The Physics of Planetary MagnetospheresUCL fnl2 Physics of Planetary... · The Physics of Planetary Magnetospheres ... thought about their properties quite as I have. ... matter most

The Physics of Planetary Magnetospheres

M. G. Kivelson UCLA

With thanks to colleagues and especially Xianzhe Jia and David Southwood

Kivelson 9/8/2008 Exploration of the Solar System, UCL, 2008 2

40 minutes. . .a luxury. . . but still. . .• Must pick and choose.• What to do?

– A bit of background:• The ideas we use are OLD.• The applications are relatively new.• Do not assume we have achieved the goal of

understanding magnetospheres.– Some idiosyncratic ways of thinking about aspects

of planetary (and other) magnetospheres and the physics they reveal. (“ Discussion of dirty linen”.)• I assume that the audience knows much about

the basics of magnetospheres, but may not have thought about their properties quite as I have.


][1( g)vvv+∇−=∇⋅+

∂∂ p

t ρContinuum mechanics

e.g., Euler’s equation (L. Euler, 1755)

Some important foundations Euler (1755)

1755

pt

∇−=∇⋅+∂∂

ρ1( )vvv


Some important foundations Maxwell (1861)

1755

1861

Maxwell (1861) equations grouped by Heaviside (1884)


Some important foundations Birkeland ~1900

1755

1861

~1900

Birkeland and field-aligned currents

Critical to understanding magnetosphere-

ionosphere coupling


Some important foundations Alfvén (1950)

1755

1822-45

1861

1950

MHD equations - Alfvén (1950)

Most magnetospheric processes can be understood to lowest order using the continuum

model that underlies MHD.


Some important foundations Space is not empty - radiation belts

1755

1822-45

1861

1950

1958

Discovery of radiation belts Van Allen (1958)

space is not empty


Some important foundations Reconnection

1755

1822-45

1861

1950

1958

1961 - 63

Magnetic reconnectionJ. W. Dungey (1961)

Breakdown of ideal MHD is required for this process but

only in a highly localized region. The boundary conditions are

still set by MHD!


Some important foundations Exploration of Earth’s magnetosphere

1755

1822-45

1861

1950

1958

1961

1961-Exploration of Earth’s (1961 ) and other (1973 )magnetospheres

Data are fundamental. Without data, theory becomes what Dessler once

named astro-geo-poetry.


Some important foundations Exploration of planetary magnetospheres

1755

1822-45

1861

1950

1958

1961

1961-

~1978-Computer simulations

A valuable tool but sometimes a false friend!


Magnetospheres can differ in many

ways

JUPITER

EARTH

GANYMEDE

Jupiter’s magnetosphere is ~100 times the scale of Earth’s. Saturn, Uranus and Neptune have magnetic fields and are embedded within magnetospheres of dimensions roughly 10 times larger than Earth’s. Ganymede’s is close to Mercury in scale.

But what does small mean?


Big vs. small: Spatial dimensions must be related to something of physical significance

• Critical for a magnetosphere are:– an external plasma, generally flowing and with kinetic

scale lengths such as Larmor radius

– a magnetized body with pmag at surface comparable to or greater than ptotal of the external plasma.

• Both internal and external parameters control structure.• Differences and similarities should be framed in terms

of dimensionless quantities. . . i.e., ratios.• E.g., one can characterize SIZE in a physical sense by

asking whether the magnetic pressure can stand off the external plasma pressure above the surface?

externalooo BpuB ]2/[2/ 222 μρμ +−≥

eremagnetosphits andbody centralofradius<<Lρ


.2

.222 ][]2/[2/ extextooo uBpuB ρμρμ ≈++≈

.2

.222 ][]2/[2/ extextooo uBpuB ρμρμ ≈++>>

.2

.222 ][]2/[2/ extextooo uBpuB ρμρμ ≈++>>• Earth

• Jupiter

• Ganymede

• Mercury

Small and big in terms of standoff

.2

.222 ]2/[]2/[2/ extoextooo BBpuB μμρμ ≈++>

SMALL!

very BIG

rather SMALL

BIG

Ganymede’s magnetopause lies at ~2 RG, but Mercury barely stands off the external plasma above its surface.

What is the Mach number? (again dimensionless!) Is there a bow shock?

• For Mercury, Earth, Jupiter and the other gas giants

– implies Mach numbers >>1. Bow shocks form and slow the flow to below the fast magnetosonic speed.

