The Earth’s Magnetosphere and its
Coupling with the Solar Wind
Stefan Eriksson
Contact: eriksson@lasp.colorado.edu
Magnetism is familiar to all of us, usually
from permanent magnets and compasses.
Iron filings are like mini-magnets, aligning
themselves with the field of the bar magnet
Magnetism is familiar to all of us, usually
from permanent magnets and compasses.
Magnetic lines of force (“magnetic field lines”) in such “dipole
fields” are directed from the magnetic “north pole” to the
magnetic “south pole”.
The Earth’s Magnetic Field
Earth has an intrinsic magnetic field, similar to that
produced by a bar magnet.
How are Magnetic Fields Generated?
The Danish professor Hans Christian Oersted
first discovered (1820) that an electric current
in a wire could deflect a compass needle.
Hans Christian Oersted
(1777-1851)
After hearing about Oersted’s findings, the
Frenchman Ampere firmly established (1820)
the relationship between electricity and
magnetism.
André-Marie Ampère
(1775-1836)
How are Magnetic Fields Generated?
An electric current (I) generates a magnetic field (B)
and this is the basis of Ampere’s Original Law:


  B  0 J
The “right-hand rule”.
The Sun
A “Plasma” Object with Dynamic Magnetic Fields
SOHO: LASCO C2
Plasma: The 4th State of Matter
solid (ice)
liquid (water)
gaseous (steam)
plasmaa conducting gas
Plasma: The 4th State of Matter
solid (ice)
liquid (water)
gaseous (steam)
plasma
A charged particle (q) will move at constant velocity (v) in a straight line
unless acted on by a force (F). In space, the most important forces for
charged particles arise from the presence of ambient electric (E) and
magnetic (B) fields:
• Electric fields (E) will accelerate particles in a direction along E:
F=qE (q: charge)
• Magnetic fields (B) will accelerate particles in a direction perpendicular
to the both B and their motion (a.k.a. Lorentz force):
F=q(v x B)
V
B
(positive charge q)
Plasma: The 4th State of Matter
solid (ice)
liquid (water)
gaseous (steam)
plasma
A charged particle (q) will move at constant velocity (v) in a straight line
unless acted on by a force (F). In space, the most important forces for
charged particles arise from the presence of ambient electric (E) and
magnetic (B) fields:
• Electric fields (E) will accelerate particles in a direction along E:
F=qE (q: charge)
• Magnetic fields (B) will accelerate particles in a direction perpendicular
to the both B and their motion (a.k.a. Lorentz force):
F=q(v x B)
Total force: F=q(E+v x B)
V
B
(positive charge q)
Space Plasma Particle Drift Motions
B
From the Lorentz force, F=q(v x B), we know that charged
particles gyrate in a circle around an axial magnetic field,
since the force acts perpendicular to its velocity.
The radius (R) of this circle is found from the balance of the
outward centrifugal force (F=mv2/R) with the inward Lorentz
force (F=qvB): R=mv/qB (a.k.a. Larmor radius)
Is this the only motion of space plasma particles?
How does the electric field effect the particle motion?
Plasma Drift Velocity due to Electric Field
dv
m
 q( E  v  B )
dt
v  v  v||
v  u   v gyro
du 
0
dt
0  E  u  B
u  E  B B 2
Equation of motion: F=ma
Look at motion perpendicular to B
and separate into average unknown
motion (u) and known gyromotion
Steady state: d/dt=0
Use cross-product with B, u.B=0
and two vector identities:
(1) a x b = - (b x a)
(2) a x (b x c) = b(a.c) - c(a.b)
B
u=ExB/B2
We may also expect this E x B drift from the following argument:
A positive ion will accelerate along E and decelerate opposite to E.
This results in a larger gyroradius R when motion is along E and a
smaller gyroradius R when motion is opposite to E.
NO large-scale currents result from this drift, why?
The total perpendicular motion in a homogeneous magnetic and
electric field consists of (1) gyration about the magnetic field and
(2) a transverse drift referred to as plasma convection.
The Sun and the Solar Wind
The sun is continually ejecting portions of its atmosphere into
interplanetary space in the form of a solar wind.
SOHO: LASCO C2
SOHO: LASCO C2
(enhanced analysis)
The solar wind is in the plasma state, and accelerates as it moves outward
from the sun. At the Earth, the solar wind speed is typically ~400 km/s, but
may exceed 1000 km/s during solar disturbances.
