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Lecture 9
Solar Wind-Magnetosphere
Interaction
Structure of the Magnetosphere
Solar Wind-Magnetosphere Interaction:
Reconnection and IMF Dependence
The Magnetosphere
The Magnetotail - Noon-Midnight View
The Magnetosphere
The Magnetotail
The Magnetosphere
The Magnetotail
• The magnetotail is the region of the magnetosphere that stretches away
from the Sun behind the Earth.
• It acts as a reservoir for plasma and energy. Energy and plasma from
the tail are released into the inner magnetosphere a periodically during
magnetospheric substorms.
• A current sheet lies in the middle of the tail and separates it into two
regions called the lobes.
– The magnetic field in the north (south)lobe is directed away from (toward)
the Earth.
– The magnetic field strength is typically ~20 nT.
– Plasma densities are low (<0.1 cm-3). Very few particles in the 5-50keV
range. Cool ions observed flowing away from the Earth with ionospheric
composition. The tail lobes normally lie on “open” magnetic field lines.
The Magnetosphere
The Magnetotail-Cross Sectional View
•
•
•
•
•
•
Green hatching near the upper and lower tail
magnetopause is the polar mantle created by solar
wind particles entering the tail.
The clear areas are the tail lobes, regions of very
low plasma density due to los s to the solar wind
along open field lines
The two regions of blue hatching on the upper and
lower edges of the plasma sheet are the plasma
sheet boundary layer (psbl)
Red stippled areas on the left and right side of the
plasma sheet are the low latitude boundary layers
(llbl)
Red horizontal hatching just ins ide the llbl is
central plas ma sheet (cps) with return flow from
the llbl
Vertical yellow hatching in the center of the tail is
also cps with return flow from the dis tant x-line
The Magnetosphere
The Magnetotail - Structure
• The plasma mantle has a gradual transition from magnetosheath to
lobe plasma values.
– Flow is always tailward
– Flow speed, density and temperature all decrease away from the magnetopause .
• Ions in the plasma sheet boundary layer (PSBL) typically flow at 100s
of km/s parallel or antiparallel to the magnetic field.
– Frequently counterstreaming beams are observed: one flowing earthward and one
flowing tailward.
– Densities are typically 0.1 cm-3.
– The PSBL is thought to be on “closed” magnetic field lines.
• The central plasma sheet (CPS) consists of hot (kilovolt) particles that
have nearly symmetric velocity distributions.
– Typical densities are 0.1-1cm-3 with flow velocities that the small compared to the
ion thermal velocity (the electron temperature is 1/7 of the ion temperature).
– The CPS is usually on “closed” field lines but can be on “plasmoid” field lines .
The Magnetosphere
The Magnetotail - Structure Continued
• The low latitude boundary layer (LLBL) contains a mix of
magnetosheath and magnetospheric plasma.
– Plasma flows can be found in almost any direction but are
generally intermediate between the magnetosheath flow and
magnetospheric flows.
– The LLBL extends from the dayside just within the magnetopause
along the flanks of the magnetosphere forming a boundary
between the plasma sheet and the magnetosheath.
• Note there is a region in the tail where the plasma mantle,
PSBL and LLBL all come together.
• The origins of the plasma mantle and the plasma sheet
boundary layer are clear but the origin of the low latitude
boundary layer is less clear.
The Magnetosphere
The Magnetotail - Typical Plasma and Field Parameters
Magnetosheath
n (cm-3)
Ti (eV)
Te(eV)
B (nT)

8
150
25
15
2.5
Tail Lobe
0.01
300
50
20
3x10-3
PlasmaSheet
Boundary
Layer
0.1
1000
150
20
10-1
Central
Plasma
Sheet
0.3
4200
600
10
6
The Magnetosphere
Reconnection
Z
X
The Magnetosphere
Reconnection
• As long as frozen in flux holds plasmas can mix along flux tubes but
not across them.
– When two plasma regimes interact a thin boundary will separate the
plasma
– The magnetic field on either side of the boundary will be tangential to the
boundary (e.g. a current sheet forms).
• If the conductivity is finite and there is no flow Faraday’s law and
Ampere’s law give a diffusion equation 
2B
B
t

