Outstanding Issues in MagnetosphereIonosphere Coupling: The Three-Dimensional
Ionosphere
R. J. Strangeway (UCLA)
GEM2000 Snowmass Workshop
Outline
M-I Coupling in Theory:
Electron and ion fluids
Field-aligned currents as mediators
Equivalence of loads
Can the ionosphere “drive” the magnetosphere? – Poynting flux
The “prompt” ionosphere
Does this theory work?
Dayside observations – Yes
Nightside observations – No
Problems posed by observations
Highly variable field-aligned current structure
Parallel electric fields
Variable ionospheric conductivity
Wave transients
The three-dimensional ionosphere
The Cowling conductivity conundrum
Conclusion
A complete understanding of M-I coupling requires the
inclusion of non-uniform ionospheric conductivity models –
both horizontally and vertically
Governing Equations of Magnetosphere-Ionosphere
Interactions
“Frozen-in” electron fluid:
E + Ui× B – j × B/ne = 0
Momentum equation:
ρ
DUi
= – ∇P + j × B – ρνin(Ui – Un)
Dt
Magnetosphere
Ionosphere
Maxwell’s Relations:
∇×B
∇× = µ 0 j
∇×E
∇× = – ∂B ∂t
Note: Displacement current is ignored. This is equivalent to ∇ • j = 0 , and assuming
wave speeds much less than the speed of light.
Role of Field-Aligned Current
The governing equations only included perpendicular currents. Field aligned
currents arise from
∇⊥ • j⊥ + ∇|| • j|| = 0 .
That is, field-aligned currents arise where there are shears in flows (for
example) that result in a divergence of j⊥. Consider a shear Alfvén wave, which
has field-aligned vorticity, and carries field-aligned current.
Thus field-aligned currents exist so as to couple the magnetospheric and
ionospheric plasmas. They flow as a consequence of the boundary conditions
imposed by the two plasma regimes.
Role of Poisson’s Equation
The governing equations did not include Poisson’s equation
∇ • E = ρq/ε0 .
This is because Poisson’s equation specifies ρ q given E, not the other way
around. It is dangerous to speak of currents moving charges, and the resultant
charge distribution making an electric field.
Example - Magnetospheric Velocity Shear
V
Magnetopause/
Magnetosphere
E
J
JxB
S
S
B
B
JxB
V
J
J
E
Ionosphere
Enhanced flow (V) at high altitude (e.g., at magnetopause because of reconnection).
Bending of field lines ( B). In northern hemisphere B opposite to V.
JxB force in magnetopause/magnetosphere, J opposite to E (= -VxB) - generator.
Field-aligned currents at edges of shear region.
Current closure requires J in ionosphere.
Current loop gives the B required by the field-line bending.
Poynting flux (S = Ex B/ 0) into the ionosphere.
Joule dissipation in ionosphere, JxB force overcomes the ionospheric drag.
Enhanced flow at high altitudes plus ionospheric drag leads to field-line bending,
and field-aligned currents. The larger the magnetospheric flow, and the higher the
ionospheric conductivity, the larger the field-aligned currents and the greater the
Poynting flux.
Equivalence of Loads
The frozen-in condition for the electron fluid, which is generally more
“robust” than for the ion fluid, demonstrates the direct equivalence between
electromagnetic and mechanical loads.
Frozen-in condition:
E + Ui× B – j × B/ne = 0
Therefore
j • E = Ui • (j × B)
Left-hand side is the rate at which electromagnetic energy is converted to
mechanical energy – positive for an electromagnetic load.
Right-hand side is the rate at which the magnetic field does work on the
plasma – positive for a mechanical load.
In the frame moving with the neutral atmosphere (primed variables)
U′i • (j × B) = ρν inU′i
2
In this frame the ionosphere must always be both a mechanical and
electromagnetic load.
Can the Ionosphere Appear to Drive the Magnetosphere?
Not in the mechanical sense, except for neutral winds.
What about electromagnetically? Can the ionosphere appear to energize
magnetospheric currents, yet still act as a mechanical load?
From the frozen-in condition for the electron fluid
j⊥ • E⊥ = Ui⊥ •
=
(B • ∇)B
µ0
– ∇|| • S||
2
– Ui⊥ • ∇ Β
2µ 0
2
– ∇⊥ • S⊥ – ∂ Β
∂t 2µ 0
∇|| • S|| < 0 when field-aligned Poynting flux flows into the ionosphere, as
occurs when the magnetosphere is a generator.
For Poynting flux to flow out of the ionosphere (as required for the
ionosphere to appear as an electromagnetic generator), there must be an excess of
magnetic flux transported into the region of outward Poynting flux. That is,
2
Ui⊥ • ∇ Β < 0
2µ 0
Note that this equation makes no assumptions concerning induction electric
fields, but it does imply that the ionosphere must be “compressible” for there to be
outward Poynting flux.