The Sun and the Solar Wind
The Sun has an intrinsic magnetic
field. The action of the solar wind is to
sweep the field out away from the sun
into space, where it forms the
Interplanetary Magnetic Field, or IMF.
Dipole magnetic field
Solar magnetic field
The plasma moves radially away
from the Sun which rotates with a
~27 day period. Since the IMF is
constrained by the plasma, the
simplest configuration has the
IMF in the form of a Parker spiral.
SOHO: LASCO C2 (enhanced)
Activity on the sun modifies this simple
Parker spiral picture, providing the IMF
with either a northward or southward
component relative to the ecliptic plane
of the Earth’s orbit.
IMF


  B  0 J
The “corrugated” Heliospheric Current
Sheet, a.k.a. the “Ballerina Skirt”
The Earth’s Magnetic Field
Like the Sun, Earth also has an intrinsic magnetic
field, similar to that produced by a bar magnet.
The Earth’s Magnetic Field
Like the Sun, Earth also has an intrinsic magnetic
field, similar to that produced by a bar magnet.
NOTE:
Geographic north
is geomagnetic
south (animation
incorrect)
Aerodynamic shock
The solar wind deforms the Earth’s dipole magnetic field, compressing the
dayside front field and sweeping the back antisunward in a comet-like shape.
The region of space that the Earth’s magnetic field carves out is the Earth’s
magnetosphere. The outermost boundary of this region is the magnetopause. A bow shock forms upstream of the magnetosphere similar to a bullet
in fluid dynamics (see example). The shocked solar wind flows around the
magnetosphere in the magnetosheath.


  B  0 J
From Ampere’s Law
we know that large-scale geomagnetic
currents form where B is rotating: magnetopause and central magnetotail.
Basic plasma and B-field parameters:
Density (cm-3)
Magnetic field
strength (nT)
Convection
speed (km/s)
2-5
2-5
400
Magnetosheath 20
20
200
Magnetotail
25
4
Solar Wind
0.01
Earth magnetic field strength at the poles (equator): 62000 (31000) nT
Analytical Bow Shock and Magnetopause
Geostationary orbit: 6.6 RE
GOES (USA)
Meteosat (Europe)
GMS (Japan)
INSAT (India)
e.t.c.
What force deflects the solar wind plasma around the Earth’s magnetosphere?
To understand this, we need to examine the forces that the plasma ions and
electrons generate as a collective “fluid”….
Forces on a plasma fluid volume element
due to B and E fields
dvi
mi
 qi ( E  vi  B )
dt
dve
me
 qe ( E  ve  B )
dt
ni qi  ne qe  0
  ni mi  ne me
u  ni mi vi  ne me ve  
j  ni qi vi  ne qe ve
Ion equation of motion
Electron eq. of motion
Plasma is quasi-neutral
over a “large volume”
i: ion
e: electron
Forces on a plasma fluid volume element
due to B and E fields
dv
m
 q( E  v  B )
dt
Particle equations of motion
du

 j  B  p
dt
Momentum “fluid” equation
  ni mi  ne me
u  ni mi vi  ne me ve  
j  ni qi vi  ne qe ve
The j x B force of the magnetopause current deflects “most”
of the solar wind plasma around the magnetosphere….
….but we know that some of the solar wind plasma leaks into
the magnetosphere. How can the plasma cross the Earth’s
protecting shield, the magnetic field?
Magnetic Reconnection
A process that in the
presence of inward flow:
• changes the field topology
by “breaking” and “mending”
individual field lines in a local
region.
• converts magnetic energy to
oppositely directed plasma jets.
Example of inward flow: Solar
wind flow toward magnetopause.
Magnetic Reconnection
B
B
Simulated outward jets from inflowing plasma.
Magnetic Reconnection
B
U=ExB/B2
B
E
Simulated outward jets from inflowing plasma. Inflow speed U corresponds
to an electric field E directed into the plane. It can be shown that the
maximum outflow speed is the so-called Alfven speed:
V  B 
A
0
Magnetic Reconnection
B
U=ExB/B2
B
E
What happens to ions (large gyroradii) and electrons (small gyroradii)
as they drift closer to the reconnection X-line where the magnetic field
is weaker?
