Chapter 6
Coupling between the ionosphere
and the magnetosphere
It’s fair to say that the ionosphere of the Earth at all latitudes is affected by the
magnetosphere and the space weather (whose origin is in the solar wind and in the
energetic particles and radiation from the Sun). Especially strong effect the space
weather has on the ionosphere of the high latitudes (auroral regions) and that of
the polar cap. This chapter is still under development in 2010 and will be extended
later to include e.g. a short summary of the solar wind (which should be familiar
to most of the students from course Avaruusfysiikan perusteet), magnetospheric
electric fields and some dynamical phenomena of coupling (auroral substorms etc.).
6.1
Magnetospheric topology
As seen above, the result of the high field-aligned conductivity is that electric fields
are mapped from the magnetosphere to the ionosphere. The magnetosphere is
largely variable; it responds actively to the properties of the solar wind and the
interplanetary magnetic field. These variations are also seen in the current systems
and electric fields of the ionosphere.
To first order the Earth’s magnetic field is that of a dipole whose axis is tilted with
respect to the spin axis of Earth by about 11◦ . However, since Earth is immersed
in the expanding atmosphere of Sun, called the solar wind, the Earth’s magnetic
field is confined in a cavity called the magnetosphere (Fig. 6.1). As the solar wind
is supersonic and super-Alfvénic at 1 AU, a bow shock forms upstream of Earth
(not shown in the figure). The solar wind is slowed and compressed before flowing
around the magnetopause. The dayside magnetic field is compressed and an extended
magnetic tail forms on the nightside.
The shape of the magnetosphere implies the presence of magnetospheric currents.
The magnetopause is formed by a current sheet that separates the solar wind magnetic field from the magnetospheric magnetic field. In order to produce a long tail,
current must flow from dawn to dusk side at the centre of the tail (Fig. 6.1). This is
known as the cross-tail current. At the center of the cross-tail current, the magnetic
119
120
CHAPTER 6. COUPLING
field revers direction, that is why it is called the neutral sheet. The cross-tail current
continues to a current flowing around the tail surface.
It is important to note, that the magnetic field lines connect different magnetospheric regions to different latitudes in the ionosphere. At low and middle latitudes
the field lines resemble dipole field lines and they are connected to a plasma region
called the plasmasphere, which contains cool dense plasma (Fig. 6.2). This region
has a high plasma content since the magnetic flux tubes fill from below with ionospheric plasma produced in the sunlit ionosphere (see section 3.11). The plasma
sheet contains less dense plasma than the plasmasphere, but the energies of electrons (typically 0.6 keV) and ions ( typically 4 keV) are much higher. Plasma sheet
is located on closed extended field lines and the plasma sheet particles carry the
cross-tail current. A relatively thin layer known as the plasma sheet boundary layer
(PSBL) is observed at the interface between the tail lobes and the plasma sheet.
The ionospheric mappings of both the plasma sheet and the PSBL form the main
part of the nightside auroral oval. In the PSBL, both the density and energy of
particles is less than in the plasma sheet.13The outermost pat of the magnetosphere
contain magnetic field lines that extend to hundreds of Re (Earth radius, 1 Re =
6370 km) tailward. These field lines are called open field lines. In the ionosphere,
the tail lobes correspond to regions known as polar caps. In the northern tail lobe,
the
field lines go toward Earth whereas in the southern tail lobe the field
1.3magnetic
M AGNETOSPHERE
lines point away from Earth.
The shape of the magnetosphere is caused by the interaction between the geoFigure
1.2field
shows
sketch
of the structure
of thefield
magnetosphere.
The
of wind
the
magnetic
andathe
interplanetary
magnetic
(IMF) carried
bysurface
the solar
magnetosphere,
the the
magnetopause
governed
by the magnetopause
currents,
also
(Fig.
6.3). Because
solar wind isis highly
conductive,
the interplanetary
magnetic
called
Chapman-Ferraro
on theofdayside.
