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IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 33, NO. 2, APRIL 2005
Two-Dimensional Gas Density and Velocity
Distributions of a 12-cm-Diameter, Triple-Nozzle
Argon Z-pinch Load
Niansheng Qi, Bruce H. Failor, Jeff Banister, Jerrold S. Levine, Henry M. Sze, and David Lojewski
Abstract—We have developed a 12-cm-diameter Ar gas Z-pinch
load, which produces two annular gas shells and a center gas
jet. The two-dimensional (2-D) gas density profiles of the load, in
– and – planes, were measured with submillimeter spatial
resolutions using the planar-laser-induced fluorescence (PLIF)
method, for conditions used in Z-pinch experiments. Due to interactions between the shells, the net gas density profile differs from
the superposition of the individual shell profiles. Narrow density
peaks are observed both at smaller and larger radii than the radius
where the shells come in contact with each other. Two-dimensional
flow velocity distributions are determined from the displacements
between the fluorescence and later time phosphorescence images.
20
The measured stream velocities of argon gas puffs are 650
m/s, higher than the ideal gas velocity due to the formation of
clusters in the supersonic gas flow. Indeed, clusters were observed
in earlier Rayleigh scattering experiments. The gas measurements
of the initial phase using the PLIF will be combined with other
density measurements of the implosion and pinch phases to better
understand the implosion dynamics and to provide initial conditions for simulation codes.
Index Terms—Argon gas puff, laser-induced fluorescence,
plasma radiation source, Z-pinch.
I. INTRODUCTION
F
OR an efficient Z-pinch plasma radiation source (PRS),
the implosion ion kinetic energy needs to be greater than
the energy needed to: 1) ionize the plasma and 2) produce the
K-shell photons [1]. One way to produce the necessary ion kinetic energy in 200–300-ns implosions for 3-keV X-rays or
100-ns implosions for 5-keV X-rays is to use large-diameter
Z-pinch loads. 12-cm-diameter, triple-nozzle argon gas puffs
have been developed as 3-keV X-ray sources for long pulse
accelerators, such as Double-EAGLE (DE) and Decade Quad
(DQ) [2]. Because of Rayleigh–Taylor (R-T) instabilities, the
pinched-plasma diameters are relatively large and the resulting
argon K-shell X-ray outputs are relatively low compared to what
is measured for 100-ns implosions. We vary the initial gas distributions in order to mitigate R-T instabilities and optimize the
X-ray K-shell yield. Since the energy coupling and the X-ray
output of the PRS are determined by the implosion history, measurements from the initial gas phase, through the magentohyManuscript received October 7, 2001; revised December 22, 2004. This work
was supported by the Defense Threat Reduction Agency.
N. Qi, B. H. Failor, J. Banister, J. S. Levine, and H. M. Sze are with the Titan
Pulse Sciences Division, San Leandro, CA 94577 USA.
D. Lojewski is with the Defense Threat Reduction Agency, Kirtland Air Force
Base, NM 87117 USA.
Digital Object Identifier 10.1109/TPS.2005.845253
drodynamics (MHD) implosion phase, to the final pinch phase
are needed. These measurements provide the critical information required to understand the implosion dynamics and refine
the theoretical models [3]–[7], so the models can better predict
load performance.
Many diagnostics have been developed for the final pinch
phase, and the radiated power, X-ray spectrum, temperature,
density, and size are measured satisfactorily. Recently, a laser
shearing interferometer and laser wavefront analyzer have
demonstrated that measurements of the plasma density profile
and/or load current are possible during the MHD implosion
phase [8], [9]. In this paper, we report on a planar-laser-induced
fluorescence (PLIF) technique to determine the density profiles
in the initial gas phase for argon PRS experiments. Development of this technique is a part of the overall effort to create
a comprehensive set of instruments to trace the gas/plasma
density profiles from the initial gas phase to the final pinch
phase.
The initial gas phase density profile determines the implosion
trajectory. The 12-cm-diameter, triple-nozzle gas puff provides
flexibility in tailoring the initial gas phase density distribution,
by being able to independently set the pressure in each of the
three plena. The pressure ranges, and associated density profiles,
that optimize the K-shell X-ray yield, are determined experimentally. In the past, measurements of the gas puff density have
been made using either a one-dimensional (1-D) high sensitivity interferometry [10], [11] or single beam laser-induced fluorescence (LIF) [12]. Planar laser-induced fluorescence (PLIF)
offers several advantages. The LIF and high sensitivity interferometry require many axial and/or radial scans to obtain a
two-dimensional (2-D) density map. Multiple scans are very
time consuming and the spatial resolution is typically limited
by the number of scans to several millimeters. Abel inversion,
which typically has large uncertainties at small radii, is needed
to unfold the interferometry data. PLIF measures the gas profiles quickly (several shots) with a high signal/noise ratio, and
high spatial resolution (submillimeter). It allows us to study the
flow trajectory, azimuthal symmetry of the density, turbulence
in the gas flow, and fine structures due to shell-on-shell interactions. This type of information could be washed out in the axial
and radial scans required by interferometry and LIF.