1
0
x
z 2
– Magnetic field diffuses down the field gradient toward the central plane
where it annihilates with oppositely directed flux diffusing from the other
side.
– This reduces the field gradient and the whole process stops but not until
magnetic field energy has been converted into heat via Joule heating (the
resulting pressure increase is what is needed to balance the decrease in
magnetic field pressure).
The Magnetosphere
Reconnection Continued
• For the process to continue flow must transport magnetic
flux toward the boundary at the rate at which it is being
annihilated.
– An electric field in the Ey ( E y  u z Bx) direction will provide this
in flow.
– In the center of the current sheet B=0 and Ohm’s law gives E y  j y 
– If the current sheet has a thickness 2l Ampere’s law gives j y  Bz  0l
– Thus the current sheet thickness adjusts to produce a balance
between diffusion and convection. This means we have very thin
current sheets.
– There is no way for the plasma to escape this system. If the
diffusion is limited in extent then flows can move the plasma out
through the sides.
The Magnetosphere
Reconnection Continued
• When the diffusion is limited in space annihilation is
replaced by reconnection
– Field lines flow into the diffusion region from the top and bottom
– Instead of being annihilated the field lines move out the sides.
– In the process they are “cut” and “reconnected” to different
partners.
– Plasma originally on different flux tubes, coming from different
places finds itself on a single flux tube in violation of frozen in
flux.
– The boundary which originally had Bx only now has Bz as well.
• Reconnection allows previously unconnected regions to
exchange plasma and hence mass, energy and momentum.
– Although MHD breaks down in the diffusion region, plasma is
accelerated in the convection region where MHD is still valid.
The Magnetosphere
Reconnection
• Acceleration due to slow shocks
– Emanating from the diffusion region are four shock waves
indicated by dashed lines (labeled separatrix).
– At the shocks the magnetic field and flow change abruptly.
• The magnetic field strength decreases
• The flow speed increase but the normal flow decreases.
 
• These structures are current sheets. The flow is accelerated by the J  B
force.
The Magnetosphere
Reconnection
• By the 1950’s it was realized that plasma flows observed
in the polar and auroral ionospheres must be driven by
magnetospheric flows.
– Flow in the polar regions was from noon toward midnight.
– Return flow toward the Sun was at somewhat lower latitudes.
– This flow pattern is called magnetospheric convection.
• If all flux tubes remained within the magnetosphere then
the flow pattern is like that in a falling rain drop caused by
viscous effects.
• Dungey in 1961 showed that if magnetic field lines
reconnected in front of the magnetosphere the required
pattern would result.
The Magnetosphere
Reconnection
•
•
•
•
When IMF Bz driven by the solar wind flow against the dayside
magnetopause is southward
reconnection occurs between field
lines 1 (closed with both ends at the
Earth) and the IMF field line 1’
– This forms two new field lines
with one end at the Earth and one
end in the solar wind (called open).
– The solar wind will pull its end


tailward ( E  usw  Bsw)
In the ionosphere this will drive
flow tailward as observed.
If this process continued
indefinitely without returning some
flux the Earth’s field would be lost.
Another neutral line is needed in
the tail.
The Magnetosphere
Reconnection Continued
• At the tail reconnection site (called an x-line) the lobe field lines (5 and
5’) reconnect at postion (66’) to form new closed field lines 7 and
new IMF field lines (7’).
• The new IMF field line 7’ is distorted and stressed and moves tailward.
• The new closed field line 7 is stressed and moves earthward.
• The flow circuit is finally closed when the newly closed field lines
flow around either the dawn or dusk flanks of the magnetosphere to the
dayside.
• The insert shows the flow pattern in the ionosphere that results.
• This flow pattern is highly simplified. Magnetospheric physics is the
attempt to understand the dynamics and transport associated with this
flow.
The Magnetosphere
Reconnection Continued
• The electric field across the magnetosphere
– The process of reconnection causes plasma to flow in the
magnetosphere and therefore creates an electric field

 
E  u  B
E   

 u PC BPC
2 RPC
where RPC radius of the polar cap, uPC is the plasma flow speed
and BPC is magnetic field strength in the polar cap. For typical
ionospheric parameters   53. kV
– The solar wind electric field across a distance equal to one
diameter of the tail (50RE) is about 640 kV. Thus about 10% of the
flux that impacts the magnetosphere interacts with it. The rest goes
around the sides of the magnetosphere.
The Magnetosphere
•
The Plasma Mantle
The plasma mantle is populated by
a mixture of magnetosheath plasma
and ionospheric plasma.
– Magnetosheath plasma is thought
to enter along open field lines in
the “cusp”.
– Ionospheric plasma is thought to
flow upward from the ionosphere
in the “polar wind”
•
Reconnection is assumed to occur
at the nose of the magnetopause.
– Magnetosheath particles flow
along the newly opened field lines
– After mirroring near the Earth they
back up the field line joined by
lower energy ionospheric
particles.
– The field line moves tailward.
•
The velocity filter
– Lower energy particles move
slower and thus take longer to
reach a given distance down tail
– In this longer time the particles
will   farther from the
E  Bcreating a energy
boundary
gradient.
Mantle
Cusp
The Magnetosphere
The Plasma Sheet Boundary Layer
• What particles enter the region earthward of the x-line?
– Time for a particle to move down the field line to the x-line t  Lx v
where LX is the length of the field line and v is the parallel velocity.
– Time for a particle to convect the radius of the tail (RT) in2electric field
corresponding to potential  and magnetic field BT t  2 RT BT

