Environmental Engineering Reference
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Ta b l e 1 . 8 Critical parameters for interaction of electrons and ions with a gas.
Gas, vapor
He
Ar
Kr
Xe
Cs
N cr ,10 21 cm 3
200
90
7
1
0.03
p cr , atm
8000
3000
300
50
1
N cr ,10 21 cm 3
6.3
2.8
2.6
2.0
0.12
3 p 3 N cr , so it is less restrictive than con-
dition (1.99). The second condition in (1.100) has the form
The first condition in (1.100) gives N
N
N 1 ( T ) ,
(1.101)
where
3
3
N 1 ( T )
D
(2 m e T ) 3/2 .
4
π
This is independent of the identity of the gas. At a temperature T
D
300 K, we have
10 22 cm 3 , corresponding to a gas pressure of 700 atm.
For a gas consisting of atoms plus ions arising from those atoms, we have the
gaseous state condition N
N 1
D
2
3/2
is the cross section of the resonant
charge exchange process, and r is the mean distance between particles. The charge
exchange cross section is relatively large, and therefore the gaseous state condition
for ions is violated at relatively small densities of the gas. Table 1.8 lists values of
gas densities N cr
σ
1, where
σ
σ 3/2 at which the criterion to have a gaseous state for
interaction of ions and atoms is violated at a gas temperature of 1000 K.
We conclude that electron-atom or ion-atom interactions in a weakly ionized gas
can be nonpairwise even when the interaction between neutral particles satisfies
the gaseous state condition. Then charged particles interact simultaneously with
several neutral particles, and the gaseous character of the interaction is lost.
/2) 1/2
D
(
π
1.3.7
Decrease of the Atomic Ionization Potential in Plasmas
A dense plasma alters the states of its constituent atoms, and thereby can change
the atomic spectrum [71-73]. In particular, spectra of metallic plasmas differ sig-
nificantly from spectra of isolated metal atoms. The greater the plasma density, the
more drastic is the change in atomic parameters, including the ionization poten-
tial. Below we estimate the decrease of the atomic ionization potential as a function
of the plasma density.
Wecanconsideranatomasanisolatedobjectstartingfromtheprincipalquan-
tum number n , for which the atomic size r n is small compared to the average dis-
tance between ions as N 1/3
i
a 0 n 2
( a 0 is the Bohr radius), the ionization potential for this quantum number and for
. Since the average size of an excited atom is r n
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