Onwind
the nightside,
the an
magnetopause
field
Bsw
is carried withcurrents
the velocity
the solar
vsw so that
electric field
e
ob
Tail l
Pla
Cross-tail
current
sma
she
et
Ring current
Magnetopause
current
Figure 1.2. The most important currents systems in the Earth’s magnetosphere are the magneFigure 6.1: Magnetosphere of the Earth.
topause current, the cross-tail current in the middle of the magnetotail and the ring
current in the inner magnetosphere. Illustration by Teemu Mäkinen.
currents encircle the lobes of the magnetotail, where the magnetic field lines are open.
6.2. CURRENT SYSTEMS AND GLOBAL CONVECTION
121
Figure 6.2: Plasma regions of the magnetosphere in the noon-midnight meridian
plane.
Esw = −vsw × Bsw is created. When the interplanetary magnetic field has a southward component, the electric field has a direction from dawn to dusk. In this case
also the geomagnetic field lines are connected to the solar wind in the way shown
in Fig. 6.3. Then the electric field produced by the solar wind dynamo is mapped
along the magnetic field lines to polar regions.
The electric field driving the neutral sheet current is oriented from dawn to
dusk and the field inside the tail lobes has the same direction. This electric field is
mapped to the polar cap where its direction is from dawn to dusk. In the F region
the electric field causes plasma flow at a velocity E × B/B 2 , i.e. from the dayside
to the nightside over the polar cap. This plasma flow makes a return flow sunward
at latitudes corresponding roughly the auroral oval. The result is that the plasma
flow makes a double-cell convection pattern. This convection electric field (Ea Fig.
6.4) points in the auroral ovalnorthward in the evening sector and southward in the
morning sector.
6.2
Current systems and global convection
The electric fields in the polar F region are mapped downwards to the E region altitudes in the manner described in Section 5.7. There they drive currents and these
currents create magnetic fields which can be observed at the ground level. Magnetic observations can be used to calculate the equivalent current systems at high
latitudes. Since the equivalent currents are mainly of the Hall type, the equivalent
current flow is expected to be in the direction opposite to the F region plasma flow.
The quiet-time equivalent currents in the polar regions are called the Sqp (solar
quiet polar) system. From the plasma flow in Fig. 6.4 one would also expect a
double-cell structure. The cells in the true Sqp system are not aligned along the noonmidnight meridian. This is caused by geometry of the interplanetary magnetic field
and the the solar wind. The polar cap equivalent current system mainly depends on
122
CHAPTER 6. COUPLING
Bsw
Esw
bo
w
sh
oc
k
vsw
Esw = -vsw x Bsw
Bsw
magnetopause
solar wind
vsw
Bsw
Figure 6.3: Magnetospheric convection during southward IMF.
Figure 6.4: Plasma convection in the northern high latitude ionosphere and associated convection electric fields.
6.2. CURRENT SYSTEMS AND GLOBAL CONVECTION
123
Figure 6.5: Contours showing the equivalent currents for different orientations of
the IMF Bz and By components (Friis-Christensen et al., 1985).
124
CHAPTER 6. COUPLING
Figure 6.6: The IMAGE north-south chain of magnetograms measured in northern
Scandinavia.
the Bz component of the interplanetary magnetic field (the z axis points northwards
of the ecliptic plane). This is shown in Fig. 6.5. The orientation of the cells is twisted
by about 3 hours from the noon-midnight meridian. The currents are weak when
Bz > 0 and are greatly intensified when Bz gets negative values. This is associated
with the fact that merging of the interplanetary and magnetospheric electric fields
takes place when Bz < 0, i.e. when the IMF has a southward component. The effect
of the By component is smaller (the y axis points towards of the dusk side of the
Earth).