– The velocity of a particle that just reaches the x-line v c 
– The critical energy is
m  L
Wc   2 x
2  2 RT BT



 Lx
2 RT2 BT
2
– Particles entering the plasma sheet earthward of the x-line will gain an
energy W 
2eE y v


4E y
v Bz
W
and end up with energy
 4E y


W 
 1W
 v BZ



'
The Magnetosphere
The Plasma Sheet Boundary Layer
•
•
•
•
•
•
Particles ejected from the weak field
region near an x-line travel along field
lines towards the Earth
Particles closest to the separatrix have the
greatest energy because they have gyrated
around the weakest B and hence travel a
long way along the E field
Particles ejected closer to the Earth have
less energy because they gyrate in a
stronger field
This effect structures the Earthward beam
as shown in the diagram
At the Earth the particles are reflected by
the converging magnetic field and they
stream backwards through the inward
beam.
However the reflected particles are
displaced towards the neutral sheet by
electric field drift
•When the particles return to the plasma
sheet they are scattered by the sharp
kink in the field at the neutral sheet
forming a hot isotropic plasma
•
•
•
•
•
•
•
A neutral line in the distant magnetotail can lead
to the formation of particle beams.
 
Charged particles E  Bdrift across the plasma
sheet
If reconnection is occurring they cross the
separatrix and enter the plasma sheet

Inside the plasma sheet there is also an E field
If the radius of curvature of the field line at the
equator is small compared to a particle’s gyroradius it will begin serpentine motion across the
tail
This causes them to drift along the E field gaining
energy
Eventually they are ejected onto a closed field line
near the separatrix after gaining energy from the
motion across the electric field.
The Magnetosphere
The Low Latitude Boundary Layer
• The origin of the low latitude boundary layer (LLBL) is
less clear than the PSBL or the plasma mantle.
– During northward IMF the LLBL seems to be a simple mixture of
magnetospheric and magnetosheath plasma.
– For southward IMF some heating by reconnection may be
required.
– Reconnection may be important for both northward and southward
IMF (the neutral line moves to the cusp for northward IMF).
– Diffusion may also be important.
– Mechanisms other than reconnection (“viscous” interactions) may
account for 10% -20% of cross magnetosphere potential.
The Magnetosphere
Magnetopause Reconnection
•
Direct evidence of quasi-steady
reconnection at the magnetopause.
– ISEE 2 spacecraft was moving
from the magnetosphere to the
magnetosheath.
– The magnetic field in
magnetosheath had BZ<0 and By>0
– As the spacecraft passed through
the LLBL and the boundary there
were large dawnward flows and
antisunward flows
– The spacecraft made several
incursions into the LLBL which
gradually increased in length.
The Magnetotail
Magnetopause Reconnection
•
Field lines at the magnetopause for Bz<0 and By>0 (top).
– Magnetic tension will move the plasma along the direction given by the heavy
arrows.
– ISEE 2 was post noon so in the LLBL and magnetosheath the flow should be
northward, dawnward and antisunward as observed.
•
Reconnection at the magnetopause can also be “patchy” and localized in
space. The left figure shows a localized reconnection event called a flux
transfer event on the magnetopause.
The Magnetosphere
The Radiation Belts and Ring Current
• The radiation belts consist of particles that circle the Earth from about
1000km to a geocentric distance at the equator of about 6RE
• Because is it easy for particles to move along the magnetic field the
radiation belts are mainly field aligned features.
• The ring current is an azimuthal current circling the Earth at equatorial
distances of 3RE to 6RE.
• There is no clear distinction between the ring current particles and the
radiation belt particles however some people use ring current for those
particles contributing most to the current and radiation belt or “Van
Allen belts” for penetrating radiation.
– Penetrating radiation refers to particles that penetrate deeply into dense
materials.
– Electrons which contribute little to the ring current contribute importantly
to penetrating radiation.
• Both gradient and curvature
drift cause ions to move around
the Earth westward and
electrons eastward.
– The resulting ring of westward
current decreases the strength
of the northward magnetic
field at the surface of the
Earth.
•This figure shows fluxes of electrons and protons in the radiation belts.
•Above 1MeV there is a “slot” in the electron distribution
separating the inner belt from the outer belt.
•There is no corresponding slot for the protons.
The Magnetosphere
The Ring Current
• Assume all ring current particles are equatorially trapped at a distance
LRE. The gradient drift gives

3mu 2 L2
uG  
eˆ
2q BE RE
• If the total number of ring current particles of type t is Nt,, the total
mt ut2
3
L
current, I  is
I 
N

2 BE RE2

t  e ,i
t
• The total energy of ring current particles is
WRC   N t
I  
2
mt ut2
2
3LWRC
2 BE RE2
• For a ring of current Ampere’s law gives
  I
B  0 eˆz
2r
• The magnetic field perturbation at the center of the Earth due to drift
motion is
.

