22nd International Symposium on Plasma Chemistry
July 5-10, 2015; Antwerp, Belgium
Shock wave properties in the interface region of an inductively coupled plasma
mass spectrometer (ICP-MS)
S. Savtchenko and H. R. Badiei
PerkinElmer Inc., Woodbridge, Ontario, Canada
Abstract: The approximate theoretical consideration and simplified numerical simulations
of the shock structure in a three–aperture ICP-MS interface are provided. The positions and
parameters for the shock waves are approximately obtained. A convenient rarefication
criterion is proposed. The degree of the shockwaves degeneration and deviation from
isomorphism due to rarefication is estimated.
Keywords: inductively coupled plasma mass spectrometry interface, shock waves, rarefied
flow
1. Introduction
In the Inductively Coupled Plasma Mass Spectrometry
(ICP-MS), the multi-chamber interface is placed
downstream of the torch in order to provide a stepwise
pressure drop and remove neutrals. A portion of the
plasma goes through the first orifice (i.e., the sampler). In
a conventional ICP-MS interface, the plasma is quasineutral, the Debye radius is much smaller than all of
dimensions, and ion fraction in-flow is low. Thus, it is
reasonable to assume, that plasma behaviour will be the
same as a neutral gas. Therefore, the neutral gas flow in
the interface is considered in this work.
The
consideration is based on a three-aperture interface design
as shown in Fig. 1. The flow passes the sampler orifice
and expands into in the form of a supersonic free jet.
Subsequently, the flow passes a skimmer cone and a third
cone called the hyperskimmer.
This leads to the
formation of a complex shock structure through the
interface. The characteristics of this structure play an
important role in the ion transmission and neutral removal
within the interface. The approximate theoretical and
simplified numerical analysis of the shock structure is
presented here.
2. Triple Cone Interface
A simplified schematic diagram of the interface is
shown in Fig. 1.
Fig. 1. Schematic diagram of the 3-aperture interface
design used in NexION® 350.
P-I-2-80
The partially ionized (~0.1%) quasi-neutral Ar plasma
passes through a three-aperture interface leading to the
low pressure chamber of mass spectrometer. Two major
roles of the interface are:
1. Differential pumping between the ICP source at
atmospheric pressure and the mass spectrometer
vacuum chamber, and
2. Maximize the transmission of analyte ions to the
downstream ion-optics while removing other unwanted
species such as neutrals, and minimizing mass bias
effects due to space charge.
In a conventional ICP-MS interface, the plasma is
expanded through the sampler orifice into the region
between the sampler and the skimmer [1-2]. The pressure
in this region is typically around 2-3 Torr and the
supersonic, isentropic expansion of the plasma results in
the creation of a free jet. Douglas et al. [3] showed that
for an interface with a sampler orifice of ~1 mm in
diameter and a gas number density of ~1.5×1018 cm-3, the
nature of the flow through the sampler is continuum
(Knudsen number Kn ~10-3) and the plasma remains
substantially neutral (Debye radius λ ~10-5 cm). Based on
such conditions, the gas flow through the sampler can be
calculated to be ~1.1×1021 s-1.
The skimmer cone is positioned within the isentropic
core of the expansion (also known as the zone of silence),
upstream of a shock structure known as the Mach disk,
and directs the ion beam into the main vacuum chamber.
Assuming that the ion beam passes through the skimmer
orifice (~ 0.9 mm dia. and 7.5 mm from the sampler)
mostly undisturbed, the gas number density at the
skimmer orifice would be in the order of ~6×1015 cm-3
and the Debye radius (λ ~3×10-4 cm) would be
sufficiently small to ensure beam neutrality. Langmuir
probe measurements reported by Niu and Houk [2] also
showed that the ion beam remains substantially neutral
(i.e., negligible charge flow) through the sampler and
skimmer and the space charge effects should not be
severe in the first stage of the vacuum chamber [1].
