Environmental Engineering Reference
In-Depth Information
for the radiative transition, and
k
0
is the absorption coefficient at the line center),
this radiation flux is equal to the flux of scattering isotropic radiation that returns
back through the plasma boundary, and this balance is determined by the degree of
atom excitation, so the excitation temperature is given by (3.107). Correspondingly,
the number density of excited atoms, as well as the flux of resonant radiation inside
the plasma, drops exponentially with distance from the plasma boundary, and a
typical depth of penetration of resonant radiation is approximately 1/
k
0
.
Another mechanism of interaction between incident resonant radiation and a
plasma takes place at high intensities of radiation and results in a chain of pro-
cesses which lead to full plasma ionization. These processes establish the electron
temperature according to (3.114), and this temperature is independent of the ra-
diation intensity. But incident radiation propagates in this regime in the form of
an ionization wave, and penetration of resonant radiation inside the plasma leads
to its full ionization. As a result, the plasma becomes transparent, and radiation
penetrates into deeper plasma layers.
Evidently, the front width for this ionization wave is approximately 1/
k
0
,and
the velocity
w
of propagation of this wave follows from the balance equation for the
energy flux
I
according to
I
wNJ
, where we assume the thermal electron energy
of approximately
T
e
to be small compared with the atomic ionization potential
J
,
N
is the number density of atoms of an ionized gas that is transformed subsequently
into the fully ionized plasma, and the energy flux is
I
D
D„
ω
j
,where
j
is the flux
of incident photons. Thus, we have
„
ω
j
JN
.
w
D
(5.136)
As follows from this formula, one can reach a high velocity of propagation of the
ionization wave in reality. For example, for an alkali metal plasma (Tables 3.3 and
3.4) at a vapor pressure of 1 Torr the light speed is attained at radiation intensity
I
10
9
W/cm
2
. Of course, in this case we are dealing with a nonrelativistic char-
acter of interaction between incident radiation and an ionized gas, and we will be
guided by lower intensities of incident radiation, but note that in reality radiation
intensities are available which exceed the above value by several orders of magni-
tude.
We assume that a transparent channel of a fully ionized plasma is conserved in
the course of propagation of resonant radiation. But this channel expands after gas
ionization because of gas heating. This creates an acoustic wave, that is, a photores-
onant plasma is a source of acoustic oscillations. Next, because of nonuniformity
of a formed plasma, atoms from external regions penetrate inside the transparent
channel and are excited by resonant radiation. Let the radius
r
0
of a radiation beam
be large compared with the mean free path of atoms in this ionized gas. Then the
atom flux inside a transparent channel results from diffusion of atoms in a plas-
ma, and a typical time for its occupation is
r
0
/
D
,where
D
is the diffusion
coefficient of atoms in the plasma. Hence, in this regime of propagation of reso-
nant radiation, it penetrates inside a plasma to a depth
L
that is estimated from the
τ
