Physical Kinetics of Ionized Gases - Fundamentals of Ionized Gases - page 185

lifetime of the excited state and taking into account the reabsorption processes, and
the rate of absorption events, which is [ j C C i (0)/2] k ω near the gas boundary, where

k ω is the absorption coefficient. We consider distances from the boundary exceeded
the mean free path of photons, 1/ k ω , and emission of spontaneous radiation as
the channel of loss of excited atoms. From this we obtain for the number density
of excited atoms

N D 3 k ω j C τ ef . (3.103)

We assumed above the flux of incident radiation to be small, which allows us ignore
stimulated radiation. In addition, collision processes involving excited atoms are
assume to be weak compared with reabsorption processes.
Let us introduce the excitation temperature T on the basis of the Boltzmann
formula (1.43) as

g g 0 exp N N 0 D

„ T . (3.104)

Taking into account the stimulated radiation in accordance with (2.148), we obtain
the balance equation for excited atoms in the form

dN
dt D

j ω k 0 N N 0

g 0
g

N
τ

j ω k 0 .

ef

In the stationary case with using the excitation temperature T we have
j ω k 0 1 exp „ T

N
τ

D .

ef

Let us introduce the typical radiation flux

N 0 g
g 0 k 0

j 0 D . (3.105)

τ ef

Table 3.3 contains the values of the specific photon flux j 0 / N 0 at g / g 0 D 1and

also of the specific typical intensity of radiation I 0 j 0 .Wehavethefollowing

connection between the flux of resonant photons j ω and the excitation tempera-
ture T :

D„ ω

j 0
exp „ T

j ω D . (3.106)

1

This connection between the flux of resonant photons in the spectral line center
and the temperature of excitation may be represented in the form

T D „ ω
ln 1 C η
η

j j 0 D g 0

g

I η D j ω σ τ , (3.107) abs ef

and Figure 3.14 gives the dependence of the reduced excitation temperature T
on the specific photon flux j 0 / N 0 in accordance with (3.107). In particular, T D