Environmental Engineering Reference
In-Depth Information
In particular, in the helium case and for strong electric field strengths, when a
ty
pi
cal electron energy exceeds the thermal atom energy significantly, we have
w
e
/
p
E
accounting for the cross section of electron-atom collision being independent
of the collision velocity. For the ambipolar temperature this gives
T
a
D
2
T
ef
.
We now consider ambipolar diffusion in the regime of a low number density of
electrons for a gas discharge plasma that is located in a cylindrical discharge tube,
and ambipolar diffusion of the plasma leads to plasma motion to the walls. Cor-
respondingly, the ambipolar electric field
E
a
that is responsible for plasma motion
to the walls is directed perpendicular to the discharge electric field. For the total
electric field strength
E
this gives
q
E
z
E
D
C
E
a
,
where
E
z
is the electric field strength of the discharge that is directed along the
z
-axis of a discharge tube. From this we have for the ambipolar temperature
T
a
when ambipolar diffusion is directed perpendicular to an external electric field
T
ef
s
K
e
@
eD
e
p
E
2
eD
e
w
a
/
E
a
D
E
z
T
a
D
w
e
(
E
z
)
D
E
,
(4.125)
w
e
(
E
)
w
e
/
@
where
T
ef
is given by (4.82). As is seen, we have different ambipolar temperatures
for electron drift along the electric field and perpendicular to it in the case of high
electric field strengths and in the case of a nonlinear dependence for the electron
drift velocity as a function of the elec
tr
ic field strength. In particular, returning to
the helium case, we find
T
a
D
T
ef
p
2. Note that this type of ambipolar diffusion
is of importance for plasma drift to the walls of a discharge tube.
To demonstrate the characteristics of ambipolar diffusion in real gases, we eval-
uate below the ambipolar diffusion coefficient of helium at room temperature and
an electric field strength of 1 and 10 Td. At room temperature and low electric field
strengths He
2
is the basic type of ion, and its mobility in helium in the limit of
low electric field strengths is 17 cm
2
/(V s) at the normal number density of atoms
according to the data in Table 4.11. This gives drift velocities of ions of 4.6
10
3
and
4.6
10
4
cm/s at the electric field strengths indicated if we consider the lim
it of low
electric field strengths. Since the thermal velocity of helium atoms
v
T
D
p
8
T
/
π
m
a
is 1.3
10
5
cm/s, the limit of low electric field strengths is suitable for ions. The
effective Townsend temperature
T
ef
defined by (4.82) is correspondingly 3.7 and
7.7 eV according to measurements [37]. From this it follows that the parameter
T
ef
/
T
is 140 and 300 at the above-mentioned electric field strengths. Accounting
for
w
E
E
1/2
T
a
/
T
is 200 and
420 at the indicated electric field strengths. This testifies to the specific character
of ambipolar diffusion in atomic (and molecular) gases. Since the elastic electron-
atom (or electron-molecule) scattering dominates over a wide energy range, and
exchange of energy in a single collision is small, an electron may have enough
energy at electric field strengths, where ions have the thermal energy. Then the
second term in (4.120) exceeds the first term significantly, and
D
a
/
in the helium case, we find the ratio
D
a
/
D
i
D
D
i
.
