and on the ground: growth, expansion and recovery.
The growth phase begins with reconnection at the nose, erosion of the magnetopause, and addition of magnetic flux to the tail.
The added flux makes the tail flare and the magnetic field in the near tail lobe is compressed and grows stronger. Energy is extracted from the solar wind plasma and stored in the magnetic field of the tail.
Eventually the stretched near-Earth plasma sheet reconnects, forming a magnetic island or plasmoid. It slowly grows until it eats its way out of the plasma sheet and into the lobes where the low plasma density allows it to reconnect flux rapidly.
At this point, the plasmoid can leave the tail and recovery can begin.

13. Magnetic Flux Inventory in a Substorm
We can understand the magnetospheric substorm by keeping an inventory of the magnetic field in three regions: the dayside closed magnetosphere, the tail lobe and the nightside closed magnetosphere or plasma sheet.
These transport rates control the amount of magnetic field in each region: the reconnection rate at the dayside magnetopause, M; the tail reconnection rate at the near-Earth neutral point, R; and the return rate between the closed field regions from the nightside to the dayside C.
When the IMF turns southward, M increases and the dayside flux drops; flux in the lobe increases until reconnection in the tail starts. The magnetic flux in the plasma sheet drops as it is convected sunward until reconnection in the tail begins and add flux faster than it can be taken away.

14. The Near Tail Current Sheet
In the region near the magnetic equator at midnight and just beyond synchronous orbit (6.7 RE), the magnetic field is very sensitive to solar wind conditions.
When dynamic pressure is high, the magnetosphere shrinks in size, the tail current moves inward and the minimum field is weak.
The field also weakens the stronger the convected southward magnetic flux is (i.e. east-west electric field in solar wind), but only slowly.
Southward fields are seldom seen here but very small fields can be observed before a substorm.

15. A Most Unfortunate Event: Galaxy 15
The past solar minimum was long and very inactive due to the low photospheric and polar magnetic fields but space weather mishaps can occur even at periods of low solar activity.
The Galaxy 15 spacecraft was a communications satellite in synchronous orbit and on April 5, 2010, it was approaching midnight and entered the shadow of the Earth as occurs near equinox for spacecraft at the Earth’s equator this time of year.
Coincidentally the solar wind dynamic pressure jumped and the interplanetary field turned strongly southward.
THEMIS saw the field in the tail lobe increase (0) and the magnetic field became more dipolar (1) at synchronous orbit.
Then the night time tail collapsed and the field at synchronous orbit became as strong as on the dayside when it is compressed by the solar wind.
Flows seen by THEMIS indicate that the night plasma pushed inward on the magnetosphere in an event that made the field much stronger than dipolar, i.e. overdipolarized it.
Possibly due to being in darkness and having energetic plasma surrounding it, the Galaxy 15 spacecraft lost its ability to accept commands but kept broadcasting its strong signals. Thus it became a rogue satellite for many months.

16. Energy Transfer and Storage
Given that reconnection occurs that links the solar and terrestrial fields, the energy transfer from the solar wind to the tail occurs quite naturally.
On the dayside, the field lines straighten and accelerate the solar wind plasma.
On the nightside, the field lines in the tail stretch and the solar wind plasma slows down. Hence, energy is removed from the flow and stored in the magnetic field in the tail.
The rate of energization can be calculated from the Poynting vector integrated over the surface of the tail.
The magnetic energy, flux and field strength of the tail increase.

17. Magnetospheric Potential Drop
A thin slab of solar wind plasma merges with the magnetospheric magnetic field at the magnetopause.
The potential drop across this slab of plasma in steady state appears across the polar cap and across the return flow in the equatorial plane.
Thus
-VswBsLsw = VpcBpcLpc
And
-VswBsLsw = VmBeqLm
If uniform Em = -VswBsLsw/Lm

18. Region-1 and -2 Currents Region-1 currents in at dawn, out at dusk
Region-2 currents out at dawn, in at dusk
Ionospheric closure currents provide j x B force to overcome drag from neutral atmosphere
Region-1/polar cap currents mainly driven by reconnection flows
Region-1/-2 and closure current provides return flow
Region-2 also shields flows from lower latitudes

19. Inner Magnetosphere Regions
From inside moving outward first is the cold (<1 ev) plasmasphere with density up to 104 cm-3.
Trapped radiation belt penetrates the plasmasphere and extends outside it.
The plasma sheet sits in the distant equatorial region and the center of the tail.

20. Formation of the Plasmasphere
The cold ionospheric plasma can move along field lines and fill them to a saturation density of about 10,000 cm-3.
The circulation of magnetospheric plasma stirred by reconnection will carry this plasma to the magnetopause if it is on open drift paths.
A sharp density boundary can form between the open and closed drift paths.
The high-density region is called the plasmasphere. Its boundary is called the plasmapause.

21. Plasmapause Evolution
Grebowksy [1970] explored how the zero energy Alfvén layer evolved as the convection electric field changed
The enhanced convection results in a “drainage plume” that convects to the dayside magnetopause
This approach, however, is flawed, because it does not consider the forces that are necessary to move the massive plasmasphere.

22. IMAGE and CRRES
Image He images of drainage plume and CRRES pass through drainage plume

23. Summary
We can measure the resultant energization of the magnetosphere with the Dst index.
Shorter scale storage and release events or substorms also occur after that more directly the auroral zones.
Space weather events can occur even at times of low solar activity.
The energy coupled into the magnetosphere through the connection of the terrestrial magnetic field to the solar wind transports the magnetospheric plasma in a process we call convection.
This variable transport produces a dynamic plasmasphere, the high-altitude extension of the ionosphere.
The more energetic the charged particles, the less they are affected by the electric fields associated with the convection pattern.