Fig. 6.6 shows observations from a chain of magnetometers, extending from
Bjørnøya in the Arctic ocean down to Pello in northern Finland. The X (northward) component of the geomagnetic field shows a similar behaviour at all sites. In
the afternoon and evening the magnetic disturbance in X shows a positive bay, but
after 20 UT (about 22:30 local time) a negative bay. The interpretation is that, in
the afternoon-evening sector, there is an eastward current causing the magnetic variation and, when the magnetic variation changes sign close to midnight, the current
direction turns westwards. If we assume that the magenetic disturbance is mainly
6.2. CURRENT SYSTEMS AND GLOBAL CONVECTION
125
Figure 6.7: Schematic figure of high-latitude currents (left) and plasma flow (right)
on the night side.
due to the Hall current, this would mean that the electric field is northward in the
afternoon and evening and southward around midnight and morning. This is in
agrement with the sketch in Fig. 6.4. The evening sector current is known as the
eastward electrojet (EEJ) and the morning sector current as the westward electrojet
(WEJ). The region between the two electrojets is called the Harang discontinuity
(HD).
Perpendicular to the eastward electrojet, a current flows northwards in the
evening sector. It is connected to a downward field-aligned current in the south and
to an upward field-aliged current in the north. In the morning sector the currents
flow in opposite directions.q A downward field-aligned current flows at the polar cap
boundary. It is divided into a current flowing over the polar cap and an equatorward
current flowing in the region of the westward electrojet. The equatorward current
is finally connected to an upward field-aligend.
The field-aligned at the poleward side of the electrojet are called Region 1 currents and those at the equator side are called Region 2 currents. Upward currents
are caused by electrons precipitating to the ionosphere from the magnetosphere. Energetic electrons produce ionisation which increases the conductivity and thus also
enhances the currents. Then conductivities are not horizontally homogeneous, and
therefore Pedersen currents also contribute to the electrojets and Hall currents are
partly connected to the field-aligend currents. Fig. 6.8 shows the average patterns of
the field-aligned currents measured by satellites when the interplanetary magnetic
field points southwards.
In reality the magnetosphere and the currents in the polar ionosphere are not stationary. The magnetosphere is not a passive circuit which transfers energy from solar
wind to high-latitude ionosphere. Actually the magnetosphere is a system which is
greatly activated when the interplanetary magnetic field turns southwards. Violent
126
CHAPTER 6. COUPLING
Figure 6.8: The average pattern of Region1/Region2 currents when the IMF is
southward. The cusp currents at high latitudes at noon depend highly on the IMF
By component (Iijima and Potemra, 1976).
changes, known as magnetospheric substorms, take place in the magnetosphere. In
the ionosphere, these changes are observed as magnetic and auroral substorms and
changes in the size of the polar cap. The energy released in the ionosphere during
substorms originates from the solar wind, but the magnetosphere has an active role
in storing the energy and releasing it in explosive bursts. The temporal changes in
substorms follow follow a certain pattern which we shall not discuss in detail here.
An essential feature in the substorm is that the cross-tail current disrupts par-
a)
b)
Figure 6.9: Disruption of the cross-tail current and formation of the substorm current
wedge as 3D (a) and 2D (b) presentation.
6.2. CURRENT SYSTEMS AND GLOBAL CONVECTION
127
Figure 6.10: Auroral images by the IMAGE satellite FUV instrument 14.7.2000
during the Bastille day storm.
tially and connects via field-aligned currents to the ionosphere. In the dawn side of
the tail, the current flows to the ionosphere, where it is connected to a strong westward current known as substorm electrojet. In the premidnight sector this current is
connected to an upward field-aligned current. The whole current system is known as
the substorm current wedge (Fig. 6.9). The same happens both in the northern and
southern hemispheres, i.e. field-aligned currents emerge from the cross-tail current
towards both hemispheres.
The substorm current system evolves with time. It starts within a narrow region
close to the midnight and typically expands toward west, east and poleward with
time, forming a substorm bulge. The whole area of the substorm bulge is filled with
particle precipitation from the magnetosphere to the ionosphere which increases
electron densities there and produces auroral luminosity. The western edge of the
auroral bulge is known as the westward travelling surge (WTS) and there the most
intense particle precipitation and upward current take place. Temporal evolution of
a substorm sequence measured by a polar orbiting IMAGE satellite is shown in Fig
6.10. The second panel shows an onset of a substorm, in this unusually disturbed
case not only in the night sector (upper part of the figure), but also in the day
sector. The third panel shows clearly the WTS and the auroral bulge. During the
course of the event, the bulge expands westward, toward dayside.