In the experiments, we have used acetone as a tracer. Pulsed
ultraviolet (UV) lasers have enabled acetone fluorescence to
be used to diagnose a wide variety of gas dynamic flows. As
a tracer, acetone provides good signal levels, has low toxicity,
and a high vapor pressure. Because it has a broad absorption
0093-3813/$20.00 © 2005 IEEE
QI et al.: TWO-DIMENSIONAL GAS DENSITY AND VELOCITY DISTRIBUTIONS
Fig. 1. Schematic drawing of the PLIF measurements and the cross section of
the 12-cm-diameter triple-nozzle.
band, it can be excited with commercially available lasers that
emit between 225 and 320 nm. Other molecules could be invesmolecules has
tigated as PLIF tracers. LIF with NO and
been widely used in environment studies. The sensitivities of the
are orders of magnitude higher
fluorescence with NO and
than for acetone, which offers the potential to increase the PLIF
sensitivity significantly. An advantage acetone has over many
tracers, such as NO, is that it has an intersystem crossing that
makes the fluorescent yield relatively insensitive to collisional
quenching [13].
A description of our experimental approach and discussions
of the results will be given below. In Section II, we: 1) describe the experiment arrangement; 2) present the results of the
gas density measurements; 3) discuss the simulations of the gas
flow; and 4) illustrate the gas flow velocity determination. The
discussions and conclusions are given in Section III.
II. EXPERIMENT DETAILS AND RESULTS
Fig. 1 shows the arrangement of the PLIF measurements. The
gas puffs are injected from the nozzle/valve hardware, which is
mounted on the top of the vacuum chamber. The hardware has a
fast opening valve and a triple-nozzle assembly. The design and
operation mechanics of the valve and nozzle are similar to the
one reported in [11]. The triple-nozzle produces three concentric gas puffs. The inner/outer diameters of the outer and inner
nozzles are 10/12 cm and 4/6 cm at the nozzle exit plane, respectively. They produce hollow, shell-like gas profiles at the
nozzle exit. The center puff is a pencil-like jet with a 1-cm-diameter opening at the nozzle exit plane. The gas pressure in each
nozzle plenum can be adjusted independently. Further tailoring
of the initial density distribution is achieved by recessing the
inner pieces of the nozzles with respect to the outer one. For the
measurements described below, a triple-nozzle with 2-cm recess
was used as shown in Fig. 1.
The chamber is about 1 m in diameter and 1 m high. A
25-cm-diameter, 50-cm-long tube is mounted on the bottom of
the vacuum chamber to allow gas expansion. The chamber is
torr. The
pumped down to a vacuum pressure of
density measurements were made 500
after the opening of
the valve, which is the time at which Z-pinch current is applied
to the gas puff in DE and DQ experiments. At this time, the gas
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flow reaches its quasi-static condition and the leading edge of
the gas flow has propagated 33 cm way from the nozzles at the
measured argon gas flow velocity of about 650 m/s. Therefore,
at the time of the measurement, the gas has not reflected back
from the bottom of the vacuum chamber nor has the flow been
disturbed by the walls.
A frequency-quadruped Nd:YAG laser (7 ns, 45 mJ, 266
nm) was used in the experiments. The line focused laser beam
mm passed through the diameter of the argon
gas puff. Several percent of the laser beam were reflected from
the vacuum window. This reflected beam was monitored by a
photo-diode to determine the relative laser energy. To produce
fluorescence, the argon gas was mixed with 5% acetone by
pressure. Fluorescence from the acetone tracer in the argon gas
was captured using a gated intensified charge-coupled device
(ICCD) camera. The ICCD camera has an array of 576 384
pixels and the pixel size is 19 m. With a demagnification of
16.5, the spatial resolution of the image is 0.313 mm. To
calibrate system, the vacuum chamber was filled with the same
argon/acetone mixture as was used in the nozzle plena and the
intensity of the fluorescence was recorded. By measuring the
fluorescence at a known gas pressure, and assuming an ideal gas
dependence of density on pressure and temperature, the linear
factor between the fluorescence intensity and the gas density is
obtained. The noise level of the 16 bits ICCD camera is about
4 bits, which gives the lower limit of the density measurements
cm for pure acetone vapor. Background images
at
were taken with the laser pulse alone in the absence of gas. After
normalizing the fluorescence to the excitation laser energy and
subtracting the background from the fluorescence images, we
calculated the ratio of the gas puff fluorescence intensity to that
of the static fill. We determined the puff gas densities from this
ratio. A detailed description of these procedures was reported in
an earlier publication [12].
By orientating the 40-mm-wide laser beam perpendicular to
the gas flow direction ( -axis) and propagating across the gas
density mapping of the
puff diameter in the x direction, a
gas puff is obtained with the ICCD camera viewing in the direction parallel to the -axis. Fig. 2 shows the measured relative
density profile at
cm, where
is the nozzle
cm . The
exit plane location. The peak density is
nozzle plenum pressures of the outer, inner, and center jet were
67, 217 and 217 torr, respectively. This pressure setting is close
to the Z-pinch implosion experiment conditions on DE. The
image is averaged over eight shots to improve the signal/noise
ratio. Fig. 3 shows the relative density as a function of azimuth
, 1.5, and 2 cm. At
and 1.5 cm locations,
angle at
the azimuthal variations of the density is about 7%. At
cm,
,
the density is approximately constant between
. The meabut it is lower in the angular region
sured azimuthal density variations are about 10%. These could
be caused by deterioration of the nozzle as it had been used in
several Z-pinch discharge shots. A 10% azimuthal variation near
the axis of the gas profile would be hard to measure using a technique, like laser interferometry, that requires an Abel inversion.
