1. ESS 154/200C Lecture 16 Planetary Magnetospheres

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. Radial Variation of the Solar Wind
The variation of density, temperature, and magnetic field strength with heliocentric distance results in changes in the Mach number of the flow relative to the planets and also the beta value of the plasma. The former affects the bow shock, magnetosheath plasma and reconnection at the magnetopause. The latter can affect plasma processes acting in the solar wind.
Two aspects of the shock and magnetosheath that are affected are the strength of the overshoot in the field strength downstream from the shock and the beta of the magnetosheath plasma that weakens the magnetic fields and produces magnetic turbulence.

4. Shock and Foreshock Geometry
The spiral angle of the magnetic field becomes ever more perpendicular to the solar direction and the flow velocity of the solar wind as the solar wind moves away from the Sun.
Statistically, the foreshock lies less in front of the nose region and more to either side.
The strong overshoot of the high Mach number outer planet shocks efficiently reflects ions and the foreshock regions have strong waves.
The upstream wave phenomena are otherwise similar to those seen at 1 AU.

5. Reconnection at the Magnetopause
Expected configuration of Mercury magnetosphere for three orientations of the interplanetary magnetic field
Voyager magnetic field observations at the Uranus magnetopause
Reconnection, once initiated, is controlled by the Alfvenic Mach number as the magnetic stresses are acting on the inertia of the plasma.
The Alfvenic Mach number is lowest at Mercury and highest at the outer planets.
At Mercury, we expect reconnection to be efficient and rapid.
At Uranus, the magnetosheath magnetic field is weak, and reconnection, slow.

6. Relative Sizes of Magnetospheres
The size of the magnetosphere is determined by the balance in pressure between the solar wind dynamic pressure and the pressure of the magnetosphere (plasma and magnetic).
The rapidly rotating magnetospheres, Jupiter and Saturn, have sources of plasma deep in the interior of the magnetosphere that become spun up to corotation speed by the ionosphere.
The centrifugal force of the corotating plasma pushes the magnetopause further out than expected from only the magnetic force balance.
Relative sizes of magnetospheres

7. Planetary Magnetodisks
Io and Enceladus provide neutral gas to the magnetospheres of Jupiter and Saturn that becomes ionized and accelerated to the rotational speed of the rest of the magnetospheric plasma which is connected to the ionosphere by the strong magnetic fields of the planets.
Angular momentum (and energy) are extracted from the planet and transferred to the equatorial plasma disk. Convection is dominated by these internal processes.
The plasma disk’s outward pressure pushes against the solar wind making the magnetosphere much larger than otherwise expected.
The flow times past the magnetosphere are much greater at Jupiter than Mercury.

8. The Compressibility of the Magnetosphere
The Earth’s magnetospheric pressure is dominated by the dipolar magnetic field which decreases in strength as r-3. Thus in a log-log plot of magnetopause position versus solar wind pressure, the slope is -1/6 or
The jovian (and saturnian) magnetic pressure falls off more slowly than this almost as -1/4 so the slope is larger in absolute terms. Thus the jovian and saturnian magnetospheres are more sensitive to solar wind pressure variations than the terrestrial magnetosphere.
Surprisingly, there is a dramatic bimodal nature to the compressibility. The dashed line shows the best bimodal fit to the magnetopause location. The unimodal (gaussian) fit does not fit the distribution at all well.

9. Mass Loading, Circulation, and Energization
The time-stationary momentum equation in the corotating frame balances the centrifugal force against the magnetic and pressure gradient forces which constitute the centripetal force.
We ignore gravity because the mass loading occurs well outside of synchronous orbit where gravity and centrifugal force balances.
For a thin current sheet in the equatorial plane, we can write the radial stress balance in terms of observable quantities. On the left is the product of mass density, the square of the angular rotation speed and the distance from the rotation axis. On the right is first the j x B force where the field is that crossing the current sheet and the current is obtained from the change in field from the top to the bottom of the current sheet. The second term is the pressure force which can be obtained from the radial variation of the magnetic pressure outside the sheet that is in balance with the pressure in the current sheet.

10. Steady-State Convection in Magnetodisk Magnetospheres
Analogous to the convection of plasma in the Earth’s magnetosphere driven by stresses external to the magnetosphere (notably reconnection with the IMF at the subsolar magnetopause), rapidly rotating magnetospheres with mass loading drive a convection system as well.
Reconnection in the terrestrial magnetosphere removes excess magnetic flux from the magnetotail.
Reconnection in the jovian and saturnian tails remove excess plasma from the magnetodisk and sends it down the tail in magnetized plasma islands.

11. Convection in a Rotating System
Near the mass-loading source, the plasma density builds until the radial stresses are sufficient to overcome the line-tying in the highly electrically conducting ionosphere. Then laden flux tubes slowly drift outward. Perhaps diffusion plays a role and perhaps interchange plays a role, but they are not essential to the convection system.
The unsigned radial magnetic flux out of the planet is fixed by the dynamo, thus any magnetic flux transported from the inner magnetosphere must ultimately return, but it has to dump its plasma load before it does so.
Reconnection allows the plasma (concentrated at the equator) to be released down the tail and emptied magnetic flux tubes to float against the outgoing tide of mass-loaded flux tubes.
In the outer magnetodisk, large regions of emptied flux tubes may move inward, but ultimately to return to the mass-loading region, flux tubes must like cylindrical bubbles become very narrow to buoyantly float inward.

