Transcript 3 nT (mV.m

ESS 154/200C
Lecture 14
Solar Wind Magnetosphere Coupling II;
The Inner Magnetosphere I
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ESS 200C Space Plasma Physics
ESS 154 Solar Terrestrial Physics
M/W/F
10:00 – 11:15 AM
Geology 4677
Instructors:
C.T. Russell (Tel. x-53188; Office: Slichter 6869)
R.J. Strangeway (Tel. x-66247; Office: Slichter 6869)
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Date
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1/6
1/8
1/11
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1/13
1/15
1/20
1/22
1/25
1/27
1/29
2/1
2/3
2/5
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2/8
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2/12
2/17
2/19
2/26
2/29
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Topic
Instructor
A Brief History of Solar Terrestrial Physics
CTR
Upper Atmosphere / Ionosphere
CTR
The Sun: Core to Chromosphere
CTR
The Corona, Solar Cycle, Solar Activity
Coronal Mass Ejections, and Flares
CTR
The Solar Wind and Heliosphere, Part 1
CTR
The Solar Wind and Heliosphere, Part 2
CTR
Physics of Plasmas
RJS
MHD including Waves
RJS
Solar Wind Interactions: Magnetized Planets YM
Solar Wind Interactions: Unmagnetized Planets YM
Collisionless Shocks
CTR
Mid-Term
Solar Wind Magnetosphere Coupling I
CTR
Solar Wind Magnetosphere Coupling II;
The Inner Magnetosphere I
CTR
The Inner Magnetosphere II
CTR
Planetary Magnetospheres
CTR
The Auroral Ionosphere
RJS
Waves in Plasmas 1
RJS
Waves in Plasmas 2
RJS
Review
CTR/RJS
Final
Due
PS1
PS2
PS3
PS4
PS5
PS6
PS7
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.
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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
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coupling with the Earth’s magnetic field.
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.
d
Dst 0  F ( E )  aDst 0
dt
(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.
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Dst 0  Dst  b( P) 2  C
(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
F(E) = d(Ey-0.5) Ey>0.50 mV/m
(9.3)
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.
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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
VD  W B  B / qB3
(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
Bdrift 
 3  oW 
ez
3
4 R E Bo
(9.5)
The particle has a gyromotional current that produces a northward field at the center of
the Earth of
Bgyro 
 o W 
ez
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4 R E Bo
(9.6)
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The Physical Interpretation of Dst Index, cont.
Summing these two contributions, we get
 o W part 
(9.7)
B part 
ez
3
2 B0 R E
The total magnetic energy of the Earth’s dipole above the surface of the Earth is
Wmag 
4
2
3
Bo RE
3o
(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)
B part
2 W part

ez
Bo
3 Wmag
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
B(nT )  Wring / 2.8 1013 ( J )
(9.10)
Thus a -100 nT Dst index corresponds to a ring current energy of 2.8 x
1015
J.
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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.
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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)
B( z )  B tanh( z / h) xˆ
0
The plasma pressure is
p( z )  p0 sec h 2 ( z / h)
(9.12)
The total pressure becomes
B 2 ( z ) / 20  p  p 0
 B 2 / 20
(9.13)
Ampere’s law gives the current in the tail in the y-direction
  B  0 j y ( z)  ( B0 / h) sec h2 ( z / h) yˆ
(9.14)
The plasma pressure gradient is balanced by the J x B force
J  B  (b 2 / 0 h) sec h 2 ( z / h) tanh( z / h) zˆ
P 


d

po sec h 2 ( z / h) z  j  B
dz
(9.15)
(9.16)
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Particle Motion in Tail
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Near X-point
Alfven (1968) pointed out that there was a very simple selfconsistent 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
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The AE Index
Stations used for the AL and AU indices
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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.
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–
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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
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Phenomenological Model of Substorm
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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.
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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.
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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.
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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.
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Energy Transfer and Storage
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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.
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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
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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
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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.
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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.
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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.
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IMAGE and CRRES
Image He images of drainage plume and CRRES pass through drainage plume
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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.