1. Earth’s Ionosphere Lecture 13
ESS200C
Earth’s Ionosphere
Lecture 13

2. Hydrostatic Equilibrium
The force of gravity on a parcel of air is balanced by the pressure gradient
Assume Tn is independent of height and integrate we obtain
The density of an atmosphere falls off (generally) exponentially.

3. Photoionization
As radiation passes through the atmosphere, it is absorbed and its intensity decreases
If this absorption is due to ion production, then
One ion pair is produced (generally) per 35eV in air
Production is a maximum when
Here
Since
So peak production occurs when
or where , where Nnm is the integrated density. This is also where the optical depth is unity.

4. Chapman Production Function
Peak production is
Production as a function of height is
Let y = (h - hm) / Hn then
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
where

5. 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.
Note: In this context nn(s) is a mass density

6. Particle Energy Deposition
Need to calculate altitude distribution of energy loss
Range-energy relation can also be written
Assume that the depth of matter traversed at x is approximated by
Where is energy particle has at point x
Solving for
Then
Curves here are for mono-energetic beams. In practice, sum over a distribution of energies.

7. 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→z-

8. Ionospheric Density Profile
Photochemical equilibrium assumes transport is not important so local loss matches local production.
If loss is due to electron-ion collisions, we get a Chapman layer
If there is vertical transport
Treating the pressure forces of electrons and ions and assuming neutrals are stationary, we obtain
Where is the ambipolar diffusion coefficient and Hp the plasma scale height
Vertical transport velocity becomes

9. 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.

10. 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.

11. Conductivity Parallel equation of motion
Perpendicular equation of motion
Conductivity tensor
Petersen conductivity (along E┴)
Hall conductivity (along E x B)
Parallel conductivity

12. Force Balance - MI Coupling

13. Maxwell Stress and Poynting Flux

14. Currents and Ionospheric Drag

15. Weimer FAC morphology

16. FAST Observations IMF By ~ -9 nT.
IMF Bz weakly negative, going positive.
Questions:
Where is the dawnside open/closed boundary?
Where do the field-aligned currents go?

17. MHD FAST Comparisons

18. MHD FACs

19. 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

20. 38700 – MHD Comparison Bx ≈ 5 nT By ≈ 3 nT Bz ≈ -5 nT
Density jump: 12 – 18 cm–3 at 11:15
dB’s generally consistent with MHD flow pattern.
Weaker dB’s in polar cap because of lower conductivity.