Because PLIF does not require an Abel inversion, the data can
be obtained with far fewer shots of the puff valve and much less
reliance on valve reproducibility.
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Fig. 2.
IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 33, NO. 2, APRIL 2005
Measured r
0 (or x-y) density profile at z = 1:6 cm. Density is normalized with the peak density, which is 5 2 10
The rest of this paper presents the measurements made in the
– plane since the gas puffs have reasonable azimuthal symmetry. An – , equivalent to – , density mapping of the gas
puff is obtained by orientating the 40-mm–wide laser beam parallel to the gas flow direction and propagating across the gas
puff diameter in the direction, with the ICCD camera viewing
along the -axis. Figs. 4–6 show the measured relative density
profiles produced by the center, inner and outer gas puffs alone.
The data were obtained by filling only one plenum with gas; the
other two plena were evacuated. Vacuum expansion of the gas is
observed as it propagates downstream of the nozzle. The density
profile of the center gas jet is Gaussian-like and has an expansion angle of 15 as shown in Fig. 4. The inner puff profile
has a shell-like shape and the expansion angle is 25 in both
the inward and outward radial directions, as seen from Fig. 5.
The gas converges toward the -axis due to the inward radial
motion. Density peaks are observed at
cm in the recm. This indicates that the gases are scattering back
gion
from the center axis region due to collisions with gas there. The
widths of the peaks are on the order of the collision mean free
path as discussed later. As shown in Fig. 6, the outer gas puff
is also shell-like. The inner and outer expansion angles of the
outer gas puff are 25 and 7 , respectively. The gas propagates preferentially inward due to the 2 cm recess of the inner
nozzle piece. Again, the gas density builds up inside the shell.
Since the radius of the outer shell is relatively large compared
with the inner shell, the accumulated gas densities produced inside the shell are relatively less. Therefore, the amplitudes of the
cm,
–4 cm due to collisions
density peaks near
with gas near the axis are lower, and the widths of the peaks are
wider.
Fig. 7 shows the measured – density profile of the argon
gas flow, where the nozzle plenum pressures of the outer, inner
and center jet were 67, 217, and 217 torr, respectively. These
pressures optimized the Ar K-shell yield during a particular experimental series on Double-EAGLE reported in [2]. The peak
cm in the region of
cm,
density is about
–3.5 cm. The measured density profile is different from
the density summation of each individual gas-puff alone. Den, 1 and
sity peaks and valleys are observed near
0 cm and indicate that there are collisions between the adjacent
gas puffs. Fig. 8 shows another measured density profile, where
the pressures in the nozzle plena were equal at 217 torr. The
mm
densities near the region of the nozzle exit plane
cm
. Scale is 2 cm/division.
Fig. 3. Relative density at r 2 (solid line), 1.5 (dotted line), and 0.5 (dashed
line) cm as a function of azimuth angle derived from the PLIF image shown in
Fig. 2.
are approximately the same as those found by superimposing
each individual gas puff (except for the center jet). In the recm, the density profile is quite different from what
gion
would be predicted by a superposition of each individual gas
puff because there are collisions between the gas puffs. Again,
as the inner and outer puffs propagate downstream along the
-axis and expand radially, density peaks are observed on either
cm location due to shell-on-shell collisions. In
side of the
the presence of the inner shell gas puff, the center jet scatters inwards and outwards several times as it propagates downstream.
cm are different than the
The densities in the region of
measurements shown in Figs. 6 and 7. The influence of the outer
shell on the densities in the center region will be studied in the
future.
To examine the outer/inner gas shell-on-shell interactions, the
gas density profiles were measured, in the absence of the center
jet, under the following conditions.
1)
2)
Both inner and outer nozzle plena were filled with the
mixed argon/acetone gas at the same pressure.
Either the inner or the outer nozzle plenum was filled
with the mixed Ar/acetone gas; the other was evacuated.
QI et al.: TWO-DIMENSIONAL GAS DENSITY AND VELOCITY DISTRIBUTIONS
Fig. 4.
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Density profile measured with the inner gas jet alone. Peak density is about 10
cm
. Expansion angle of the jet is about 15 with respect to the z -axis.
Fig. 5. Density profile measured with the inner gas puff alone. Peak density is about 10
respect to the z -axis.
cm
. Inward and outward expansion angles are about 25 irc with
Fig. 6. Density profile measured with the outer gas puff alone. Peak density is about 10
respect to the z -axis.
cm
. Outward angle is about 7 and the inward angle
3)
Either the inner or outer plenum was filled with the
mixed Ar/acetone gas; the other was filled with pure Ar
gas.
Case A was one of the profiles tested in previous Z-pinch experiments, whose density profile is the same as shown in Fig. 8
cm due to presence of the center
except in the region of
gas jet. In Case B, the density profile of each individual gas shell
propagating into vacuum is measured without interactions with
the other one, and the density profiles are shown in Figs. 5 and
6 above. Because the fluorescence is only from the excited acetone molecules, in Case C, the density of the gas puff produced
from each individual nozzle is measured with the perturbations
from each adjacent gas puff.