Magnetic Reconnection
B
+
_
B
Their gyroradii will get larger, such that ions “decouple” from
the local B field before the electrons. Electrons reach closer to
X-line before being carried away (ExB) by newly reconnected
fields.
Magnetic Reconnection
B
EH
+
_
B
An inward directed electric field (EH) is set up. We refer to it
as the Hall electric field.
Magnetic Reconnection
B
+
_
BH
B
Current loops also develop near the X-line. We refer to them as Hall
currents (JH). The corresponding magnetic field from the right-hand
rule (Ampere’s Law) is referred to as the Hall magnetic field (BH).
Magnetic Reconnection
in Earth’s Magnetosphere
IMF Bz<0
Southward IMF leads to dayside magnetic reconnection since the magnetic
fields on either side of the dayside magnetopause are mostly anti-parallel.
New “open” fields (one end in the IMF; the other at the Earth) are added to
the magnetotail B-field where eventually near-Earth reconnection results and
closes some of these “open” fields.
Magnetic Reconnection
in Earth’s Magnetosphere
Coronal Mass Ejection
Magnetic Reconnection
in Earth’s Magnetosphere
ICME with Magnetic Cloud Flux Rope
Magnetic Reconnection
in Earth’s Magnetosphere
IMF Bz>0
There is no/little dayside magnetic reconnection for
northward IMF since the magnetic fields on either
side of the dayside magnetopause are mostly parallel….
Magnetic Reconnection
in Earth’s Magnetosphere
….however, the lobe field tailward of the two cusps are oppositely directed
to the draped northward IMF and reconnection jets have been confirmed in
several reports.
Reconnection not only provides a means of getting energy and mass
from the solar wind into the magnetosphere. It also sets up a large-scale
convective motion within the magnetosphere.
Original sketch by Dungey (1961) of
global circulation driven by dayside
& nightside reconnection.
The 3-D Magnetosphere
Within the magnetosphere, there are a zoo
of distinct regions, each
with characteristic
plasma populations
affected by different
dynamical processes.
Regions: the plasmasphere
Plasmas flowing out from the Earth’s ionosphere form
a cold, dense population that corotates with the Earth.
The outer boundary of the
plasmasphere is the
plasmapause. It is defined by
the competing effects of Earth’s
corotation and magnetospheric
convection (ExB).
Convectively-driven plasmas
Co-rotating plasmas
Regions: the plasma sheet and lobes
Field lines which have reconnected at the magnetopause
are swept back into the tail, forming the northern and
southern lobes of the magnetotail.
Reconnection in the tail
creates a closed-field region
near the magnetic equator
called the central plasma
sheet. This region is
dominated by ExBconvection.
The boundary of the plasma sheet is the
Alfven layer, and is defined by the
competing effects of gradient-curvature
drift and magnetospheric convection.
Basic plasma and B-field parameters:
Density (cm-3)
Magnetic field
strength (nT)
Convection
speed (km/s)
Plasma mantle 1
25
5
Plasma sheet
0.01
10
4
Plasmasphere
1000
>100
<1
Regions: ring current
How is this current formed well within the closed field region?
Plasma Drift Velocity due to General Force F
(example gradient magnetic field)
u  E B B
2
E F q
u  F  B qB
v
2
What happens to an ion that ExB-convects Earthward
with velocity v toward a stronger magnetic field B?
Plasma Drift Velocity due to General Force F
(example gradient magnetic field)
u  E B B
2
E F q
u  F  B qB
2
F   B
u  B  B qB 2
Gyroradius is R=mv/qB. A larger field
strength B will result in smaller gyroradii
for both ions and electrons. Opposite
gyromotions due to charge q result in
opposite drift motion directions.
An electric current is generated due to
the gradB drift!
A magnetic field with a non-uniform strength in a direction
perpendicular to the local magnetic field results in the grad-B
drift.
On the other hand, a magnetic field that is non-uniform in a
direction parallel to the magnetic field will cause a particle to
experience a force away from the regions of strong magnetic
field:
Fm   || B
S. Elkington, Feb 22, 2009
Charged particle motion in Earth’s geomagnetic field
The Earth has an intrinsic magnetic field
that is roughly a dipole. Charged particles
moving under the influence of the Earth’s
magnetic field therefore execute three
distinct types of motion.
