Download ESS 154 Solar Terrestrial Physics

ESS 200C
Lecture 13
The Earth’s Ionosphere
• Ionospheric studies
– The radiation from the Sun at short wave lengths
causes photo ionization of the atmosphere resulting
in a partially ionized region called the ionosphere.
– Guglielmo Marconi’s demonstration of long distance
radio communication in 1901 started studies of the
ionosphere.
– Arthur Kennelly and Oliver Heaviside independently
in 1902 postulated an ionized atmosphere to account
for radio transmissions. (Kennelly-Heavyside layer is
now called the E-layer).
– Larmor (1924) developed a theory of reflection of
radio waves from an ionized region.
– Breit and Tuve in 1926 developed a method for
probing the ionosphere by measuring the round-trip
for reflected radio waves.
• The extent of the ionosphere
– There are ions and electrons
at all altitudes in the
atmosphere.
– Below about 60km the
charged particles do not play
an important part in
determining the chemical or
physical properties of the
atmosphere.
– Identification of ionospheric
layers is related to inflection
points in the vertical density
profile.
Region
Primary Ionospheric Regions
Altitude
Peak
Density
108 –1010 m-3
D
60-90 km
90 km
E
90-140 km
110 km
Several x 1011 m-3
F1
140-200 km
200 km
Several 1011-1012 m-3
F2
200-500 km
300 km
Several x 1012 m-3
Topside
above F2
• Diurnal and solar cycle
variation in the
ionospheric density
profile.
– In general densities are
larger during solar
maximum than during
solar minimum.
– The D and F1 regions
disappear at night.
– The E and F2 regions
become much weaker.
– The topside ionosphere
is basically an extension
of the magnetosphere.
• Composition of the dayside
ionosphere under solar
minimum conditions.
– At low altitudes the major ions
are O2+ and NO+
– Near the F2 peak it changes to
O+
– The topside ionosphere
becomes H+ dominant.
• For practical purposes the ionosphere can be thought
of as quasi-neutral (the net charge is practically zero
in each volume element with enough particles).
• The ionosphere is formed by ionization of the three
main atmospheric constituents N2, O2, and O.
– The primary ionization mechanism is photoionization by
extreme ultraviolet (EUV) and X-ray radiation.
– In some areas ionization by particle precipitation is also
important.
– The ionization process is followed by a series of chemical
reactions which produce other ions.
– Recombination removes free charges and transforms the
ions to neutral particles.
• Neutral density exceeds the ion density
below about 500 km.
• Ionization profile
– Let the photon flux per unit
frequency be 
– The change in the flux due to
absorption by the neutral gas
in a distance ds is d  n   ds
where n(z) is the neutral gas
density,   is the frequency
dependent photo absorption
cross section (m2), and ds is
the path length element in the
direction of the optical
radiation. (Assuming there are
no local sources or sinks of
ionizing radiation.)
– ds  sec  dz (where  is the
zenith angle of the incoming
solar radiation.
– The altitude dependence of
the solar radiation flux  
becomes




  ( z )    exp   sec     n( z ' )dz ' 

z


–
  sec     n( z ' )dz ' is called
z
the optical depth.
– There is usually more
than one atmospheric
constituent attenuating
the photons each of
which has its own cross

section.
  sec      t n( z ' )dz '
t
z
 ( z )    exp(  )
– The density (ns) of the neutral
upper atmosphere usually obeys a
hydrostatic equation
nmg  
dp
d (nkT )

dz
dz
where m is the molecular or atomic
mass, g is the acceleration due to
gravity, z is the altitude and p=nkT
is the thermal pressure.
– If the temperature T is assumed
independent of z, this equation has
the exponential solution
 ( z  z0 )
n  n0 exp
H
– For multiple species
  sec    t nt ( z ) H t
t
– The optical depth increases
exponentially with decreasing
altitude.
– In the thermosphere solar
radiation is absorbed mainly via
ionization processes. Let us
assume that   

i
– Each absorbed photon creates a
new electron-ion pair therefore
the electron production is
Si ds  n vi  ( z )ds
where Si is the total electron
where H  kT mg is the scale
production rate
height of the gas, and n0 is the
density at the reference altitude z0.
(particles cm-3s -1).
– For this case
 z ' z0 
   sec     n0 exp 
dz '  sec   n( z ) H

 H 
z
– Substituting for n and  (z )gives
 z  z0
 z  z0  
Si  n0  i  exp  
 sec   i Hn0 exp 
  –
H
H



– The altitude of maximum ionization
can be obtained by looking for
extremes in this equation by
calculating
– This gives
sec i Hn( zmax )   ( zmax )  1
– Choose z0 as the altitude of
maximum ionization for
perpendicular solar radiation
– This gives
S0 
H
e 1
This is the Chapman
ionization function.
– The maximum rate of
ionization is given by
Smax  S0 cos 
dS i
0
dz
z0  z max
where
 