Figs. 9 and 10 show the densities measured in Case B and C
cm, respectively. The dotted and dashed lines are the
at
25
with
traces of the density from the inner and outer puff, respectively.
For comparison, the measured density in Case A (thicker black
line) is also shown. The measured gas produced from the inner
puff (or the outer nozzle) in Case B matches well with that in
cm (or
cm). The two
Case A in the region of
gas shells are not simply merged into each other when they excm, but most of them are scattered back
pand radially to
from there. Fig. 10 shows the density profiles measured when
the inner (dashed line) or the outer (dotted line) nozzle plenum
was filled with the mixed argon/acetone gas, while the other one
was filled with pure Ar gas (Case C). Both the inner and outer
gas puff are scattered back in the presence of the other one. The
cm. At
cm,
interface of the two puffs is located at
the densities produced from the outer and inner puff in Case B
cm , and it is also the minimum denare equal, about
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IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 33, NO. 2, APRIL 2005
Fig. 7. Density profile measured in the presence of the outer, inner, and center gas puffs. Plenum pressures for the outer, inner, and center jet were 67, 217 and
217 torr, respectively.
Fig. 8. Density profile measured in the presence of the outer, inner, and center gas puffs. Plenum pressures for the outer, inner, and center jet were equal: 217 torr.
Fig. 9. Comparison of the gas density profile in Case A (solid line) and Case
Bat z = 20 mm. Dotted line (or dashed line) is the profile when the inner (or
outer) nozzle plenum was filled with the mixed gas, while the other one was
evacuated (no gas).
sity between the two interaction peaks in Case A. Most of the
gas from the inner and the outer puff are scattered back from the
interface, while a small amount of gas diffuses through the interface with a diffusion length of 0.5 cm, as shown in Fig. 10. For
cm ,
an ideal gas, the collisional cross section is about
so the free-path length is on the order of 1 cm at a density of
cm , which agrees with the observed collision mean free
path of 0.5 cm. Because the mean free-path lengths are relatively short, the scattered gases, from the interface, are again
scattered back from the locations on the other side of the interface, where the density is approximately the same as that at the
interface as shown in Fig. 10. Therefore, density peaks are produced several mm away on both sides of the interface. The shape
of the peaks is close to a Gaussian and the widths of the peaks
are close to the collision mean free path length. Integrating the
density over the cross section, the mass in the peaks (Case A)
is equal to the integral of the mass obtained beyond the intercm in Case B. Therefore, from the measurements
face
in Cases A–C, one can derive the amplitudes, widths, and positions of the peaks due to puff-on-puff interactions. Fig. 11 plots
the sum of the two gas puff densities (dotted line) measured in
Case C, which matches reasonably well with the measurements
(thicker black line) in Case A. The density difference between
Case A and the summations of Case C measurements is 10%
in the regions of
cm and
cm. It is about 20%
in the puff-on-puff interaction region, which could be due to the
relatively high shot-to-shot variations there.
The density peaks produced in the interaction region be4.5 cm in Fig. 11) have
tween two puffs (i.e., 3.5 cm
not been clearly observed in Abel-inverted laser interferometry
data. However, narrow density structures have been observed
in Raman scattering data from supersonic nozzles operated
continuously [14], [15]. We have made Raman and Rayleigh
scattering measurements and found reasonable agreement
between density profiles determined via Raman scattering and
those found via LIF as presented below.
QI et al.: TWO-DIMENSIONAL GAS DENSITY AND VELOCITY DISTRIBUTIONS
757
Fig. 10. Comparison of the gas density profile in Case A (black line) and Case
C at z = 20 mm. Dashed line (or dotted line) is the profile when the inner (or
outer) nozzle plenum was filled with the mixed gas, while the other one was
filled with pure Ar gas.
Fig. 12. Densities obtained from Raman scattering (solid line) and LIF (dotted
line) experiments.
Fig. 11. Comparison of the gas density profile in Case A (solid line) and the
sum of the inner and outer gas density profiles measured in Case C (dotted line)
at z = 20 mm.
Fig. 13. Relative signals of Rayleigh scattering from a pure argon.
Using an approach developed for diagnosing flames, [16] we
used an interference filter [630 nm, 10 nm full-width half-maximum (FWHM)] to isolate the Raman signal from methane in
a 50/50 mixture of argon and methane. We used a double shell
nozzle [11], [12] that was recessed 2 cm to produce a gas profile
to diagnose. A frequency-doubled Nd:YAG laser (5 ns, 200 mJ,
532 nm) passed through the puff axis and was focused to 0.2 mm
in the direction perpendicular to the puff axis with a 1 meter
focal length cylindrical lens. In the other dimension the laser
beam had an unfocused height of 5 mm. As with the PLIF measurements, a uniform backfill was used to calibrate the system
sensitivity. Because Raman scattering is extremely weak compared with the acetone fluorescence, 100 laser shots were integrated on a liquid nitrogen cooled charge coupled device (CCD)
camera to obtain the density profile shown in Fig. 12. The comparison between the LIF and Raman profiles is acceptable, con-
sidering the number of shots included in the Raman data. The
point to emphasize here is that the relatively narrow density
peaks in the LIF data are also seen in the Raman data. Thus, the
Raman measurements confirm the validity of the acetone LIF
measurement approach in this case.
