1. INTRODUCTION
Photoabsorption imaging using tuneable optical lasers is a
well-established technique for tracking the evolution of dilute and
nonemitting dynamic samples. For example, it can be used to measure the
evolution of momentum distributions in expanding atomic
Bose–Einstein condensates (Hecker-Denschlag
et al., 2002). It has also been used successfully to
measure late phase absorption in laser plasma plumes (Williamson et al., 1999). However, for
more dense samples (e.g., laser–plasma plumes in the early stages
of formation and growth) the analysis of absorption signals can be
complicated by the need to invoke the full radiative transfer equation.
Moving to the vacuum ultraviolet (VUV) spectral range, where one can
excite inner-shell and multiply excited resonances, which decay
predominantly by autoionization, greatly relaxes this restriction. In
fact, in most cases the probability for autoionization dominates over
that for photon emission (fluorescence) and one can readily rely on a
simple Beer–Lambert prescription to describe the beam
attenuation. The measurement made (total photoabsorption) is then also,
in effect, a measure of the total photoionization signal and hence the
technique can legitimately be termed “photoionization
imaging.”
Probing plasma plumes with VUV light has a number of other advantages
over optical probing, including the ability to access the resonance
lines of ions, which usually lie in the VUV. In addition, refraction of
the VUV probe beam by the plume density gradient, which typically
scales as λprobe2 (Attwood
et al., 1975), is reduced. Because the VUV beam has a
coherence length of typically less than a few microns (Turcu et al., 1993), absorption images are
free from the interference effects observed on images obtained in laser
absorption experiments. Finally the absorption image data, representing
as they do the dark or nonemitting species in the plume, complement the
usual optically filtered and gated emission images that provide
insights only into the spatial distribution of excited state plasma
species (Geohegan, 1993).
We demonstrated some time ago the proof of principle and application
of photoabsorption imaging as a plasma plume diagnostic (Hirsch et al., 2000). Encouraged by those
positive results we designed and have just completed the construction
and characterization of a new experimental facility called VPIF
(vacuum-ultraviolet photoabsorption imaging facility) to fully exploit
the potential of this novel diagnostic (Hirsch
et al., 2003). We report here some early results from a
study of the ion-integrated column density and expansion dynamics of
ground-state-selected Ba+ ions in a laser–plasma plume
using the VPIF. We chose singly ionized barium to showcase the
technique because its VUV photoion spectrum is now well known, with
resonance positions and absolute photoionization cross sections available
(Lyon et al., 1987). These measured data
facilitate the extraction of integrated column densities [NL =
∫n(l)dl] directly from the
photoabsorption images (see below). In addition, the VUV absorption
spectra of atomic Ba (Rose et al.,
1980) and Ba2+ (Hill et
al., 1982) have also been measured and their complex
structure unravelled so that transitions with excitation energies
unique to Ba+ may be isolated to ensure photoabsorption
images are free from contamination by neighboring charge states in the
plasma plume. The aforementioned isolated resonances of Ba+
have peak cross sections that ensure that the VUV absorption is not
saturated at the high end of the integrated column density scale
(shortly after Ba plasma ignition) while providing good absorption
during the expansion phase up to a few hundred nanoseconds after
breakdown. Barium is also a component of the High
Tc superconductor yttrium barium copper
oxide (YBCO) and data on the expansion of the individual atomic
components in an expanding plasma plume would be valuable for
comparison with the multi-element YBCO plasma and of interest to the
relevant laser-deposited thin superconducting film community (Reade et al., 1992). Finally barium,
released at high altitude, forms plasma clouds that are used to probe
space weather conditions (Horwitz & Moore,
2000). It is known that these lowly ionized Ba plasma clouds move
rapidly, typically 1–10 km/s (Wescott et
al., 1993) and hence an expanding laser-produced Ba plasma
plume could make for an interesting and potentially useful comparative
model system.
2. EXPERIMENT
A schematic diagram of the setup is shown in Figure 1. It produces a pulsed, collimated, and
wavelength-tuneable VUV (30–100 nm) beam of approximately square
cross section of 4 mm on each side that can be passed through a dynamic
(or static) sample and the attenuation recorded on a VUV sensitive
charge-coupled device (CCD). Here the continuum backlight was a
laser-produced gold plasma that provided VUV pulses of ca. 20 ns
duration at a repetition rate of 10 Hz. This “source”
plasma was formed by focusing the 800-mJ/8-ns/1064-nm output
from a Continuum Surelite laser to a spot size of <60 μm onto a
gold rod. Radiation from the source plasma was focused by an optimized
toriodal mirror onto the entrance slit of an Acton Research Corp. VM521
vacuum monochromator. The exit beam was then collimated by a second
toroid before being directed through the expanding Ba plasma plume.
Using 50-μm/50-μm exit/entrance slits, we obtained a
resolving power (λ/Δλ) of >1000 at a wavelength of
50 nm.
Schematic diagram of the vacuum-UV photoabsorption facility
(VPIF).