128
6.3
CHAPTER 6. COUPLING
Cowling channel model of auroral electrojets
The auroral oval (one in both hemispheres) is a region of higher conductance than
its surroundings. The auroral oval exists at all times, even during the northward
IMF, but is then much weaker and smaller in size. As Fig. 6.7 shows, the oval
is typically during southward IMF connected to field-aligned currents close to its
edges. Inside the oval, more narrow structures of enhanced precipitation exist, like
auroral arcs, which typically have their own current systems with both horisontal
and field-aligned currents.
When auroral precipitation takes place in the ionosphere, there are two basic
ways the ionosphere-magnetosphere system may behave. One is to generate enhanced currents, including field-aligned currents, and the other is to produce a
polarization electric field inside the high-conducting area. Let’s study the case of
high-conductance slab, which is restricted in the north-south direction (y), but extended in the east-west direction (x) in Fig. 6.11. The magnetic field is vertical.
For simplicity, let us assume that conductances are zero outside slab. If the electric
field in the slab has both the x and y components, the height-integrated horizontal
current in the slab is
Jx
Jy
!
=
ΣP
ΣH
− ΣH
ΣP
!
Ex
Ey
!
.
(6.1)
If we assume that no field-aligned currents can flow at the edges of the slab, a polarization electric field in the north-south direction must form so that the northward
current is zero
Jy = ΣH Ex + ΣP Ey = 0.
(6.2)
Note that Ey is now the total electric field, which can be interpreted to be a sum
of a convection and polarization electric field. From the eq. above, we can get a
necessary relationship between the components of the electric field
Ey = −
ΣH
Ex .
ΣP
(6.3)
Then the horizontal current can flow only in the direction of the high-conductance
y
J
B
x
Figure 6.11: Schematic figure of enhanced conductance slab, which is restricted in
the north-south direction (y), but extended in the east-west direction (x).
6.4. EQUATORIAL ELECTROJET
129
slab and it is
ΣH
Σ2
Jx = ΣP Ex − ΣH Ey = ΣP Ex + ΣH
Ex = ΣP + H
ΣP
ΣP
!
Ex .
(6.4)
Hence we have arrived at the Cowling conductance
Σ2H
ΣC = ΣP +
,
ΣP
(6.5)
which now gives the enhanced east-west current density in the slab. Even though it
is known that Region 1 and 2 currents exist, the Cowling channel model has been
suggested to the auroral electrojets (the eastward and the westward electrojet) and
also for the substorm electrojet. Partial polarisation may take place, but it’s not
entirely clear how important it is in various situations.
6.4
Equatorial electrojet
Close to magnetic equator, the geomagnetic field is horizontal and the ionosphere
is a horizontal conducting slab. According to eq. (5.52), a northward electric field
Ex creates a northward current given by jx = σk Ex and an eastward electric field
Ey creates an eastward current jy = σC Ey . In principle, a strong meridional (northward) current should be generated by Ex , since σk has a high value (see Fig. 5.9).
However, at a few degrees from the equator values of σk decrease and this current
will produce a polarisation electric field that prevents the flow of the meridional
current.
No steep gradients limit the zonal current. In addition σP σH at about
2
/σP gets very high
100-km height, so that the Cowling conductivity σC = σP + σH
values there (see the height-integrated values in Fig. 5.9). The global tidal winds
create a zonal component of the tidal electric field, which has been measured by
the incoherent scatter radar facility at Jicamarca, Peru. This electric field is very
small in amplitude, 1 mV/m, and it is eastward on the dayside and westward in the
nightside. The resulting current is the equatorial electrojet which flows eastwards
in the daytime. At night a weaker westward equatorial electrojet is observed. The
equatorial electrojet flows at low altitudes; rocket measurements have showed that
it lies at altitudes between 90 and 130 km, which is determined by the height profile
of the Cowling conductivity.