We also obtained Rayleigh scattering data in this configuration, by changing to an interference filter centered on the laser
line (532 nm, 10 nm FWHM). Because Rayleigh scattering increases strongly (to the sixth power) with scatterer radius or, in
this case, cluster radius, the profile shown in Fig. 13 looks much
different than the Raman one. Where the Raman profile indicates gas density peaks due to puff interactions, the Rayleigh
signal approaches the level expected for unclustered gas. In regions where the puff is freely expanding, however, the Rayleigh
signal is high. These data are consistent with condensation and
cluster formation in the center of the puff and destruction of
clusters in the interaction regions between the puffs. As will be
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IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 33, NO. 2, APRIL 2005
Fig. 14.
Calculated density profile of the outer gas puff alone using the BMF model.
Fig. 15.
Calculated density profile of the inner gas puff alone using the BMF model.
shown later, the measured Ar puff velocity requires that energy
from condensation be added to the gas internal energy in order
to produce the observed gas flow rate. Clusters in Ar gas puffs
have also been observed experimentally and predicted theoretically by others [17]–[19].
Using the measured density profiles described above, a zerodimensional (0-D) snowplow model indicates that the 4 cm
long implosion plasmas should reach pinch the -axis simultaneously. Thus, there should be no time delay between X-ray
and the anode
cm .
emission at the cathode
However, in PRS experiments on DE, it was observed that X-ray
emission starts at the cathode and moves toward the anode with
a time lag of 10 ns [2]. It is very likely that the outer gas puff
expands radially even beyond the return current conductor so
that in the initial current flow time, the PRS load is electrically
, rather than
shorted to the return current conductor near
at
cm. It takes time for the implosion current to propagate
from the cathode to the anode and this would result in delayed
cm, the densities
X-ray emission from the anode side. At
–
cm . These densities are too low
are estimated to be
to be measured with a 5% acetone dopant, but they are important to know in order to match the X-ray emission times along
the axis with simulations. A ballistic flow model (BFM) [20]
is used to fit the measured individual puff density profiles. The
BFM is described as
(1)
and
is the modified Bessel function
where
of zero order. The BFM treats flow from a gas-puff nozzle as
with a Gaussian
emanating from a thin annulus of radius
about a nozzle tilt angle
and
distribution in polar angle
propagates the distribution ballistically forward in . Four parameters in the model, (the gas-source offset from the nozzle
exit plane), , , and
determine the 2-D density shape.
is the line density after integrating over the cross section.
Figs. 14–16 show the fitted density profiles of the outer puff,
the inner puff and the center jet, respectively. Figs. 17–19 comand 3.5 cm
pare the measured and fitted densities at
for the outer puff, the inner puff and the center jet, respectively.
The BFM parameters are listed in Table I. The BFM fits the measurements of the center jet and the outer puff very well. For the
inner puff, the BFM only fits the measurements in the region of
cm, but in the center region the fitting is not satisfactory since the BFM does not take account of the collisions of
the gas shell with the gas near the -axis, which converge due
to inward radial motion, Thus, with the derived parameters of
the outer gas puff in the BFM, we can estimate the magnitude
cm .
of the exponentially decaying density at large radii
By using this estimated density profile the agreement between
measured and calculated X-ray emission times as a function of
(from cathode to anode) is much improved.
The PLIF measurement uncertainty is 17%, which consists
of 8% systematic and 9% random uncertainties. The 8% systematic uncertainty can be reduced through extremely careful,
precise and frequent calibrations of the pressure gauges and the
image magnifications. Thus, the overall uncertainty could be reduced to 9%. The details of the error analysis are given below.
QI et al.: TWO-DIMENSIONAL GAS DENSITY AND VELOCITY DISTRIBUTIONS
Fig. 16.
759
Calculated density profile of the center gas jet alone using the BMF model.
Fig. 17. Comparison of the measured (solid lines) and fitted (dotted lines)
relative densities of the outer gas puff alone at z = 0:5 (thinner lines) and
3.5 cm (thicker lines). Peak density is about 10 cm .
Fig. 19. Comparison of the measured (solid lines) and fitted (dotted lines)
relative densities of the center gas jet alone at z = 0:5 (thinner lines) and 3.5
cm (thicker lines).
the image. The uncertainty is at least one pixel on each edge of
the nozzle. The 12.8-cm-diameter nozzle was measured 490
3 pixels long, which gives an uncertainty of 0.7% in radial position and 1.4% in the integrated (over the puff cross section) line
density. As long as the imaging system is unchanged, there is
no relative error in the magnification between images.
B. Uncertainty in the Gas Pressures ( 7%)
The pressures in the vacuum chamber static fill calibration
are in the range of 1–10 torr. There is a 5% uncertainly in
the pressure reading. The uncertainties of the pressures in the
nozzle plena are 2%. The sensitivities of the pressure gauges
used are relatively stable, but could shift over a period of several
months. Thus the relative variation of the pressure readings in a
day- or week-long experiment is negligible.