Furthermore, the Knudsen number (Kn ~ 0.4) for such
1
conditions indicates that the nature of the flow at the
skimmer orifice is in transition from continuum to
effusive.
Literature reports [4], however, suggest that the
assumption of an undisturbed plasma passing through the
skimmer orifice may not be entirely valid. In practice, a
small shock region should be considered on the tip of the
skimmer cone (surrounding the orifice), causing an
increase in the gas pressure and temperature within the
shock region. The pressure within the shock region could
be as high as a few Torr and with temperatures close to
that of the plasma. However, experimental results
reported later by Tanner et al. [5] suggested that the effect
of shock wave surrounding the skimmer tip on the gas
flow was minimal (due to the overall size of the skimmer
orifice compared to the surrounding shock region) and is
more or less limited to a slight scattering of the ion beam.
This may eventually cause a slightly larger angle of
dispersion on the flow downstream of the skimmer
orifice.
Downstream of the skimmer in a typical interface,
however, highly mobile electrons diffuse away from
positive ions [6], leading to the formation of a charge
separation zone with an electron sheath at the inner
surface of the skimmer. The polarization field of the
charge separation zone is somewhat offset by the slower
diffusion of positive ions (in order of their mobility),
leaving a net positive charge on the axis of the ion beam.
Such condition in which electron and ion fluxes are
considered equal is generally termed ambipolar diffusion.
The consequence of this separation is significant space
charge effects, causing strong defocusing of the ion beam,
high mass bias, and susceptibility to matrix effects.
Different approaches are taken by others, and published
in the literature, to overcome the adverse effects of space
charge downstream of the skimmer. In one example,
Tanner et al. [7] used a blunt reducer plate with an offaxis orifice (0.2 mm dia.), significantly smaller than the
skimmer orifice, to deliberately induce the formation of a
shock wave and reduce the ion current entering the
downstream ion optics in order to reduce the space charge
field. In another work by Turner [8], ions were
accelerated by using relatively high bias potentials
(-2 kV) behind the skimmer orifice to reduce ion density
and consequently the space charge effects. Houk and
co-workers [9] used a heated filament (from an electron
impact analyzer) behind the skimmer to supplement the
ion beam with electrons and balance its excess positive
charge in order to reduce ion space charge repulsion.
In NexION® 350, a third cone (i.e., not a blunt aperture)
with a 1-mm orifice is positioned on-axis behind the
skimmer cone (~3.5 mm), to create an intermediate
vacuum stage (P2 region in Fig. 1) between the skimmer
and the downstream ion optics. The P2 region is
evacuated by the Holweck stage of the turbo-molecular
pump. The third cone further reduces the gas load into
the main vacuum chamber by removing the neutrals that
have undergone re-expansion downstream the skimmer
2
and improves ion/gas ratio [10]. As mentioned earlier,
the slight flow re-expansion is produced by the attached
shock around the skimmer tip. Otherwise, mostly
unperturbed free jet passes through the third cone. This
can essentially be considered a secondary skimming
process. Assuming such conditions, the flow passing
through the third cone is calculated to be still in transition
from continuum to effusive (Kn ~0.8) with a gas number
density of ~3×1015 cm-3. This leads to a Debye radius in
order of ~4×10-4 cm which suggests that the nature of the
flow through the third cone can still be considered as
plasma. The gas flow passing through the third cone can
also be estimated to be ~1×1018 s-1, based on a
semi-logarithmic interpolation between the continuum
and effusive calculations. This corresponds to an ion
current of ~170 µA passing through the third cone, if we
assume that the plasma is still ~ 0.1% ionized. The
reduced current through the third cone reduces the overall
magnitude of the space charge field and improves ion
transmission efficiency through the downstream ion
optics which in turn, offsets the effect of reduced ion
current.
3. Results
The shockwaves, mentioned above, are shown on Fig 2.
