1. ESS 154/200C Lecture 13 Solar Wind Magnetosphere Coupling 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. Solar Wind-Magnetopause Coupling: Stress on the Magnetopause
Drag or tangential stress on the magnetopause transfers momentum to the magnetosphere from the solar wind.
Drag causes flows in the magnetosphere and can stretch the magnetosphere in the anti-solar direction.
Possible means of applying stress include:
Diffusive entry of flowing solar wind
Impulsive penetration of flux tubes
Solar wind induced waves on the boundary
Kelvin-Helmholtz induced waves on the boundary
Limitations on these processes
Gyroradius is small
Flux tubes in magnetosheath and magnetosphere cannot be completely parallel so they cannot penetrate
Need magnetospheric dissipation to induce flows
Most efficient process at Earth: Reconnection

4. The Three-Dimensional Reconnecting Magnetopause
Magnetic reconnection occurs between magnetic fields of opposite polarity or direction.
There is some debate on whether the fields have to be antiparallel at the reconnection point or can there be a “guide field.”
When the interplanetary field is antiparallel at the nose of the magnetosphere, connected magnetic field is carried over the poles and into the tail.
Currents flow across the dayside magnetopause and around the lobes of the tail. They also flow across the tail in the plasma sheet.
Plasma flowing sunward near the magnetopause on closed field lines will drive region 2 currents along field lines to the auroral ionosphere.
Plasma flowing anti-sunward across the poles can likewise drive currents in the polar cap.

5. The Reconnecting Tail
The field and plasma added to the tail will make larger tail lobes.
If the tail does not reconnect in the plasma sheet the tail grows fatter and flares. The tail then contains more magnetic energy.
Reconnection helps create a hot plasma sheet in the center of the tail.
The tail field geometry is much different than that on the dayside magnetopause.
The tail field is antiparallel except for the component across the current sheet.
This field normal to the sheet could go to zero at a point where reconnection could begin.
On the magnetopause, the normal component begins by being zero. Anti-parallel fields appear by the IMF rotating into anti-alignment.

6. How Can We Deduce the Merging Law? Proxy Measures for Reconnection
It is difficult to measure the rate of magnetic reconnection because the reconnection point moves and because the region reconnecting might be quite extensive.
Measuring flows in the polar cap are much better but need a large area to be monitored and the flows may not be perfectly recording reconnection.
Geomagnetic activity provides a good proxy measure. It integrates over all reconnection regions.
AM is a linear magnetic index available every three hours for many years based on mid-latitude magnetic records.
By subtracting winter daily variation from the summer daily variation, we find that there is a diurnal variation. Activity is greatest in the summer when the northern magnetic pole is pointing to the Sun and greatest in the winter when the south pole is pointed toward the Sun.
The activity varies with the size of the southward field but not the northward field.
The function sin4 (θ/2) is a good approximation to the angular dependence of reconnection. Since AM is an integral measure of “reconnection,” this sensitivity to IMF direction is a strong constraint on the reconnection “law.”

7. The Size of the Region of Anti-Parallel Fields
If we adopt a very strict reconnection law, that only antiparallel fields reconnect, then we can use the size of the antiparallel field region to predict the reconnection rate.
The four panels to the right show (in black) the antiparallel region where magnetosheath and magnetospheric fields would be antiparallel as a function of IMF direction (arrows).
The top two panels have small regions of reconnection. In addition, these regions have open field lines at the magnetopause and hence would not lead to tail flux build up.
If we make a more realistic model with a tilted dipole, we can calculate the variation of the antiparallel field region versus clock angle and tilt. The strongest reconnection should occur for 0° tilt. The least for high tilt.
We note that the maximum at each tilt angle occurs at an angle away from 180° (due south) equal to 180° – tilt angle.
Since the field strength appears to control geomagnetic activity, a high Mach number that causes high beta in the magnetosheath should reduce activity and it seems to do so.

8. The Observed Magnetopause: High-Beta Magnetosheath
To study magnetopause, it is best to use its natural coordinate system, LMN.
We use the field orientation along the field in the magnetosphere for L.
We use the normal to the magnetopause for N.
Can be cross product of magnetic fields on either side of magnetopause.
Can be minimum variance direction if field in sheath is moving.
On right is magnetopause crossing in B for high beta magnetosheath.

9. Physics of a Magnetic Field-Plasma Boundary
The non-reconnecting magnetopause is a pressure-balanced boundary with mainly plasma on one side and mainly field on the other side.
There is a current layer where the field is decreasing.
The current crossed into the magnetic field J x B, is a force equal to the pressure gradient in the plasma. It is not an additional force.

10. Magnetopause for Northward and Southward IMF
Northward IMF
Southward IMF
The magnetopause is very sensitive to the direction of the IMF.
For northward IMF, we see a plasma depletion layer where the magnetic field increases.
Inside the magnetosphere, there are weak plasma boundary layers.
For southward fields, we have strong flows at the boundary that signify reconnection.