Fig. 18. Comparison of the measured (solid lines) and fitted (dotted lines)
relative densities of the inner gas puff alone at z = 0:5 (thinner lines) and
3.5 cm (thicker lines).
A. Uncertainty in the Image Magnification ( 1.4%)
The calibration of the image size to the physical gas puff dimension is obtained by measuring the diameter of the nozzle in
C. Uncertainty in Fluorescence Intensity in the Static Gas Fill
Calibration ( 2.5%)
The ICCD background in the gas puff density measurements
can be baseline subtracted at large radial positions (say 12 cm)
since there is very little gas there. This cannot be done in the
static fill calibration, where the whole chamber is filled with the
mixed gas so no baselines are observable. The intensity variation of the ICCD at the baseline location is about 50 and the
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IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 33, NO. 2, APRIL 2005
TABLE I
PARAMETERS USED IN THE BFM TO FIT THE DENSITY PROFILES OF THE
OUTER PUFF SHELL AND THE CENTER JET
Fig. 21.
t = 500
Image of relative intense fluorescence (coincident with the laser at
s) and the weak phosphorescence gated 30, 50, and 70 s after the
laser pulse.
TABLE II
MEASURED FLOW (V ) AND RADIAL EXPANSION (V ) VELOCITIES OF THE
Ar AND He GAS PUFFS
Fig. 20. Time integrated image of the emission from the laser excited acetone.
Point focused laser beam passed through the gas puffs at z = 1 cm. Weak
phosphorescence shows the trajectory of the gas flow.
fluorescence signals of the static fill are
an uncertainty of 2.5%.
D. Shot-to-Shot Variations (
2500. Thus, there is
6%)
This is simply the estimated reproducibility of the puff valve
plus the uncertainty of the laser energy. It will be reduced if the
measurement is made in PRS experiments, not in the test-bed
reported here.
The radiation emission of the laser excited acetone tracer has
a narrow intense fluorescence pulse coincident with the laser
pulse followed by weak, relatively slowly decaying phosphorescence. Fig. 20 shows the time integrated LIF image of the
gas puff without a center jet, where a point focused laser beam
cm.
passed through the inner and the outer gas puff at
The nozzles used were not recessed. Intense fluorescence cocm from
incident with the laser pulse is observed at
the nozzle exit plane. As the gas flows downstream, the relatively slowly decaying phosphorescence shows the gas puff trajectory. To measure the flow velocities, four gate pulses (one
co-incident with the laser pulse and three delayed 30, 50, and
after the laser pulse) were applied to the ICCD camera
70
to capture the fluorescence and phosphorescence images simultaneously in the point focused LIF experiments. Fig. 21 shows
a typical image obtained from the inner and outer Ar gas puff
with nonrecessed nozzles. From the displacements of the phosphorescence at later times, Ar flow velocities (along the -axis)
of 650 20 m/s and radial expansion velocity of 170 30 m/s
are derived as shown in Table II. To obtain 2-D velocity mapping, an array of slits was inserted in the optical path of the line
focused laser beam before reaching the gas puff in the PLIF experiments. Images of the fluorescence or phosphorescence were
captured by gating the ICCD camera either co-incident or delayed with respect to the laser beam. Fig. 22 shows the image
of the fluorescence coincident with the laser pulse and Fig. 23
Fig. 22. Image of the fluorescence coincident with the laser pulse.
Fig. 23. Image of the phosphorescence captured 15 s after the laser pulse.
Relative displacements of the emission between the fluorescence (Fig. 22) and
the phosphorescence are about 1 cm.
shows the image of the phosphorescence captured 15
after
the laser pulse. A 2-D flow velocity map can be derived from
these two images by measuring the position shifts during the 15
time separation. Using these methods, the Ar gas puff velocities are also found to be 650 20 m/s. For an ideal gas, the
,
maximum velocity of the gas flow is
is the sound
where is the ratio of the specific heats and
velocity. This maximum velocity is 574 m/s for Ar
QI et al.: TWO-DIMENSIONAL GAS DENSITY AND VELOCITY DISTRIBUTIONS
761
at a nozzle plenum temperature of 300 K. The Ar gas puff velocities exceed the ideal gas value. As shown above, Rayleigh
scattering measurements indicated that condensation occurs in
the Ar gas puff and clusters are formed, which results in the release of additional energy to drive the gas expansion. Computer
simulations of the gas flow indicate that there will be cluster
formation in argon, which is consistent with the measured gas
flow velocities [18]. As a further check, the Ar gas in the nozzle
plena was replaced by helium gas. As the critical temperature
of He is much lower than that for Ar, condensation or clusters
are not expected in He gas puffs. We found that the He gas puff
velocities are 1600 30 m/s as shown in Table II. This value is
maximum velocity.
lower than the 1787 m/s
know that the collisions produced peaks on both sides of the
puff-on-puff interface. These peaks make the profiles depart
from the BFM fit. Because we can calculate the locations and
amplitudes of these density peaks, we are working to modify
the BFM to better predict the density profiles. We think that
such a model, which would provide reasonable density profiles
(for various nozzle plenum pressure settings) as inputs for
implosion modeling, will be useful for Z-pinch simulations.