At the same time, the inviscid flow assumption, used in
the one-dimension approximation becomes questionable
considering rarefication. Volchkov et al. [11] show that
shockwaves thicken with rarefication. This leads to
contraction of the supersonic core of the jet, where the
one-dimensional approximation is valid. The criterion is
the value of the modified Reynolds number:
R L = Re/N1/2
(1)
Here Re is the Reynolds number in the orifice and N is
the pressure ratio. Ref. 11 also shows that for R L ~200
and larger, flow may be considered as inviscid and
one-dimensional approximation can be used, if upstream
of the skimmer R L ~ 50 and upstream of the
hyperskimmer R L ~ 1. Hence, a more practical approach
is to take shockwave thickening into consideration which
can be estimated using Eqn. (2) [11].
Δ/L ~20/(20+R L )
(2)
Here Δ is the shockwave thickness; L is the dimension of
the shock structure (typically, size of the zone silence).
As shown by Eq. (2), the thickness of the shockwave on
the skimmer (Fig. 2) is comparable to the size of the
shock structure but still distinguishable within the zone of
silence. For the hyperskimmer, however, the shockwave
becomes almost indistinguishable from the jet structure.
Thus, it can be assumed that for the case of the
hyperskimmer (Fig. 2), the rarefication leads to complete
contraction of the core of the jet and to the degeneration
of the shockwave density. Thus, as gas rarefication
becomes more significant, the shockwaves progressively
P-I-2-80
thicken, degenerate in density, and finally, disappear. To
illustrate such situations, a numerical simulation for a
simple supersonic free jet expansion through the aperture
is shown in Fig. 3. Calculations are performed using
ANSYS FLUENT [12].
skimmer
hyperskimmer
a)
Fig. 2.
Shockwave forms on both, skimmer and
hyperskimmer.
4. References
[1] H. Niu, S. Luan, H-M. Pang and R.S. Houk.
Spectrochim. Acta B, 50 (1995)
[2] H. Niu and R.S. Houk. Spectrochim. Acta B, 51
(1996)
[3] D.J. Douglas and J.B. French. J. Anal. Atom.
Spectrom., 3 (1988)
[4] G.E. McMichael and J.B. French. Phys. Fluids, 9
(1966)
[5] S.D. Tanner, D.J. Douglas and J.B. French. Appl.
Spectrosc., 48, 11 (1994)
[6] A. Fridman. Plasma Chemistry. (New York:
Cambridge University Press) Chapter 3 (2008)
[7] S.D. Tanner, L.M. Cousins and D.J. Douglas.
Appl. Spectrosc., 48 (1994)
[8] P. Turner, T. Merren, J. Speakman and C. Haines.
in:
Plasma
Source
Mass
Spectrometry:
Developments and Applications. (G. Holland and
S.D. Tanner; Eds.) (Cambridge, UK: Royal Society
of Chemistry) (1997)
[9] N. Praphairaksit and R.S. Houk. Anal. Chem., 72
(2000)
[10] H.R. Badiei, D. Bandura, V. Baranov, K. Kahen and
S. Tanner. US Patent No. US 2011/0253888 A1
(2011)
[11] V.V. Volchkov, A.V. Ivanov, N.I. Kislyakov,
A.K. Rebrov,
V.A.
Sukhnev
and
R.G. Sharafutdinov. J. App. Mech. Tech. Phys., 14,
2 (1973)
[12] ANSYS, Inc. (3255 Kifer Road, US-95051 Santa
Clara, CA, USA)
P-I-2-80
b)
c)
Fig. 3. A) Contours of velocity magnitude (m/s).
Pressure drop from 10 Torr. b) Contours of velocity
magnitude (m/s). Pressure drop from 1 Torr to 0.1 Torr.
RL = 34. Transition flow (no shockwaves). c) Contours
of velocity magnitude (m/s). Pressure drop from 0.1 Torr
to 0.01 Torr. RL = 3. Transition flow(no shockwaves).
3