12. Substorms in a Rapidly Rotating Mass-Loaded Magnetodisk
In the terrestrial magnetosphere, substorms produce flows and a more dipolar magnetic field and greatly reduce the magnetic flux in the tail. Angular momentum conservation is a minor issue.
In the jovian and saturnian tails, substorms are even more dramatic, producing large north-south field components and enhanced field strengths as the reconnected magnetic field piles up against the plasma sheet. The in-rushing and out-rushing magnetized plasma conserves angular momentum and twists the field in the longitudinal direction.
The overall magnetic flux in the tail does rise and fall as at Earth and plasmoids form, but most of the activity is associated with internal forcing as opposed to solar wind-driven stresses.

13. Radiation Belts
The large electric fields associated with the dynamics of the jovian and saturnian magnetospheres produce energetic charged particles that can drift inward in these dynamic systems and produce strong radiation belts. These radiation belts are stressful on our technological systems and make exploration difficult.
Uranus and Neptune have more benign radiation belts.

14. Ion-Cyclotron Wave Generation 1
The gases that escape from Io and Enceladus are neutral, but they soon are ionized by three processes:
Photo ionization
Impact ionization
Charge exchange
Once ionized, the charged particles feel the electric field of the flowing magnetized plasma around them and drift and gyrate with the corotation speed.
The resulting ion distribution is very anisotropic, a ring in velocity space, that is unstable to the growth of ion-cyclotron waves very close to the ion-cyclotron frequency because there is no motion along the magnetic field.
If an ion charge exchanges to produce a fast neutral, it can travel far across the magnetosphere, producing a magnetodisk far from the mass-loading body. The disk of fast neutrals can be identified by the ion-cyclotron waves associated with the re-ionization of the neutrals.
The difference between the Galileo and Voyager encounters with Io illustrates this.

15. Ion-Cyclotron Wave Generation 2
At Jupiter, the fast neutrals extend about 20 RIO outside of Io.
At Saturn, the fast neutrals extend about 50 RE outside of Enceladus.
The ion-cyclotron waves are near SO+2 and SO+ gyro frequencies at Io and near H2O+ ion-gyro frequencies near Enceladus.
The waves pulse in amplitude much like terrestrial ion-cyclotron waves (pearls).
They are strongly transverse to the magnetic field with a small compressional component.
There are also mirror-mode waves formed.

16. Ion-Cyclotron Wave Generation 3
The growth rate increases as the ring density increases.
The growth rate increases as the ring velocity increases.

17. Mirror-Mode Wave Generation
The same anisotropy (PT > PII) leads to mirror-mode wave growth as ion-cyclotron wave growth, but occasionally mirror-mode waves dominate even though the growth rate of the ion-cyclotron waves is greater.
While this is puzzling, it may occur because of the different directions of propagation of the waves. The ion-cyclotron waves move along the field line and damp. The mirror-mode waves do not propagate but just are carried outward in the equator.

18. Radio Wave Generation
Both electrons and ions can have unstable distributions. When electrons are unstable they generate waves at much higher frequencies than the ions.
Many of the phenomena seen in the outer planetary magnetospheres are very similar to those in the Earth’s magnetosphere.
However, in the jovian and saturnian magnetospheres, there are radio wave emissions associated with strong field-aligned currents that are much more intense than on Earth. There also are radio emissions from the radiation belts.

19. Atmosphereless Moon Plasma Interaction
Moons with electrically conducting interiors will exclude an external magnetic field when the field changes as it does when the Moon moves from the magnetosheath to the magnetotail. This enables one to determine the size of any highly electrically conducting core.
In a flowing plasma, the rocky or icy exterior of most moons absorbs the plasma.

20. Flowing Plasma Interactions with Atmospheres and Magnetic Fields
Magnetic field inferred at Ganymede
Ganymede has an internal magnetic field that is aligned with the external jovian field.
Perhaps it is a self-sustaining dynamo, but because of its alignment with the jovian field with little tilt, it may rather be an amplification of the jovian field.
Magnetic field during a Europa flyby
Europa has a conducting ocean and a thin atmosphere. The magnetized flowing plasma is diverted by Europa, leading here to a weak bow shock formation.

21. Summary
Each of the magnetized planets has a unique magnetosphere. They all contain dynamic, circulating or convecting plasma, but the different boundary conditions and differing energy sources produce different outcomes at each planet.
Mercury with a weak internal field in a strong solar wind magnetic field is dominated by the solar wind interaction.
Earth with a dense atmosphere and moderately strong magnetic field has an inner magnetosphere that is quiet with a plasmasphere and permanent radiation belt but with a dynamic outer magnetosphere and tail.
Jupiter in a high Mach number solar wind flow is less affected by the solar wind. The 1000 kg s-1 mass addition to the magnetosphere by Io dominates its magnetospheric dynamics.
Saturn is in an even higher Mach number flow and little affected by the solar wind. Its internal magnetic field is rotationally symmetric and its moon Enceladus deposits 200 kg s-1 into the magnetosphere causing a dynamic magnetosphere.
These differences are helpful in understanding better the underlying processes.