Characteristic
time scales:
• Gyro: ~ millisecond
• Bounce: ~ 0.1-1.0 s
• Drift: ~ 1-10 minutes
Regions: ring current
Earth
Drift motion in closed-field regions of the magnetosphere leads to currents in
space encircling the Earth. The ring current is formed by energetic electrons
and ions gradB-drifting across field lines in opposite directions (ions drift
westward) about the Earth.
The Dst index measures the energy content of the ring current by measuring
the magnetic perturbation at Earth caused by this current. Negative
excursions in Dst characterize geomagnetic storms.
Regions: the Van Allen Radiation Belts
The high-energy component of the
ring current forms the radiation
belts. These are comprised of
relativistic electrons and protons,
with MeV energies (as opposed to
the keV ring current populations).




Discovered by James Van Allen in
1958 via a Geiger counter on
Explorer I.
Trapped electrons and ions
drifting in orbits encircling Earth.
Two spatial populations: inner and
outer zones.
Energies from ~200 keV to >
several MeV.
Regions: the polar cap
The polar cap defines the
ionospheric separatrix between
the “open” and “closed” field
lines of the magnetosphere.
It may be seen in terms of
ionospheric currents, electric
fields, and plasma flows.
Particles are accelerated and
precipitate at the edge of the
polar cap where they form the
auroral oval.
V=ExB/B2
SUN
High-latitude electric field pattern.
To the Sun
Statistical high-latitude field-aligned current pattern.
To the Sun
Magnetic storms and auroral activity
As reconnection proceeds at the magnetopause,
more of the magnetospheric field lines become
“open”. The polar cap increases its size, and the
auroral oval is driven to more southern latitudes.
Aurorae
‘Space Weather’
Discharge damage to spacecraft
Power grids, transformers
Polar airline routes
Polar Airline
Routes
P
ol
arP
1 ol
ar P
ol
aPol
r ar 4
3
Hon 2
g
Kon
g
No
Radiorth
Blackout
Pol
During
e Events
Particle
C
hi
c
a
g
o
Hazards to human
activity in space
Growth phase:
~1-2 hours
Geomagnetic substorms
In contrast to the simple picture of steady
reconnection and convection, sometimes
energy is stored in the tail and then released
episodically. Such events are known as
substorms.
Expansion phase:
few minuts
Growth phase: Energy is stored, and the tail
becomes very stretched. The plasma sheet
begins to thin.
Expansion phase: Field lines reconnect at
the near-Earth neutral line (NENL) and
release the energy stored in the tail.
Energy flows away from the reconnection site.
Field lines near Earth go from stretched to
dipole-like, and particles are injected from the
reconnection site both down the tail and into
the inner magnetosphere.
Summary
• The sun expels its atmosphere and fields in the form of a solar wind & IMF
• Earth’s intrinsic magnetic field carves out a cavity in the solar wind known
as the magnetosphere:
• Compressed sunward, stretched antisunward
• Reconnects with the solar wind IMF
• Various processes and particle populations define fundamental regions of
the magnetosphere:
• Bow shock and magnetopause
• Magnetotail lobes and plasma sheet
• Plasmasphere
• Ring current and radiation belts
• The solar wind & IMF can cause dynamic activity in the magnetosphere:
• Enhanced convection, substorms, storms
• Auroral activity
• Plasmasphere erosion
• Radiation belts
• Space Weather!
Magnetopause Reconnection
Example Observations
Lobe Reconnection Event
Cluster C1
Cluster C3
The Sun
IMF
Plasma Jets at Earth’s Magnetopause
Observed by Two Satellites
magnetosphere
cusp
magnetosheath
IMF
Northward IMF MHD Simulation
XZ GSM Plane at 1900 UT
Solar wind
magnetosheath
magnetosphere
Bow Shock
Northward IMF MHD Simulation
XZ GSM Plane at 1900 UT
Solar wind
magnetosheath
magnetosphere
Bow Shock
High-Latitude Electrodynamics
Example Observations During Storm
TIMED/GUVI
TIMED/GUVI
TIMED/GUVI
To the Sun
SUN
E’=E+VxB (Galilean transform. from K’ (solar wind) at V to K (Earth))
E’=0 (no electric field in highly conducting solar wind)
E=-VxB