 0

z
 z 
Si  S0 exp 1   sec  exp   
 H 
 H
– If we further assume that the
main loss process is ionelectron recombination with
a coefficient a and assume
that the recombination rate is
a ne2
– Finally if we assume local
equilibrium between
production and loss we get
S i  a ne2
– The vertical profile in a simple
Chapman layer is
ne 
1
z
sec 
 z 
exp  

exp   
a
2
 H 
 2 2H
S0
– The E and F1 regions are
essentially Chapman layers
– Additional production, transport
and loss processes are
necessary to understand the D
and F2 regions.
• The D Region
– The most complex and least understood layer in the
ionosphere.
– The primary source of ionization in the D region is ionization by
solar X-rays which ionize both N2 and O2
– Lyman-a ionization of the NO molecule.
– Precipitating magnetospheric electrons may also be important.
– Initial positive ions are N2+, O2+ and NO+
N 2  O2  O2  N 2
– The primary positive ions are O2+ and NO+
– The most common negative ion is NO3 The first step in making a negative ion is
e  O2  M  O2  M
• The E Region
– Essentially a Chapman layer formed by EUV ionization
– The main ions are O2+ and NO+
– Although nitrogen (N2) molecules are the most common in the
atmosphere N2+ is not common because it is unstable to charge
exchange. For example
N 2  O2  O2  N 2
N 2  O  NO  N
N 2  O  O   N 2
– Oxygen ions are removed by the following reactions
O   N 2  NO  N
O   O2  O2  O
• The F1 Region
– Essentially a Chapman layer.
– The ionizing radiation is EUV at <91nm.
– It is basically absorbed in this region and does not penetrate
into the E region.
– The principal initial ion is O+.
– O+ recombines in a two step process because recombination
of oxygen is slow.
 First atom ion interchange takes place
O   N 2  NO  N
O   O2  O2  O
 This is followed by dissociative recombination of O2+ and NO+
O2  e  O  O
NO   e  N  O
• The F2 Region
– The major ion is O+.
– This region cannot be a Chapman layer since the
atmosphere above the F1 region is optically thin to most
ionizing radiation.
– This region is formed by an interplay between ion sources,
sinks and ambipolar diffusion.
– The dominant ionization source is photoionization of atomic
oxygen
O  h  O   e
– The oxygen ions are lost by a two step process
• First atom-ion interchange
O   O2  O2  O
O   N 2  NO  N
• Dissociative recombination
O2  e  O  O
NO   e  N  O
– The peak forms because the loss rate falls off more rapidly
than the production rate.
– The density falls off at higher altitudes because of diffusionno longer in local photochemical equilibrium.
• Ionospheric conductance
– The dense regions of the ionosphere (the D, E and F regions)
contain concentrations of free electrons and ions. These mobile
charges make the ionosphere highly conducting.
– Electrical currents can be generated in the ionosphere.
– The ionosphere is collisional. Assume that it has an electric field but
for now no magnetic field. The ion and electron equations of


motion will be
qE  m  u
i in i


 eE  me en ue
where  in is the ion neutral collision frequency and  en is the
electron neutral collision frequency.
• For this simple case the current will be related to the electric
  u  u 
field by

j   0 E  e i e 
ne 

is a scalar conductivity.
where  0
– If there is a magnetic field there are magnetic field terms
in the

momentum equation. In a coordinate system with B along the zaxis the conductivity becomes a tensor.
 P  H 0 


   H  P
0
 0
0
 0 

– Specific conductivity – along the magnetic field
 1
1 



m

m
i i 
 e e
 0  e 2 ne 
– Pedersen conductivity – in the direction of the applied electric
field

i
1
1 


2
2
2
2



m



m
e
e
i
i
i 
 e
 P  e 2 ne 
e
– Hall conductivity – in the direction perpendicular to the applied
field
 

1
1 

 H  e 2 ne  2 e 2
 2 i 2



m



m
e
e
i
i
i 
 e
where  e and  i are the total electron and ion momentum transfer
collision frequencies and  e and i are the electron and ion
gyrofrequencies.
– The Hall conductivity is important only in the D and E regions.
– The specific conductivity is very important for magnetosphere
and ionosphere physics. If  0   all field lines would be
equipotentials.
 Electric fields generated in the ionosphere (magnetosphere) would
map along magnetic field lines into the magnetosphere
(ionosphere)
–
–

  

Assume ageneralized Ohm’s law of the form j    E  u  B
and that u  0
The total current density in the ionosphere is

 



B E
j   0 E   P E   H
B
–
where  and refer to perpendicular and parallel to the
magnetic field.
Space plasmas
so
 are quasi-neutral





  J       E     0 E
 P
   
 H
where
–
–
 0
 H 

P 
j

The current continuity equation can be written      E  
s
where s is along the magnetic field.
Integrate along the magnetic field line from the bottom of the
ionosphere to infinity. Since the field lines
are
 nearly

s






j





ds
E



E
equipotentials we can write
     
   
 

where the perpendicular height integrated conductivity tensor
 P  H 
is



0



 H

P



• Ionospheric
Pedersen
conductance
viewed from dusk.
• Note the large daynight asymmetry.
This results from of
ionization by solar
EUV radiation.
• Ionospheric Hall and
Pedersen conductance
from a simulation of the
magnetosphere during a
prolonged period with
southward IMF.
• The white lines show the
ionospheric convection
pattern.
• Precipitation from the
magnetosphere
enhances both the Hall
and Pedersen
conductances at night.
Pedersen Conductance
Hall Conductance
• Field aligned currents
from the simulation in
the previous
calculation.
• Cold colors indicate
currents away from
the Earth and hot
colors indicate
currents toward the
earth.
•
The high latitude
currents are caused
by the vorticity of
polar convection
cells.
• Within the high latitude magnetosphere (auroral zone and
polar cap) plasmas undergo a circulation cycle.
– At the highest latitudes the geomagnetic field lines are “open” in
that only one end is connected to the Earth.
– Ionospheric plasma expands freely in the flux tube as if the outer
boundary condition was zero pressure.
 For H+ and He+ plasma enters the flux tube at a rate limited by the source.
 The net result is a flux of low density supersonic cold light ions into the lobes.
 The surprising part is that comparable O+ fluxes also are observed.