Environmental Engineering Reference
In-Depth Information
6.3.5
Passage of Cluster Plasma Flow through an Orifice
There are various methods for generation of metal cluster beams. The first stage
of this process is formation of an atomic vapor, and then the total conversion of
metal atoms into metal clusters proceeds in a flow of a buffer gas. We analyze
below the next stage of generation of a cluster beam, that is, its extraction from the
aggregation chamber by passage of this flow through an orifice. We will be guided
by the geometry of the aggregation chamber near the orifice according to Figure 6.1
that provides a laminar flow of a buffer gas. But reduction of the cross section of
the aggregation chamber near the exit orifice can lead to cluster attachment to walls
near the orifice, and this process determines the efficiency of the cluster beam
generation. The subsequent separation of the buffer gas flow and cluster beam is
made in a simple manner by pumping. Since the momentum of a buffer gas atom
is small compared with the momentum of a cluster, buffer gas atoms are removed
from the flow by pumping, and this flow is transformed into a cluster beam. In
the following stage, clusters may be charged by a weak crossed electron beam, and
then a beam of charged clusters is governed by electric optics.
In considering the behavior of clusters in a buffer gas flow near the exit orifice,
we assume the orifice radius
0
to be large compared with the mean free path of
λ
buffer gas atoms,
, which corresponds to the gas-dynamic character of the
flow. When a gas reaches the orifice, its velocity increases up to the sound speed
and increases sharply near the orifice. Clusters are moving far from the orifice with
the flow velocity, but their drift velocity
w
0
may differ from the flow velocity near
theorificeandisgivenby(6.2),
w
0
0
)
2/3
,where
c
s
is the sound speed. The
cluster drift velocity is affected by the small parameter
D
c
s
(
ντ
ντ
,where1/
ν
is the time
for relaxation of the cluster momentum and
is the time for variation of the flow
velocity. Table 6.5 contains examples of this under the flow conditions in Table 6.4,
and
w
0
is the drift velocity of clusters at the orifice under these conditions when
the equilibrium between the buffer gas flow and clusters is violated.
We also give simple estimations for attachment of clusters to the walls of the
aggregation chamber near the orifice. When clusters are located in all the cross
section of the tube or its conic part, the dependence of the cluster flux
j
to the walls
on the tube and cluster parameters is
j
τ
2
,where
D
cl
is the diffusion coef-
D
cl
/
ficient for clusters in a buffer gas and
is the radius of the current cross section.
Ta b l e 6 . 5
Character of relaxation of the cluster momentum near an orifice of radius
0
D
1mm
for the parameters of the argon flow with metal clusters under the conditions in Table 6.4.
Compound
MoF
6
IrF
6
WF
6
WCl
6
ντ
0.13
0.087
0.051
0.06
w
0
/
c
s
0.70
0.53
0.37
0.41
w
0
,10
4
cm/s
7.8
5.3
4.7
5.0
