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ESS200C
Earth’s Ionosphere
Lecture 13
1
Hydrostatic Equilibrium
• The force of gravity on a parcel of air is balanced
by the pressure gradient
nn mn g 
 dp
d
  (nn kTn )
dh
dh
• Assume Tn is independent of height and integrate
we obtain
nn  n0 exp[ (h  h0 ) / H n ]
• The density of an atmosphere falls off (generally)
exponentially.
2
Photoionization
•
As radiation passes through the
atmosphere, it is absorbed and its
intensity decreases

•
dI
 nn I
ds
If this absorption is due to ion
production, then
Q  C
•
dI
 Cnn I
ds
•
One ion pair is produced (generally)
per 35eV in air
Production is a maximum when dQ  0
•
Here I
•
Since ds  dh sec 
ds
dnn
dI
  nn
ds
ds
1 dnn  1 dnn
cos 

cos  
nn ds
nn dh
Hn
•
So peak production occurs when H n nm sec   1
or where N nm  1, where Nnm is the
integrated density. This is also where
the optical depth is unity.
3
Chapman Production Function
•
Peak production is
Qm  Cnm I m  CI cos  /[ H n exp(1)]
•
Production as a function of height is
Q  Qm exp[1  (hm  h) / H n  exp[( hm  h) / H n ]]
•
Let y = (h - hm) / Hn then
Q  Qm exp[1  y  exp(  y)]
•
•
•
•

Below the peak y is negative and exp (-y)
dominates
Above the peak y is positive and –y
dominates
If we reference local production rate to
maximum at subsolar point, we obtain
Q  Qmo exp[1 z  sec  exp(z)]
hm  hm 0  H n ln(sec  )
Qm  Qm 0 cos 
where
z  (h  hm 0 ) / H
4
Particle Impact Ionization
•
•
•
•
•
In many situations, particle impacts
can be the principal source of
ionization
– Solar proton events in polar cap
– Auroral zone during substorms
– Satellites with atmospheres in
planetary magnetospheres
A primary particle can produce
energetic secondary electrons that can
ionize. These electrons can also
produce x rays when they decelerate
Charge exchange can occur for ions
producing a fast neutral
Process is very non-linear; often is
numerically stimulated
Range energy relation is a good
approximation. Allow calculation of
stopping altitude.
R( 0 )  5.05 10 6  00.75 g  cm 2 ( protons, air ,1  100keV )
R( 0 )  4.30 10 7  5.36 10 6  01.67 g  cm  2 (electrons,0.2  50keV )

Range   nn ( s)ds
0
Note: In this context nn(s) is a mass density
5
Particle Energy Deposition
•
•
•
Need to calculate altitude distribution
of energy loss
Range-energy relation can also be
written
0
d
R( 0 )   
0 d / dx
Assume that the depth of matter
traversed at x is approximated by
0
x  
0
•
•
d
 R( 0 )  R(loc )
d / dx
Where  loc is energy particle has at
point x
Solving for  loc

loc  [ A ( A0  x)]
1
1

1
dloc / dx  (loc
)( A ) 1
•
Then
•
Curves here are for mono-energetic
beams. In practice, sum over a
distribution of energies.
6
Bremsstrahlung/ Ion Loss
• Electrons scatter much more
easily than ions.
• A decelerating or accelerating
electric charge produces
electromagnetic energy.
• This braking radiation tends to
be in the x-ray range and this
produces further ionization.
• Once produced electrons are
lost by three processes:
– Radiative recombination
• e+x+→x+hυ
– Dissociative recombination
• e+xy+→x+y
– Attachment
• e+z→z7
Ionospheric Density Profile
•
Photochemical equilibrium assumes transport is not important so local loss matches
local production.
ne
QL 0
t
•
If loss is due to electron-ion collisions, we get a Chapman layer
Q  L  ne2
ne  (Q /  )
•
•
1
2
If there is vertical transport
ne
 (neueh )
QL
t
h
Treating the pressure forces of electrons and ions and assuming neutrals are
stationary, we obtain
 dn
n 
neu pl   D  e  e 
 dh H p 
•
Where D  k (Ti  Te ) / miin is the ambipolar diffusion coefficient and Hp the plasma
scale height
k (Ti  Te ) / mi g
•
Vertical transport velocity becomes u  (n m  ) 1  dpT  n m g 
pl
e i in
e i 

 dh

8
The Earth’s Ionosphere
•
•
The electron density in the ionosphere
is less than the neutral density.
For historical reasons, the ionospheric
layers are called D, E, F
–
–
–
–
•
•
•
D layer, produced by x-ray photons,
cosmic rays
E layer, near 110 km, produced by UV
and solar x-rays
F1 layer, near 170 km, produced by
EUV
F2 layer, transport important
Enhanced ionization in the D-region
leads to absorption of radio waves
passing through because it is
collisional with neutrals.
At night, ionosphere can recombine,
but transport, especially from high
altitudes can be important
In polar regions where field is vertical,
a polar wind of light ions can form
similar to the solar wind.
9
Collision Frequencies
•
•
•
•
Ion and electrons collide with neutrals
as they gyrate. How they move in
response to electric fields depends
very much on the collision frequency
relative to the gyro-frequency.
If the gyro-frequency is much lower
than the collision frequency, ions and
electrons move in the direction of the
electric field or opposite to it. This will
produce a current.
If the collision frequency is much lower
than the gyro-frequency, ions and
electrons drift together perpendicular
to the magnetic field.
Since the ions and electrons have
different gyro-frequencies and collision
frequencies, a complex set of currents
may be produced. This is treated with
a tensor electrical conductivity.
10
Conductivity
qE  mi vinui
 eE  mevenue
j   0E
qE  ui  B  miv inui
eE  ue  B  me v en ue

  1  2 0  Ex 

 
j     2  1 0  E y 
 0
0  0  Ez 


2
2
v
v
1
1
1  [
( 2 en 2 ) 
( 2 in 2 )]ne e 2
me ven ven   e
mi vin vin  i
2 [
v
v
1
1
( 2 e en 2 ) 
( 2 i in 2 )]ne e 2
me ven ven   e
mi vin vin   i
 0 [
1
1

]ne e 2
me ven mi vin
•
Parallel equation of motion
•
Perpendicular equation of motion
•
Conductivity tensor
•
Petersen conductivity (along E┴)
•
Hall conductivity (along E x B)
•
Parallel conductivity
11
Force Balance - MI Coupling
j = ne(U i – U e)
12
Maxwell Stress and Poynting Flux
13
Currents and Ionospheric Drag
14
Weimer FAC morphology
15
FAST Observations
IMF By ~ -9 nT.
IMF Bz weakly negative,
going positive.
Questions:
• Where is the dawnside
open/closed boundary?
• Where do the fieldaligned currents go?
16
MHD FAST Comparisons
17
MHD FACs
18
dB’s Scaled to Ionosphere
dt = -411s
dt = -51s
Time
Time
Scaled dB’s largely
agree. Mapped by √B.
Even small scale
structures can show
persistence.
UT and ephemeris data for FAST only
19
38700 – MHD Comparison
Bx ≈ 5 nT
By ≈ 3 nT
dB’s generally consistent
with MHD flow pattern.
Bz ≈ -5 nT
Weaker dB’s in polar cap
because of lower
Density jump:
conductivity.
12 – 18 cm–3 at 11:15
20