2.3. DSMC method
In reference to the experimental design of an AO generator illustrated
in Figure 1 , the well-known direct simulation Monte Carlo
(DSMC) method is adopted to track the cascades of collisions induced by
the injection of 300eV O+ into the tube chamber of the
AO generator, with an O2 pressure of 0.14Pa in the
chamber.[25-30] Briefly, the conditions of rarefied gas dynamics are
assumed, the Boltzmann equation describing the dynamic behaviors of the
gaseous species in a single intake of O2 flowing through
the tube chamber, with and without the injection of a 300eV
O+ are solved with the computational treatments
extensively elucidated by Bird.[30]
An exemplar of a collision event simulated by this DMSC approach is
depicted in Figure 4 , with the snapshots in the right column
representing the process of a pulse of O2 flowing
through the collision chamber modeled as a tube. This pulse of
O2 flowing through the collision chamber is assumed to
have an average molecular density of 0.4×10-3M. The
exact molecular density distribution at each geometric location at a
given time is random, and can be higher or lower than this average
molecular density due to Brownian motions. The pumping operation moves
this pulse of O2 at a speed of about 80cm per 0.65ms. In
comparison, the snapshots in the left column depicts the evolutions of
collision cascades induced by the activation of the O+injection electrode. More specifically, the left snapshot ofFigure 4(a) shows a blue spot (a drop in molecular density) at
the middle section of the tube at the snapshot time of 0.07ms. Since in
the presence of an average molecular density of
0.4×10-3M of O2, the average collision
mean-free-path of O is about 8cm, the location of this blue spot at the
middle-section of the tube (40cm from the left tube-opening) implies
that the injected O+ has gone through about 3
collisions with large impact-parameters, i.e., 3 “missing-target”
collisions with little energy-loss to its collision partners. At time
near 0.07ms, a head-on collision has occurred and a cascade of
collisions has been initiated. Some O2 molecules
engaging themselves in this first cascade of collisions are moving away
from the central location of the cascade. This causes a drop in the
molecular density and the evolution of the blue spot. In the left
snapshot of Figure 4(a) , additional cascades of collisions have
been initiated by the first cascade of collisions at the snapshot time
of 0.15ms, particularly at the proximity of the first cascade of
collisions but several cascades of collisions have also been randomly
generated far away from the first cascade of collisions. The presence of
such “follow-up” cascades of collisions all induce a drop in molecular
density and can be located by those blue spots in the snapshot. While
most “blue spots” are moving forward to the right exit of the tube,
some “blue spots” are moving backward to the left entrance of the
tube, as random backscattering is inevitable. The left snapshot ofFigure 4(c) shows that the first aggregate of
collision-cascades is exiting the tube at 0.25ms. Since this aggregate
of collision-cascades leaves the tube quickly, the “bullet” initiating
the collisions must carry a relatively high kinetic energy; as such,
dissociation-collisions may have occurred. If so, some AOs exit the tube
at 0.25ms. Similarly, the probability of AO production near the first
cascade of collisions depicted by the blue spot in the left snapshot ofFigure 4(a) is high. Hence, the left snapshot of Figure
4(f) predicts that a relatively high flux of AOs leaves the tube at the
snapshot time of 0.55ms.
In short, coupling AIMD and DSMC simulations confirms adequate AO
generation by firing 300eV O+ into a cloud of
O2 at a 0.14Pa, and offers fundamental mechanistic
understanding of the relevant dissociative and non-dissociative events
in this innovation technology for generating a high flux of AOs.
Experiments for the Generation and Exploitations of AOs
Design and Operation of a Practical High-Flux-AO Generator
The AO generator depicted in Figure 1 comprises four compact
ECR heads each with a power of 200W, arranged in a close-packed array as
an expandable plasma source. The mesh electrodes coupled to the
O2 plasma source allow the extraction of positively
charged oxygen ions which are mainly O+, with a
kinetic energy of 300eV into the drift-tube with a diameter of 30cm. For
a total power of 800W, the experimental data in the present work show
that the ion flux density can reach 1×1015 atoms
cm-2 s-1 at the extraction aperture
with a beam of 300cm2. While the ion flux density is
practically confined to this level, the diameter of the plasma source
and ion source can be expanded by incorporating more compact ECR heads.
Perceivably, an array of 9 ECR heads, with a total power of 1800W, can
be used to make an ion source with a beam near 700cm2with an ion flux density of 1x1015 ions
cm-2 s-1.
Three aperture electrodes are incorporated in the drift-tube to
facilitate ion extraction into the drift tube for the production of AOs
in the drift-tube and to limit ions and hot-electrons leaving the
exit-end of the drift-tube for the prevention of undesirable damage of
the workpiece-specimen placed at the exit of the AO generator. They are
also aligned such that the ultraviolet radiation from the intense plasma
is blocked.
In the operation of the AO generator, the number of non-dissociative
collision partners n is determined by both the length of the
drift chamber and the mean free path of O2:
\begin{equation}
\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ n\ }=2^{\frac{l}{\lambda}}\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\left(1\right)\nonumber \\
\end{equation}\begin{equation}
\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ λ}=\frac{-\mu v_{m}}{P}\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\left(2\right)\nonumber \\
\end{equation}\begin{equation}
\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ v}_{m}\ =\left(\frac{2K_{B}T}{m}\right)^{\frac{1}{2}}\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\left(3\right)\nonumber \\
\end{equation}where l and \(\lambda\) respectively represent the length of the
drift chamber and the mean free path of O2; μ is
gaseous viscosity;[31] P denotes the O2pressure in the drift-tube; v m represents the
most probable velocity of O2; KB is the
Boltzmann constant; T is the temperature in the drift-tube, andm is the mass of O2. The length of the drift
chamber in this work is 80cm. In a typical operation, P is 0.14
Pa, T is 300K and λ is 8cm; as such, the number of
non-dissociative collisions can be roughly 1000. Among these collision
partners, only one carries a positive charge in the completion of all
these collisions; thus, charge transfer is not particularly important.
The average energy of these particles is roughly about 175meV. Hence,
they are slightly more chemically active than their counterparts at
300K. As for AO generation, merely the first 2-4 rounds of
collision-cascades initiated by a 300eV O+ are violent
enough to cause O2 dissociation. The following Kapton
erosion tests reveal that on the average, 24 O2dissociations are induced by one 300eV oxygen ion injection.