Imaging of acetone phosphorescence has been used to measure the gas puff flow velocity. The measured value for He, 1600
30 m/s, is consistent with the gas internal energy at room temperature, but the value for Ar, 650 20 m/s, is too high. However, Rayleigh scattering data indicates the presence of clusters
in the gas puff and provides an explanation for the high argon
gas flow velocity. Energy released by the condensation of the gas
into clusters supplies the additional energy required to produce
the observed flow rate. Notice that the flow velocities measured
from the PLIF are from the acetone molecules. The flow velocity
of 650 20 m/s for argon puffs agrees with the interferometer
measurements, where the velocities are derived from pure argon
gas flow rise-times at different locations [22]. This indicates
that the acetone molecules have the same velocities as the argon
due to collisions, which is also consistent with the PLIF results
from helium gas puffs.
In the future, we plan to investigate other tracers that may
have advantages over acetone for a particular application.
Laser-induced fluorescence can also be used to measure ionization of the argon gas during the early implosion phase.
Combining PLIF measurements of the initial gas profile with
the laser shearing interferometer and laser wavefront analyzer
measurements for the imploding plasma density, [8], [9] and
the diagnostics of the pinch phase [23] will lead to improved
understanding of large diameter Z-pinch implosions.
III. DISCUSSION
In summary, we have demonstrated that the gas density profiles and flow velocity of Ar gas puff Z-pinch loads can be determined by using the PLIF method. The PLIF measurements were
made for a 12-cm-diameter triple puff nozzle that was installed
volume to minimize contrion a vacuum chamber with a
butions due to gas reflecting from the chamber walls. The PLIF
setup allows us to make measurements in planes either perpenplane) or parallel to that axis
dicular to the load axis (the
(the – plane). Measurements in the
plane indicate that
the azimuthal symmetry of the puff is 10%.
Due to puff-on-puff interactions, the measured density profiles are different than those found by superimposing the profiles for each individual puff. Density peaks are observed on
both sides of the puff-on-puff collisional interface with widths
of 0.5 cm. Such puff-on-puff interactions were not observed
for a similar 8-cm diameter, double puff nozzle using a high
sensitivity interferometer as reported in [11] and [20]. In those
interferometer measurements, the densities of the 8-cm-diameter gas puffs were measured at three downstream locations,
, 2, and 3.8 cm. The puff-on-puff collisions would
i.e.,
cm, where the
be expected in the chordal scans at
overlap of the two shells is significant. However, the steps in
cm location, which
the chordal scans were 0.5 cm at
could have smeared out the 0.5-cm–wide collision peaks especially after Abel inversion. For puffs produced by a slightly
different type of 12-cm-diameter nozzle, the density peaks and
valleys, induced from the puff-on-puff collisions, have been observed using an interferometer with chordal scan steps of 0.2 cm
[21]. Measurements of puff-on-puff density peaks using Raman
scattering agree with the PLIF data.
We have also used an analytic flow model (BFM) fit for the
individual outer, inner, and the center jet gas puffs. The BFM
provides estimates of the densities at large diameters, where the
densities are too low to be derived accurately using the PLIF,
that are needed to bring hydrocode calculations in to better
agreement with experimental measurements. The BFM does
not take into account the effects of puff-on-puff collisions. The
fitting of the inner puff alone agrees with the measured gas discm and the converged gas profile in the
tribution only at
cm is difficult to model. However, the center
region of
gas density can be reasonably calculated with the presence of
the center jet. From the puff-on-puff PLIF measurements, we
ACKNOWLEDGMENT
The authors would like to thank P. Grunow for his assistance
in the experiments. The authors also appreciate the fruitful comments and suggestions provided by the referee of this paper.
REFERENCES
[1] N. R. Pereira and J. Davis, “X-rays from Z-pinches on relativistic electron-beam generators,” J. Appl. Phys., vol. 64, pp. R1–R2, 1988.
[2] J. S. Levine, J. W. Banister, B. H. Failor, N. Qi, Y. Song, and H. M.
Sze, “Long implosion time (240 ns) Z-pinch experiments with a large
diameter (12 cm) double-shell nozzle,” Phys. Plasmas, vol. 11, no. 5, p.
2054, 2004.
[3] Y. K. Chong, J. W. Thornhill, R. Terry, R. W. Clark, and J. Davis, “Dynamics of a radiating large diameter argon gas puff on the DQ simulator,” in Proc. 2004 IEEE Int. Conf. Plasma Sci., Baltimore, MD, Jun.
28, 2004, p. 290.
[4] A. Chuvatin, L. I. Rudakov, A. L. Velikovich, J. Davis, and V. I. Oreshkin, “Heating of the on axis plasma in long-implosion plasma radiation sources,” in Proc. 2004 IEEE Int. Conf. Plasma Sci., Baltimore,
MD, Jun. 28, 2004, p. 361.
[5] K. G. Whitney, J. W. Thornhill, J. P. Apruzese, J. Davis, C. Deeney,
and C. A. Coverdale, “Enhanced energy coupling and X-ray emission
in Z-pinch plasma implosions,” Phys. Plasmas, vol. 11, pp. 3700–3714,
2004.