– In the magnetosheath:• near the nose, the flow

slows further• around the flanks,

the flow reaccelerates.• For Ganymede:

– implies Mach numbers <1. No upstream shock. Spreiter et al. [1966]

]2/[][ .2

.2

extoext Bpu μρ +>>

.2

.

.2

.2

]2/[][

]2/[][

extoext

extoext

Bp

Bu

μ

μρ

<<

<<


Mercury/Ganymede:topology is the same despite

greatly different forms• Closed field lines (here at low

latitudes both for Ganymede and Mercury).

• Open field lines linked to polar cap again found in both cases but the geometry differs– bent back into bullet shape at

Mercury and other planetary magnetospheres

– rising in a cylindrical shape for Ganymede

• We will return to a way of thinking about this difference.


Many aspects of magnetospheric

structure and dynamics can be understood using

concepts of MHD

• Useful tools include: pressure balance, MHD waves. No E||but field-aligned currents.

• Kinetic processes contribute (reconnection, diffusion, interchange, E||), but the boundary conditions that control those processes are established by MHD conditions.

• MHD discontinuity (tangential, rotational) and wave analysis give insight into the physics of the system.– The basic wave excitations

are illustrated to the left.– Only the shear Alfvén wave

carries a field-aligned component of the current!


External boundariesas MHD waves/discont.• Bow shock: a steepened fast

mode wave.• Magnetopause: partly a

tangential discontinuity and elsewhere, largely a rotational discontinuity.– Across the discontinuity,

• rotational: field lines connect the solar wind to the polar cap ionosphere with no sharp change of field or density magnitudes.

• tangential: pressure balances but both B and thermal pressure can change across boundary.

Kaymaz et al., 1994


Some internal boundaries• Plasma sheet boundary: Slow

mode front: ~ pressure balance with increase of thermal pressure balancing decrease of magnetic pressure.

• Polar cap boundary separates anti-solar (sunward) flows on open (closed) field lines. Mixed.

• Plasmapause: A different sort of boundary - a separatix bounding flow streamlines that encircle the planet (Brice, 1967).

• HOW IS COROTATIONAL FLOW IMPOSED?

• Source of plasma in the plasmasphere is at or close to the planet, i.e., the ionosphere at Earth or a close-in moon at the outer planets.

• At Earth the plasma diffuses out from ionosphere along a flux tube. In the absence of forces, outward moving plasma near the equator loses angular velocity (L = ρω2r = const.) When plasma diffuses upward along flux tube, its ωdecreases as r increases.– The plasma is frozen to the field - the field bends back

(considerably at Jupiter, negligibly at Earth)!– j generated: when the plasma slows, the field “curls”.

– Near the equator, jr (<0) exerts force to accelerate the slowed plasma), but j must be divergenceless, so FACs couple to ionosphere.

Why does plasmaspheric plasma ~corotatewith the planet? (Earth, Jupiter, Saturn)

rjBr oμϕϑ

ϑϑ=

∂∂ )(sin

sin1

radial current

projection of field lines


Current closes in ionosphere• There it exerts a force to decelerate ionospheric

rotation.• Normally the atmosphere can provide the momentum

needed to keep the ionosphere corotating with the surface, but it is also possible for the two ends to “compromise” so that rotation ends up being a bit slower than corotation along the entire flux tube.

• Please note that thisargument does not invokean E-field. In idealMHD, E = -vxB, and E is a consequence of the flows.

• May be convenient to thinkin terms of E but not necessary. FOR EARTH. Reverse

arrows for Jupiter/Saturn!


Planetary rotation:Is it important?

• The time to impose changes of external conditions on the magnetosphere is of order the time required to flow from the nose of the magnetosphere to the “distant neutral line”, or, let’s say roughly 4 to 10 times the distance to the nose of the magnetosphere.

• This time may be usefully compared with the rotation periods.

• Evidently rotational effects matter most at Jupiter.

• Rotation is absent at Ganymede Insignificant at Mercury.

No rotation

2-5 minutesGanymede

10 hours

16 to 40 hours

Jupiter

1 day10 to 30 min

Earth

59 days 0.5 to 1.5 min

Mercury

Rotation period

Flow time

Body

MHD and dynamics• A magnetosphere is a highly coupled system. When one end of a flux tube moves, the motion of the other end must correspond.

• Can discuss in terms of current circuits such as the substorm current wedge.– similar to the previous

argument.• The concept is useful but flawed.

– Plasma currents not confined to wires!

– Currents are defined by curl of B. (From j get B through integrodifferential equations such as Biot-Savart law.)

• More appropriately: distant parts of the system coupled by WAVES.– How does that work?


