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Photoionization reactions can be written


where M represents an atom or molecule. The only requirement is that the photon energy h tex2html_wrap_inline592 exceed the relevant ionization potential tex2html_wrap_inline594 . Since typically tex2html_wrap_inline594 exceeds 10 - 20 eV, this means that only radiation with tex2html_wrap_inline598 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 tex2html_wrap_inline600 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 tex2html_wrap_inline604 is the optical depth given by


tex2html_wrap_inline606 is the neutral density, and tex2html_wrap_inline608 is the photon-absorption cross section. Figure 16.5 shows that tex2html_wrap_inline538 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 tex2html_wrap_inline538 and the height z (or h) [Luhmann, 1995].

Assuming that tex2html_wrap_inline606 is an exponential function, as in Eq. (16.5), then the integral can be performed to yield


where tex2html_wrap_inline620 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 tex2html_wrap_inline538 increases, the altitude for a given tex2html_wrap_inline624 increases, so that the total ionization rate decreases (since tex2html_wrap_inline626 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.

next up previous
Next: Impact Ionization and Losses Up: Ionospheric Physics Previous: Ionospheric Physics

Iver Cairns
Thu Sep 23 17:08:59 EST 1999