9. Ionization and Energy Exchange Processes
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Transcript 9. Ionization and Energy Exchange Processes
9. Ionization and Energy Exchange Processes
1. Solar extreme ultraviolet (EUV) is the major
source of energy input into the
thermospheres/ionospheres in the solar system.
2. Electron precipitation contributes near the
magnetic poles.
3. l > 90 nm causes dissociation (O2 O+O)
4. l < 90 nm causes ionization
5. Energy losses (sinks), from the ionosphere’ point
of view, are airglow and the heating of the neutral
atmosphere (thermosphere)
6. Energy flow diagram in Fig. 9.1
9.1 Absorption of Solar Radiation in the Thermosphere (1)
The photon flux I(s) decreases along its path s through the atmosphere.
The flux change dI due to path element ds is
dI s I s n s ds
dI s a I s n s ds
9.1a
9.1b
where a , the constant of proportionality, is usually called the absorption
cross section. Of course, a depends on the wavelength l. To understand
the principle of "layer formation" we assume monochromatic radiation for
our dicussion. The positive direction for ds is from the sun towards the earth.
If the solar rays have an angle with the vertical (solar zenith angle,
Fig. 9.2), then
ds sec dz
dI z a I z n z sec dz
9.2
9.1c
9.1 Absorption of Solar Radiation in the Thermosphere (1a)
dI z a I z n z sec dz
dI
a n sec dz , or after integration from z to :
I
I a
ln
n z sec dz
I z z
a
I z I exp n z sec dz
z
9.1c
9.3
9.1 Absorption of Solar Radiation in the Thermosphere (2)
To get an estimate for the variation of I with z, we assume an
exponential decrease of n with height:
z z0
n z n z0 exp
9.4
H
and assume a , H, and are constant. Then the optical depth or
optical thickness becomes:
a n z sec dz a n z sec H
z
I z , I exp a n z sec H
9.5
9.1 Absorption of Solar Radiation in the Thermosphere (2a)
In general:
I z , , l I l exp z , , l
9.9
Here l is added to the variables because I (=I at top of thermosphere)
and a are functions of l. The simple realtion 9.4 holds only for
an isothermal atmosphere. If T is not constant we can write
z dz
z dz
T z0
T z0
n z n z0
exp
exp .
n z0
T z
T z
z0 kT / mg
z0 H
kT
H
is the neutral gas scale height.
mg
9.1 Absorption of Solar Radiation in the Thermosphere (3)
The vertical columnar content n z dz can easily be calculated.
z0
Set d dz / H , then
z0
0
0
n z dz n H d n
kT
d
mg
T 0
T 0
Since n n 0
exp d n 0
exp 0 :
T
T
0
T 0
kT
z n z dz n 0 T exp 0 mg d
0
0
kT z0
kT z0
n z0
exp 0 d n z0
exp 0
mg 0
mg
n z dz n z0 H z0 , or:
z0
9.17
0
9.1 Absorption of Solar Radiation in the Thermosphere (3b)
n z dz n z H z
9.16
z
To derive this equation equations we only had assumed that g and m
do not vary with height. If we assume that a is height independent,
the optical depth for plane geometry becomes
z
z
z, l , a n z sec dz sec a n z dz sec a l n z H z .
For a gas with different constituents:
z, l , sec sa l ns z H s z .
9.3 Photoionization (1)
Photons that exceed the ionization energy threshold can produce
electron-ion pairs when absorbed by neutral particles. Th excess
energy is transfered to the kinetic energy of the electron, or used
to excite the ion. If the probability for an absorbed photon to produce
an electron-ion pair is , the production rate is
PC z , I z , n z a I n z a e
9.21
with
z, l , sec a l n z H z .
Sidney Chapman (1932) was the first to derive this Chapman
production function. The two factors in the product n z e have
opposite trends: with decreasing height, n increases, while e
decreases because increases. At what height will PC be a maximum?
9.3 Photoionization (1a)
Answer: at the height where dPC / dz 0.
dPC d
sec a n z H
a
a d
I n z e I
nze
0
dz dz
dz
For an isothermal gas (i.e., H = const):
sec a n z H dn
a
0
1 n z sec H e
dz
1 n zmax sec H 0 n zmax sec H
a
Notice at the height of max production
max n zmax sec a H 1
a
1
9.3 Photoionization (2)
But for constant H:
n z max n0 e
1
n0 e
sec H
From (9.21):
a
zmax z0
H
zmax z0
H
zmax z0 H ln n0 sec a H
PC zmax , I n zmax a e max
PC zmax ,
a 1
I
e
I n zmax a e 1
sec a H
I cos
He
9.22
1
9.23
The maximum production rate occurs at local noon.
The height of max production increases with according to 9.22 .
This has ben observed for the E and F1 layers in Earth's ionosphere.
11.4 Ionospheric Layers
Earth's ionosphere is usually stratified in D, E, F1, and F2 layers during
the daytime. At night, only the F2 layer survives. When transport
processes can be neglected, the ion continuity equation becomes
dn e
Pe Le
11.49
dt
In equilibrium, i.e., during most of the daytime Pe Le .
The loss is mainly caused by recombination of electrons with ions.
If we assume one dominant ion, then
n e ni , and the loss L e ne ni ne2 . Therefore
Pe kd ne2 ,
where kd is ion/electron recombination rate.
11.51
11.4 Ionospheric Layers (2)
Using the Chapman production function (9.21) for Pe :
Pe I n z a e
11.52
with
z sec a n z H
11.53
z z0
n z n z0 exp
H
z z0
a 1
Pe I n z0 e exp 1
H
11.54
z z0
z
z
a 1
a
0
H
I n z0 e exp 1
sec Hn z0 e
H
11.4 Ionospheric Layers (3)
z z0
z z0
a
Pe I n z0 e exp 1
sec Hn z0 e H
H
For convenience (and convention) we select the height of
maximum production as our reference height z 0 zmax . But
a 1
sec a Hn zmax 1. Therefore the production rate becomes
z z0
z z0
Pe I n z0 e exp 1
e H
H
Using 11.51 :
a 1
Pe kd ne2
11.4 Ionospheric Layers (4)
1 z z0
1
a 1
ne kd I n z0 e exp 1
e
2
H
1 z z0
ne n0 exp 1
e
2
H
z z0
H
z z0
H
Chapman profile; n0 , z0 are the
electron density and altitude of the ionization maximum, i.e., the layer peak.
An alternate form is obtained if we choose as reference height the
altitude of maximum production for overhead sun, i.e., for =0.
At this height z 0 , 0 1 and
z 0 , 0 sec 0 a n 0, 0 H 1 a n0,0 H 1
z z0
z z0
H
Pe I n z0 e exp 1
sec e
H
a 1
1 z z0
ne n0,0 exp 1
sec e
2
H
z z0
H