What happens, for example, when reconnection starts in the tail?

Some equatorial plasma moves earthward.The field near the equator bends, partly out of the plane of the drawing. Bend out of the plane Alfvénic perturbation.It drives j|| along the background field.At the ionosphere, the signal is partially transmitted/reflected (impedance mismatch).When the perturbation reaches the opposite ionosphere, it is partially transmitted and partially reflected.Transmitted signals produce j⊥ that sets ionosphere into equatorward motion.Signals stop when both ends move together.

On the ground, this is recorded as a high latitude Pi2 with decreasing period.


Analogous arguments apply to the perturbations induced by a conducting moon (e.g., Io)

• Interaction with the moon slows the flow near the equator.

• We usually show the perturbations (the Alfvén wing picture) projected into the prime meridian plane of the moon. Here the slowed flow makes the perturbation look compressional.

• But the field also bends outward from the prime meridian so that |B| does not change. ALFVÉNIC prtrbtn.

• The signal goes to the ionosphere, possibly partially reflected at the boundary of the Io torus.

• Mismatch of impedance leads to partial transmission and partial reflection. Multiple bounces produce nested decametric arcs.


Why does the front bounding the Alfvén wing tilt?

• Information is carried by Alfvén waves only along the background field in the plasma rest frame.

• But the plasma is in motion relative to the moon.• In the moon’s rest frame, the propagating wave is

found at an angle to the field given bytan α = v/vA

This angle defines the “Alfvén characteristics”

I shall show you that these characteristics also determine theloci of planetary magnetopauses!

B

vVA Front

α


In the solar wind, the Alfvén speed is << u.

(Take Bsw southward and MA ~6 then α = tan-1MA ~ 80º. )

The bullet-shaped magnetospheres of the planets in the segments with flux tubes connected to the solar wind arises because of the large Alfvén angle implied by high MA.Does that really work? Yes.


For Earth, Jupiter, etc., an open magnetopause is the locus of the “kink” propagating

away from the reconnection point into the solar wind, i.e., the Alfvén wing “front” previously introduced [see (a)].

(c) shows that the flux tubes bulge. Those bulges or bends are imposed by the j|| carried by Alfvén waves.


In Jupiter’s magnetosphere, u is small compared with the Alfvén speed.With MA ~ 0.7 near the center of the plasma torus, Ganymede’s Alfvén wing bends by ~35º. Simulation of X. Z. Jia, UCLA, 2008

ux and field lines in the XZ plane


Simulation: a valuable tool with pitfalls.We start with Ganymede!

• Ganymede’s magnetosphere provides a useful model for investigating simulations.– Upstream conditions are steady. One cannot argue

that discrepancies between observations and simulations arise from changes in upstream conditions.

– Small scale and constrained Alfvén speeds enables us to use small grid scales over large parts of the system.

– Reasonably good coverage in multiple Galileo flybys enables us to test success of predictions in different parts of the magnetosphere.

The “us” referred to above is Xianzhe Jia, UCLA graduate student.I thank him for his contributions.


Jia’s MHD model of Ganymede’s magnetosphere has enabled us to establish how sensitive

results are to: • effects of changing grid sizes• varied inner boundary conditions at

Ganymede’s ionosphere.• different ways of modeling the resistivity of

the plasma and the moon.

• Grid sizes were critical to getting the magnetopause location and spatial scale correctly. – Current density and current paths can be

seriously misrepresented if spatial grids are too large.


Ganymede’s magnetosphere

• Intrinsic magnetic field that creates a mini-magnetosphere.

• As at Io, interaction with magnetospheric plasma drives current towards and away from Jupiter.

• .

From Jia’s simulation, 2007Ganymede field lines and parallel current


+Y

Facing +X direction, flow into the page

this is a composite image that includes By >0 and By = 0 orientations

GanymedeHST STIS image135.6 nm10/30/1998

M. McGrathMOP 2007

X. Jia (UCLA)

Simulations are tested by comparison with in situ measurements from GLL passes and from aurora, etc. Here good agreement with HST images.


Ganymede intrinsic field magnetosphere aurora, latitudinal dependence of surface weathering

McGrath et al. Jupiter, 2004.

Khurana et al., 2007


Inner boundary condition• The simulation evolved from the version developed by J.

Linker to simulate Io.– Linker assumed v=0 at 1.05 RG

• For Ganymede, this assumption led to very odd behavior near the ionosphere (neither source nor sink) that propagated through the entire simulation.