[6] M. R. Douglas, C. Deeney, and N. F. Roderick, “The effect of load thickness on the performance of high velocity, annular Z-pinch implosions,”
Phys. Plasmas, vol. 8, pp. 238–248, 2001.
762
[7] J. Schumer, D. Mosher, B. Moosman, B. Weber, R. Commisso, N. Qi,
J. Schein, and M. Krishnan, “Two-dimensional MHD simulations of a
neon Z-pinch on hawk,” IEEE Trans. Plasma Sci., vol. 29, no. 2, pp.
488–495, Apr. 2002.
[8] N. Qi, J. Schein, J. Thompson, P. Coleman, M. McFarland, R. Prasad,
M. Krishnan, B. Weber, B. Moosman, J. Schumer, D. Mosher, R. Commisso, and D. Bell, “Z-pinch imploding plasma density profile measurements using a two-frame laser shearing interferometer,” IEEE Trans.
Plasma Sci., vol. 30, no. 1, p. 227, Feb., 2002.
[9] N. Qi, R. R. Prasad, K. Campbell, P. Coleman, M. Krishnan, B. V. Weber,
S. J. Stephanakis, and D. Mosher, “Laser wavefront analyzer for imploding plasma density and current profile measurements,” Rev. Sci. Instrum., vol. 75, p. 3442, 2004.
[10] B. V. Weber, S. J. Stephanakis, and B. Moosman, “Differential phase
shift interferometer for measuring axisymmetric gas distribution for high
power Z-pinch research,” Rev. Sci. Instrum., vol. 70, p. 687, 1999.
[11] Y. Song, P. Coleman, B. H. Failor, A. Fisher, R. Ingermanson, J. S.
Levine, H. M. Sze, E. Waisman, T. Cochran, J. Davis, B. Moosman, A.
L. Velikovich, B. V. Weber, D. Bell, and R. Schneider, “Valve and nozzle
design for injecting a shell-on-shell gas puff load into a Z-pinch,” Rev.
Sci. Instrum., vol. 71, p. 3080, 2000.
[12] B. H. Failor, S. Chantrenne, P. L. Coleman, J. S. Levine, Y. Song, and H.
M. Sze, “Proof-of-principle laser-induced fluorescence measurements of
gas distributions from supersonic zozzles,” Rev. Sci. Instrum., vol. 74, p.
1070, 2003.
[13] M. C. Thurber, F. Grisch, B. J. Kierby, M. Votsmeier, and R. K. Hanson,
“Measurements and modeling of acetone laser-induced fluorescence
with implications for temperature-imaging diagnostics,” Appl. Opt.,
vol. 37, p. 4963, 1998.
[14] G. Tejeda, B. Mate, J. M. Fernandez-Sanchez, and S. Montero, “Temperature and density mapping of supersonic jet expansions using Raman
spectroscopy,” Phys. Rev. Lett., vol. 76, p. 34, 1996.
IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 33, NO. 2, APRIL 2005
[15] B. Mate, I. A. Graur, T. Elizarova, I. Chirokov, G. Tejeda, J. M. Fernandez-Sanchez, and S. Montero, “Experimental and numerical investigation of an axisymmetric supersonic jet,” J. Fluid Mech., vol. 426, p.
177, 2001.
[16] D. F. Marran, J. H. Frank, M. B. Long, S. H. Staerner, and R. W.
Bilger, “Intracavity technique for improved Raman/Rayleigh imaging
in flames,” Opt. Lett., vol. 20, p. 791, 1995.
[17] K. Y. Kim, V. Kumarappan, and H. M. Milchberg, “Measurement of the
average size and density of clusters in a gas jet,” Appl. Phys. Lett., vol.
83, p. 3210, 2003.
[18] W. M. Scott, K. E. Tatum, and E. S. Powell, “Numerical simulation of
cold flow for initialization of gas-puff z-pinches,” in Proc. 2004 IEEE
Int. Conf. Plasma Sci., Baltimore, MD, Jun. 28, 2004, p. 290.
[19] J. Zweiback, T. Ditmire, and M. Perry, “Femtosecond time-resolved
studies of the dynamics of noble-gas cluster explosions,” Phys. Rev. A,
Gen. Phys., vol. 59, pp. R3166–R3169, 1999.
[20] D. Mosher, B. V. Weber, B. Moosman, R. J. Commisso, P. Coleman, E.
Waisman, H. Sze, Y. Song, D. Parks, P. Steen, J. Levine, B. Failor, and
A. Fisher, “Measurement and analysis of gas-puff density distributions
for plasma radiation source z-pinches,” Laser Particle Beams, vol. 19,
p. 579, 2001.
[21] P. Coleman, private communication, Nov. 2004.
[22] B. Weber, private communication, Jun. 2003.
[23] B. H. Failor, P. L. Coleman, J. S. Levine, Y. Song, H. M. Sze, P. D. LePell,
C. A. Coverdale, C. Deeney, L. Pressley, and R. Schneider, “Charge-coupled device systems for recording two-dimensional mult-mega-ampere
Z-pinch data,” Rev. Sci. Instrum., vol. 72, p. 2023, 2001.
Authors photographs and biographies not available at the time of publication.