Fig. 6.12 shows an example of magnetic observations from a set of sites on both
sides of the magnetic equator (this is from west Africa, where the magnetic equator
lies on the northern hemisphere). The figure shows the latitudinal variation of the
two magnetic components H (meridional) and Z (vertical) and the declination D.
A different curve has been plotted for each hour. The results indicate that the H
component is greatly increased in daytime around the magnetic equator, which is a
manifestation of an eastward current. The equatorial electrojet was originally found
from this kind of magnetic observations. Note that this figure is in accordance with
The Sq current system shown in Fig. 5.10.
130
CHAPTER 6. COUPLING
Figure 6.12: Magnetograms showing the equatorial electrojet.
Figure 6.13: Equatorial electrojet current densities inferred from 2600 passes of the
CHAMP satellite over the magnetic equator between 11:00 and 13:00 local time
(http : //geomag.org/inf o/equatoriale lectrojet.html)
6.5. JOULE HEATING BY IONOSPHERIC CURRENTS
6.5
131
Joule heating by ionospheric currents
The magnetosphere and ionosphere exchange energy in the form of electromagnetic
energy flux accompanied by electric fields and field-aligned currents, by particle
fluxes, and by plasma waves. In the following, we will concentrate on the first form
of energy, the electromagnetic energy.
The exchange of energy between plasma and electromagnetic field is described
by Poynting’s teorem
∂W
+∇·S+j·E=0 ,
(6.6)
∂t
where W = (0 E 2 + B 2 /µ0 )/2 is the energy density in the electromagnetic field,
S = E × B/µ0 is the Poynting vector and j · E is the energy exchange per unit
volume per unit time between the field and plasma. In a steady state, the equation
above becomes as
∇·S+j·E=0 ,
(6.7)
indicating that any plasma volume gaining energy (j · E > 0) is a sink of electromagnetic energy flux (∇ · S < 0). Thus currents flowing in the direction of the electric
field dissipate energy.
The ionospheric Joule heating is calculated in the frame of reference of the neutral
atmosphere. When the neutral atmosphere is moving at a velocity u, the electric
field in the frame of reference of the neutral atmosphere E0 is given by Lorentz
transformation
E0 = E + u × B
(6.8)
and then the electric field in the Earth-fixed frame of reference is E = E0 − u × B.
The current density in the ionosphere doesn’t depend on the frame of reference
and is according to (5.2)
j = σ · (E + u × B) ,
(6.9)
where σ is the conductivity tensor.
Now, the electromagnetic energy exchange rate in the ionosphere can be expressed as follows by using eq. (6.8)
j · E = j · E0 − j · (u × B) = j · E0 + u · (j × B) .
(6.10)
The first term on the right hand side, j · E0 is the Joule heating rate and the second
term u · (j × B) is the mechanical energy transfer rate to the neutral gas. By using
eq. (6.8) and (6.9), Joule heating rate becomes as
j · E0 = σP {E + (u × B)}2 .
(6.11)
The Joule heating defined this way corresponds to heating due to collisions between
ions and neutrals and the thermal energy is distributed roughly evenly between these
species. The effect of Joule heating can be seen in increased ion temperature Ti .
132
CHAPTER 6. COUPLING
The Joule heating rate in the equation above depends on height as follows
qj (z) = σP (z){E + (u(z) × B)}2
(6.12)
since large-scale E maps with a constant value to the E region and B can be considered as constant within the rather small altitude range (about 90–200 km) that
contributes to Joule heating.
The neutral wind height profile u(z) in the E region is often unknown. It can be
ignored if u E/B, which is often the case in the auroral ionosphere. In that case
the equation above is simplified to
qj (z) = σP (z)E 2
(6.13)
and then the height dependence of Joule heating rate is the same as for Pedersen conductivity. In this case, the height-integrated Joule heating rate Qj can be
expressed by using the height-integrated Pedersen conductivity ΣP
Qj =
Z z2
z1
qj (z)dz =
Z z2
z1
σP (z)dz E 2 = ΣP E 2
(6.14)
where z1 is at the base of the E region and z2 is at or below the F region maximum.
The unit of Qj is W/m2 .