2005/05/07 | 查普曼函数[Chapman Function]
类别(℃〖化学〗) | 评论(0) | 阅读(79) | 发表于 14:10
The rate of photoionization between heights z and is equal to

(1)

where for solar zenith angle ,
(2)

is the absorption cross-section, and n(z) is the number density of the absorbing gas. Assume an isothermal atmosphere so
(3)

Plugging (3) into (2) yields

(4)

Plugging (4) into (1) gives
(5)

(6)

But is monotonic, so f(x) and have maxima and minima at the same values of x. Therefore, there are extrema at
(7)

(8)

This is a maximum since
(9)

Physically, there are many absorbers but few photons near the surface, and many photons but few absorbers at the top of the atmosphere. The product of the two must therefore have a maximum where the two are balanced. Solving (8), the maximum is at
(10)

and the photoionization rate at this level is
(11)

The integrated rate over the entire atmosphere is then


(12)
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