Environmental Engineering Reference
In-Depth Information
passage of an electric current through a gas under the action of an electric field
was achieved at the beginning of the twentieth century and was represented in
the simplest form in topics by Townsend [47-49]. The basis of self-sustaining gas
discharge is the ionization balance resulting from formation and loss of charged
particles (electrons and ions) and it is convenient to express this balance in terms
of the first Townsend coefficient [47-49].
3.3
Radiation Transfer and Kinetics of Excitations in a Plasma
3.3.1
Equilibrium of Resonantly Excited Atoms in a Plasma
Excited atoms in a plasma result from inelastic collisions of atoms with electrons,
and therefore the equilibrium number density
N
of atoms in a given excited state
is determined by the Boltzmann formula (1.43) with the electron temperature
T
e
if only electron-atom collision processes are of importance. In the case of radiative
transitions in accordance with the scheme in Figure 2.19, the balance equation for
the number density of excited atoms has the form
dN
dt
D
N
τ
N
e
N
0
k
ex
N
e
N
k
q
,
(3.64)
where
k
ex
and
k
q
are the rate constants for excitation and quenching of an atom by
electron impact and
is the lifetime of an excited atom resulting from its transport
outside the plasma or photon emission. Because the cross sections of atom excita-
tion and quenching of an excited atom state by electron impact are connected by
the principle of detailed balance (2.53), the number density of excited atoms in the
stationary case
dN
/
dt
τ
D
0is
N
0
N
e
k
ex
N
e
k
q
N
D
.
(3.65)
C
1/
τ
In the limit of a long lifetime
of the excited state, the solution of the balance
equation (3.64) gives the Boltzmann distribution (1.43), and hence (3.65) may be
represented in the form
τ
!1
N
B
N
D
,
(3.66)
1
C
1/(
N
e
k
q
τ
)
where
N
B
is the Boltzmann number density (1.43) of excited atoms, which cor-
responds to thermodynamic equilibrium between excited and nonexcited atomic
states. Formula (3.66) has broader applicability than just application to resonantly
excited states. It is necessary to take as
the lifetime of an excited state with respect
to its decay by any channel other than electron collisions; in particular, as a result
of collisions with atoms or as a result of transport to walls. We assume here that
τ
