Photoionization reactions can be written
where M represents an atom or molecule. The only requirement is that the photon energy h exceed the relevant ionization potential . Since typically exceeds 10 - 20 eV, this means that only radiation with nm can cause photoionization. Any excess photon energy appears primarily as kinetic energy for the escaping photoelectron. Photoelectron energies can thus range from zero to hundreds of eV.
Consider a plane-parallel atmosphere which has a certain photon flux at wavelength incident at the top. Photoionization causes the photon flux to decrease (and the number of photoelectrons and ions produced to increase) along the path. The flux at altitude z is given by
where is the optical depth given by
is the neutral density, and is the photon-absorption cross section. Figure 16.5 shows that is the angle between the line-of-sight path and the zenith direction.
Figure 16.5: Geometry of the ray path, showing the zenith angle and the height z (or h) [Luhmann, 1995].
Assuming that is an exponential function, as in Eq. (16.5), then the integral can be performed to yield
where is the scale height for neutrals.
This equation can be used to model the source of ionization as a function of altitude, the degree of absorption of the radiation, and changes in the ionosphere with time-of-day (through the zenith angle dependence). Pursuing this last point, as increases, the altitude for a given increases, so that the total ionization rate decreases (since is lower then). This implies considerable variations in the locations and amounts of ionization produced as a function of time during the day. These daily motions and variations in the ionosphere, when considered in conjunction with recombination and other loss processes, give rise to changes in the magnetic field observed on the ground, the so-called diurnal variations that must be substracted when attempting to quantify space weather effects.