11. Flux Transfer Events: Transient Reconnection
Magnetic reconnection is not always steady.
Sometimes, twisted magnetic tubes appear with hot particles in them that appear to be draining hot particles from the magnetosphere.
These have been called flux transfer events.

12. Flux Transfer Events: A Flux Rope Model
Here are two orthogonal sketches of an FTE.
It is thought to represent patchy reconnection.
The reconnection starts and stops.

13. Dungey’s Reconnecting Magnetosphere
The first real insight into how the IMF controls reconnection and the circulation of plasma came from J.W. Dungey in 1961.
He first examined southward IMF and proposed that reconnection occurred at the nose and convected plasma and field over the poles to the tail (bottom).
There, reconnection occurred in the center of the tail and returned plasma and field from an ‘open’ state (one foot on the Earth) to a ‘closed’ state with both feet on the Earth.
In 1963 (top), he examined northward reconnection which builds up closed flux on the dayside and causes flow across the polar cap toward the Sun.
This idea found strong opposition until the observations shown earlier from the ISEE 1 and 2 spacecraft.

14. Convection Driven by Reconnection
We can understand the plasma (and field) circulation better if we draw more field lines and number them.
The field lines ‘open’ the magnetospheric field (1), convect over the pole (2, 3, 4), and enter the tail (5), reconnect (6), and flow back to the dayside in the ‘closed’ state (7, 8, 9).
The atmosphere through its agent, the ionosphere, opposes this convection and acts to slow down the flow.
Field aligned currents and twisted flux tubes (right) transmit the stress needed to pull on the ionosphere and overcome its drag.

15. Region 1 and Region 2 Field-Aligned Currents
If we look back at the field-aligned currents in the northern hemisphere, we see a branch that closes in the magnetopause driven by the solar wind and branches at dawn and dusk driven by magnetospheric flows.
The currents are labeled R1 and R2, depending on whether they are poleward (R1) or equatorward (R2) of the auroral electrojects.
Looking down on the current systems (right) we see how the field-aligned currents map to the ionosphere.

16. Perturbations Over the Polar Cap
Spacecraft flying at low altitudes over the auroral and polar regions can measure these flows.
The left panel shows a set of measured flows.
The right-hand panel shows the inferred circulation pattern.

17. How the Electric Field in the Solar Wind Enters the Magnetosphere
We can supply the reconnected magnetic field with a small channel in the solar wind.
The convected magnetic flux VSW BS LSW represents a potential difference φSW.
This convected magnetic flux/electric potential drop is also seen in the magnetosphere in steady state, but in the magnetosphere, the scale size is LM and the magnetic field is stronger so the flow is slower.
The flow over the polar caps is only about 1 km/s.

18. A Current Sheet
The tail has as its center a field-reversing current sheet that is quite symmetric in the north-south direction.
If there were dissipation in the current sheet, the magnetic fields on either side of the sheet would slowly annihilate each other heating the plasma and causing a very weak electric field, Ey, as the tail lobes very slowly drifted toward each other.
This is far too slow a process to energize the solar flares on the Sun or the reconnection in the Earth’s magnetosphere.

19. The Point of Reconnection
Magnetic energy will eventually be annihilated at a plane current sheet but this is far too slow to explain dynamic processes at the Sun nor at the Earth.
To speed up the process, Sweet and Parker decided to limit diffusion to a small region called the diffusion region.
This still was too slow so H. Petschek added the role of standing waves radiating from the diffusion region.
This was still faster but not fast enough.
The process at the X-point is not collisional diffusion but collisionless processes.

20. The Effect of a Guide Field
There has been a lot of debate over whether reconnection is possible for fields that are not exactly antiparallel.
This component of the field that is not antiparallel has been called a guide field.
In the particle-in-a-cell kinetic code shown here, the reconnection begins almost immediately when there is no guide field, i.e. for anti-parallel fields. The onset takes much longer if there is a guide field.
Returning to reconnection at Earth’s magnetopause as revealed by geomagnetic activity, if guide field reconnection occurred, there would almost always be reconnection. However the field needs to be at least southward at the nose before significant reconnection occurs. There is a very strong argument in favor of antiparallel reconnection only.

21. The X-Point in a Fully Kinetic Code
Computers are becoming faster and faster all the time so it is now possible to do meaningful simulations with large numbers of ions and electrons in a particle-in-a-cell simulation.
In this simulation by Karimabadi et al. (2007), a region with strong electric field and flows is formed collisionlessly.
One of the reasons for the odd behavior of the reconnection region is the very large ratio of the mass of the proton to the mass of an electron.

22. Summary
In this lecture we have presented a simple model of how the energy flux in the solar wind couples into the terrestrial magnetosphere.
The plasma conditions in the solar wind are modified by the shock so the Mach number of the solar wind flow relative to the Earth is important.
The magnetic field strength and orientation are also important. Since the Earth’s rotation axis is tilted with respect to the solar direction, the Earth’s sensitivity to the IMF direction varies with time of day and time of year.
Strong coupling can occur during the passages of ICMEs past the Earth.