Environmental Engineering Reference
In-Depth Information
Let us find the criterion of the ambipolar diffusion regime for plasma propaga-
tion. We denote by
L
a typical distance over which plasma parameters vary remark-
ably, and this distance exceeds significantly the mean free path of charged particles
in the gas. From the Poisson equation we have for a typical difference between the
electron and ion number densities
E
eL
.
The estimate for the electric field strength resulting from charge separation has the
form
Δ
N
j
N
i
N
e
j
4
π
r
D
L
Δ
N
N
2
,
where
r
D
is the Debye-Hückel radius (1.13). From this it follows that quasineu-
trality of this plasma
Δ
N
N
corresponds to the criterion
r
D
L
,thatis,the
criterion of plasma existence.
4.4.7
Double Layer
When Langmuir [97, 98] identified plasma as a specific type of gas, he was guided
by gas discharge and divided the gas inside a gas discharge tube into two parts, the
plasma and the plasma sheath. The plasma is a uniform quasineutral gas including
electrons and ions, and according to Langmuir [97], “we shall use the name plasma
to describe this region containing balanced charges of ions and electrons.” The
plasma sheath is formed near electrodes and according to the Langmuir analysis of
the positive column of a mercury arc in 1923 [99], “Electrons are repelled from the
negative electrode while positive ions are drawn towards it. Around each negative
electrode there is thus a sheath of definite thickness containing only positive ions
and neutral atoms.”
Thus, we have that if a uniform quasineutral plasma involving electrons and ions
is formed in some spatial region, the plasma becomes nonneutral at its boundary.
In the case of gas discharge these boundaries relate to the electrodes and walls of
the gas discharge chamber, and these regions are called the plasma sheath or dou-
blelayer.Asanexampleoftheplasmatypeweanalyzetheplasmaofthepositive
column of gas discharge within the framework of the Schottky model [100]. Then
electrons and ions are formed in the positive column as a result of collision of
electrons with gas atoms, and the loss of charged particles results from ambipolar
diffusion of the plasma to the walls, and the ionization balance has the form
D
a
0
ν
D
N
a
k
ion
,
ion
2
where
D
a
is the coefficient of ambipolar diffusion,
is the
ionization rate,
N
a
is the number density of gas atoms,
k
ion
is the rate constant for
ionization in electron-atom collisions, and the mean free path of charged particles
0
isthetuberadius,
ν