Region 1
Current Loop
RA
Ionospheric
Flow
RP
Rs
Rcx
RA
Region 2
Current Loop
Rcx
L
What About the “Prompt” Ionospheric Response?
The incompressibility of the ionosphere is invoked to explain the prompt
response of the entire polar ionosphere to changes in the IMF. [See Lockwood and
Cowley, 1999, and Ridley et al., 1999 for more discussion.] The implication is that
the polar ionosphere is driving the magnetosphere, since it appears to be moving en
masse before the nightside magnetosphere can “know” about changes on the
dayside.
However, the Poynting flux argument suggests that, because the ionosphere
is incompressible, there is insufficient divergence of the horizontal flux transport to
supply the upward Poynting flux to drive the magnetosphere.
The answer [Lockwood and Cowley, 1999] is the presence of induction
electric fields, which shield magnetospheric motion from the ionosphere.
Simulation results [Maynard et al., Spring AGU, 2000] support this idea.
The ionospheric convection pattern doesn’t change until the modified current
systems are fully established.
ISM Field-aligned Currents: BY Switch
Merging starts 2:15
2:12
2:16
2:20
2:28
2:32
∆E pattern established
2:24
Simulation time (hr:mm)
Field-Aligned Current Differences from 2:10: BY Switch
Hint of difference pattern
2:12
2:24
2:16
2:28
Simulation time (hr:mn)
Difference pattern grows
2:20
2:32
ISM Potential Patterns: BY Switch
Merging starts 2:15
2:12
2:16
2:20
∆E pattern established
2:24
2:28
Simulation time (hr:mm)
2:32
ISM Potential Differences from 2:10: BY Switch
Merging starts at 2:15
2:12
2:16
Hint of difference pattern
2:20
Difference pattern established
2:24
2:28
Simulation time (hr:mm)
2:32
Magnetosphere-Ionosphere Coupling – Dayside Observations
On the dayside, where ionospheric conductivity is uniform, the simple M-I
coupling picture is largely correct. Strong equivalence between E and δB:
δ B = µ 0ΣpE
i.e., δ B[nT] = 1.26 Σp[S] E [mV/m]
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Magnetosphere-Ionosphere Coupling – Nightside Observations
The large amount of structure in the nightside particle and field observations
make it difficult to relate local observations to processes occurring at either lower
or higher altitudes.
Data show:
Highly variable field-aligned current structure – current closure?
relationship between magnetospheric and ionospheric flows?
Particle acceleration – parallel electric fields
“pathological” distributions – strong wave-particle interactions, non
“Knight”-type current carriers
Alfvén wave transients – imperfect coupling, inertial Alfvén waves,
Alfvén wave resonator
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The Cowling Conductivity Conundrum
Cowling conductivity, originally applied to the equatorial ionosphere, is also
often applied to the auroral ionosphere.
In terms of height-integrated conductivity and current intensity:
J p = ΣpEx, J h = ΣhEx = –J p2
J p2 = ΣpEy2, J h2 = ΣhEy2 = Σ2hEx/Σp
Ey2 = ΣhEx/Σp
This can also be written in terms of conductivity and current density:
jp = σ pEx, jh = σ hEx = – jp2
jp2 = σ pEy2, jh2 = σ hEy2 = σ h2Ex/σ p
Ey2 = σ hEx/σ p
Assuming E x is uniform, then since σ h/ σp varies as a function of altitude, Ey2
∇× ≠ 0 .
varies as a function of altitude, and ∇×E
The variation of σh/ σp as a function of altitude means that j rotates with
respect to E (i.e., Hall currents become important). If the Hall conductivity is nonuniform horizontally, then either ∂B ∂t ≠ 0 , or the Hall currents must close in the
magnetosphere. How does the magnetosphere respond?
[E = 50 mV/m, H = 500 km, ∂B ∂t = 100 nT/s]
Conclusions
•
The mechanical (MHD, “B, v”) view of magnetosphereionosphere coupling works very well for uniformly conducting
ionospheres. (Note, vertical gradients don’t matter if the
conductivities are uniform horizontally.)
•
There is a strong equivalence between electromagnetic and
mechanical loads in the ionosphere. This equivalence can only
appear to break if there is a divergence of horizontal flux
transport (~ Poynting flux).
•
Understanding M-I coupling in the nightside ionosphere
requires not only the inclusion of parallel electric field effects,
which modify the horizontal structure of the conductivity, but
also the inclusion of vertical structure in the conductivity
models. (Hall current closure.)