• So Jia dropped that assumption and tried others to get solutions that I shall show you in the next slide.– First Jia tried constraining the tangential flow at the

ionosphere. You will see that this gives a totally non-physical solution.

– A more valid assumption is to require continuous vperp(to B). This means that the ionospheric part of the flux tube moves with the rest of it. Flow along B is allowed.

Vθ and Vφcontinuous

Vperp continuous

Very different flows over the polar cap and very different Vpc, but magnetic signatures change little on 6 GLL passes.


Vθ and Vφcontinuous

Vperp continuous

Magnetic signatures on GLL flybys for different inner b.c., little difference. Fit not fully satisfactory for either.

What other simulation parameters matter? Resistivity, both inside Ganymede and elsewhere matters.


Vperp continuous

Resistivity Using bc giving vperpcontinuous, change the resistivity of the interior of the moon.(small outside)

The reconnection rate changes markedly, as do the flow out of polar cap and the form and location of the magnetopause.

0.5 1 1.5 2 2.5 310

-4

10-3

10-2

10-1

100

101

r (RG)

η

diffeta13diffeta17

lower interior resistivity

higher interior resistivity


0.5 1 1.5 2 2.5 310

-4

10-3

10-2

10-1

100

101

r (RG)

η

diffeta13diffeta17

Vperp continuous Resistivity

This fit to B is almost too good to be true, but results from use of physically sensible b.c. Fits to other passes are as good.


What about simulations of Earth’s magnetosphere?

• Two runs for close to same conditions of sw, one from BATSRUS and one from GGCM.

• When the IMF turns southward, the dayside magnetosphere is eroded far more in the OpenGGCM(in which the resisitivity depends on the local current density) than in the BATSRUS code (which assumes ideal MHD wherein only numerical resistivity leads to reconnection).

• Also, the Vx component of flow in the ionosphere differs for the two simulations. Correspondingly, the cross polar cap potential in the OpenGGCM is much higher than the BATSRUS result.


Solar wind input (5 nT north, then 5 nT south)BATSRUS OpenGGCM


Northward BzBATSRUS: Ideal MHD

OpenGGCM: Current-dependent resistive MHD


Southward BzBATSRUS: Ideal MHD OpenGGCM: Current-dependent

resistive MHD


BATSRUS: Ideal MHD OpenGGCM: Current-dependent resistive MHD


Lesson• Put the physics into your simulations.

• See how the simulated magnetosphere works.

• But be very cautious about inferring magnetospheric structure and/or dynamics from the results of computer simulations.

• Anything you think you have learned must be tested by comparison with real data.


Turning to kinetic processes• Rotation modifies familiar processes. Assume rigid

corotation. then the momentum equation becomes

• In a rotating magnetosphere, gravitational acceleration may dominate at the ionospheric end of a flux tube and rotational acceleration at the other end. Can’t simplify!

• Spatial dimensions need to be considered. A 10 keV heavy ion (m =20 AMU) moving outward from Jupiter covers 1 RJ in 3 min. In the outer part of the magnetosphere, flux tube lengths are of order 100 RJ. A round trip bounce may require a full Jovian rotation period (10 hours). The 2nd adiabatic invariant is not conserved.

)]([/ˆ2)/(

rΩΩg

n

××−+−⋅+−∇=

δρμμσ o

co Bb

RbBpunm


Centrifugal acceleration and its effects on magnetospheres of rapidly rotating planets

• Interchange can become important.– Jupiter and Saturn have important sources of

heavy ions deep within the magnetosphere.– System energy is minimized by interchange of full

and depleted flux tubes. Leads to a fundamental instability that is an important transport mechanism.


Interchange conditions: The condition for instability is determined by relative flux tube content. . .but the rate of transport is limited by the resistance of the ionosphere because in interchange the entire flux tube must move as a unit.


Interchange event at Jupiter


Take away messages• Magnetospheres are complex systems with properties

resulting from interactions at scales from local to global, all highly coupled by field-aligned currents (carried by MHD waves). Thinking in terms of waves is useful.

• Spatial scales matter – because coupling is not instantaneous, – because the relevant forces may differ in regions

near and far from the planet, – because it takes finite times for particles to move

from one end of a field line to another.• Simulations are invaluable tools but we should use them

to identify what to look for in our data. We should not think that extracting results from simulations has proved anything.


I look forward to hearing other talks

• Please come share your interests with me during the next few days.

• I look forward to hearing about your work.

Documents

The Physics of Planetary MagnetospheresUCL fnl2 Physics of Planetary... · The Physics of Planetary Magnetospheres ... thought about their properties quite as I have. ... matter most