3 0WRC
Bdrift  
eˆz
4 BE RE3
The Magnetosphere
The Ring Current
• There also is a contribution from the gyrational motion of
the ring current particles about the magnetic field.

W
• Each particle has a magnetic moment    B L3 eˆz whereW  12 mu 2
E
is now the energy of each particle.
• This produces a field at the center of the Earth

 
0 W
ˆ
Bgyro  0
e

eˆ
z
3
3 z
4 LRE
4 B0 RE


• Since the contribution from the gyrational motion is
opposite to that from the gradient drift motion and since
depends only on the particle energy
BRC 
  0 WRC
eˆ
3 z
2 B0 RE
B
The Magnetosphere
The Ring Current
• The total energy in the Earth’s dipole magnetic field (  B 2 d 3 x 2 0 )
above the surface of the Earth is
Wmag 
• Therefore
4 2 3
BE RE
3 0

B
2 WRC

eˆz
BE
3 Wmag
• This is called the Dessler-Parker-Sckopke relationship
• The change in the magnetic field at the Earth is used a measure of the
amount of energy in the ring current. The parameter which gives the
change in B is the DST index and is a standard measure of magnetic
storms.
• After some corrections for the conductivity of the Earth we get that
100nT depression in B is equal to 2.8X1015J.
The Magnetosphere
The Plasmasphere and Alfven Layers
B0 RE3
• Assume that the Earth’s magnetic field is a dipole BE  3
r
where rRE is the equatorial distance and B0 is the equatorial field
strength of the Earth’s field.
• Assume equatorial mirroring particles (ie. 900 pitch angle) W   BE
 
• Plasma in the equatorial plane E  B drifts toward the Sun. This
corresponds to motion in a dawn-dusk electric field convection   E0 r sin 
• To this “cross magnetosphere” electric field we must add the effects of
the Earth’s rotation
– The corotation electric field causes particles
to rotate eastward with the

Earth
( corotation)  B
  E reˆ
2
B
where  E is the angular velocity of the Earth ( 2 24 h) and ê is
eastward.
3

B
R
d

0 E
corotation
– The corotation potential becomes
 E
dr
r2
The Magnetosphere
The Plasmasphere and Alfven Layers
  E B0 RE3
• The corotation potential becomes  corotation
r
• We can write all of the drifts of equatorial particles
in the following form

uD 
where
 eff   E0 r sin  

B   eff
B2
 B0 RE3
qr
3

 B0 RE3
E
r
The Magnetosphere
The Plasmasphere and Alfven Layers
• For zero energy particles (  0)
 eff   E0 r sin  
 E B0 RE3
r
• Contours of constant  eff
• Near the Earth the corotation
term dominates the effective
potential while far out in the tail
the convection potential
dominates.
• On the dusk side the two terms
fight each other and at one
point the velocity is zero.
• The solid line shows a
separatrix inside of which
plasma from the tail can’t enter.
• Cold particles that lie inside the
separatrix go continuously
around the Earth. They form the
plasmasphere. It is filled with
dense cold plasma from the
ionsophere.
The Magnetosphere
The Plasmasphere and Alfven Layers
•
For hot particles the effective potential becomes
 B0 RE3
hot
 eff   E0 sin  
qr 3
where we have assumed that the azimuthal motion of the particles is greater
than rotation.
–
–
–
–
In the far tail all particles move earthward
Near the Earth hot positive particles move westward.
Near the Earth hot negative particles move eastward.
Negative particles are closer (farther) to the Earth at dawn (dusk) than are
positive (negative) particles.
• The surface inside of which particles can’t penetrate is the Alfven
Layer.
•These images of the Earth’s plasmasphere was taken by the EUV
camera on the Image spacecraft on May 24, 2000.
•The 30.4nm emission from helium ions appears as a pale blue
cloud.
•The “bite out” in the lower right is caused by the Earth’s shadow.
•The emission at high latitudes is from aurora and is thought to be
caused by 53.9nm emission from atomic oxygen.
Northward IMF
The Magnetosphere
Field Aligned Currents
• There is one more major set of currents in magnetospherefield aligned or Birkeland currents
– The field aligned currents extend from the magnetosphere to the
ionosphere.
– Region 1 currents are at high latitudes and flow into the ionosphere
on the dawn side of the magnetosphere and out on the dusk side.
– Region 2 currents at lower latitudes flow into the ionosphere on the
dusk side and out on the dawn side.