The Ba “sample” plasma was formed by focusing the
300-mJ/15-ns/1064-nm output from a Spectron SL404G laser onto a
Ba slab to a line some 3 mm long and 100 μm high using a
cylindrical lens. The barium plasma was occluded from the direct view
of the CCD by retracting the Ba slab until its surface lay some 0.50 mm
behind a knife edge. The parallel VUV beam just clipped the knife edge
and so the VUV beam passed 0.5 mm above the target surface. The effect
was to reduce significantly the unwanted radiation from Ba plasma that
fell on the CCD. In addition we placed a thin (200 nm thick) aluminum
foil between the Ba target and CCD to further reduce unwanted UV and
visible emission from the expanding (Ba) plume that extended beyond the
knife edge and is probed by the CCD.
The Ba+ ions were tracked by recording the time-resolved
attenuation of the pulsed VUV beam, tuned to the 46.7-nm inner-shell
resonance array of singly ionized barium as the expanding plasma plume
moved through it. This feature (as yet unclassified but tentatively
assigned as a 5p–6d array) is well isolated
from any nearby resonant structure in Ba and Ba2+. The
attenuated beam was allowed to fall on the CCD array where the spatial
distribution of the absorption signal
∫Iλ(L)dλ was recorded
by firing the continuum source laser at a delay Δτ after the
barium plasma breakdown. Here,
∫Iλ(L)dλ is the VUV
flux transmitted through a sample of length L, contained
within the monochromator bandwidth (Δλ) and integrated by the
CCD array over the ca. 20-ns VUV pulse duration.
These measured values can be related directly to the equivalent width
Wλ for a plasma length L, following
the equation
where ∫Iλ(0)dλ is the
unattenuated VUV flux, contained within the monochromator bandwidth
(Δλ) and integrated by the CCD array over VUV pulse width.
3. RESULTS AND BRIEF DISCUSSION
In Figure 2 we show time-resolved maps of
equivalent width (Wλ) for Ba+
recorded on the 46.7-nm, 5p–6d resonance for
various delays Δτ in the range 100–700 ns. The effective
pixel size in each image is 78 × 78 μm2 because we
bin 6 × 6 (13 × 13 μm2) CCD pixels to
improve image signal-to-noise ratio. The continuum beam bandwidth was
0.1 nm using 100-μm/100-μm entrance/exit slit widths.
The focused laser beam is coming from the left-hand side and forms a
horizontal line plasma on the Ba surface. The images show clearly how
the Ba+ plasma (ground state) component appears from behind
the knife edge (which provides the sharp defining edge on the
right-hand side of each image) at early times. It expands
differentially along the target normal and lateral directions to form
initially semi-elliptical plumes (at least in the vertical plane imaged
here). At later times the plasma appears to decouple itself from the
target surface to form a ball-like plume before dissipating. This phase
of the expansion into vacuum is difficult to observe in gated emission
images of plasma plumes. The main reason is that the density of emitting
species tends to drop below the detection threshold of intensified CCD
cameras at long time delays (Neogi & Thareja,
1999). Because photoabsorption cross sections for atoms and
ions are highest in the VUV, we should be able to better track the
“end-of-life” phase of plume expansion using the VPIF.
Time-resolved (equivalent width) maps of the Ba+ (46.7 nm)
resonance. The bandwidth of the VUV probe beam was 0.1 nm.
For a continuum source with a flat intensity distribution over the
beam bandwidth Δλ one can show that the equivalent width
distribution for an absorbing plasma column of length L may be
written as
where N is the species density (in cm−3),
L is the absorbing plasma column length, and
σλ is the absolute cross section profile. Because
the absolute cross section for the transition array in the 46.7 nm
region is known (Lyon et al., 1987) we
have been able to convert maps of equivalent width (Fig.
2) into corresponding Ba+ integrated column density maps
using Eq. (2) and the following procedure. Briefly we generate a table of
values of equivalent width Wλ for a range of
NL values and construct a plot of NL versus
Wλ. We then make a fit to the
NL(Wλ) curve that may be used to
convert, with a simple MATLAB routine, each equivalent width pixel
value into a corresponding integrated column density value. In Figure 3 we show a sequence of such integrated
column maps for time delays spanning 100–500 ns following barium
plasma breakdown. At these time delays, and for the on-target
irradiance used, we know from our studies of Ba and La plasmas in dual
laser plasma spectroscopy experiments (Köble
et al., 1995) that the plasma is composed predominantly
of a mixture of atomic and singly ionized barium. The gray scale covers
the observed range of column density, approximately 5 ×
1014 cm−2 to 4 × 1015
cm−2. The upper limit is set by the need to avoid
saturated absorption and the lower limit by the noise floor in the
images. We are currently working to improve the dynamic range by
improving the source flux (Murphy et al.,
2003), reducing the detector noise floor and also reducing
further the residual background emission that falls on the CCD
detector.
Spatial distributions of integrated column density extracted from the
maps of equivalent width for the 46.7-nm resonance at interlaser delays
in the 100–500-ns range.
In Figure 4 we demonstrate the tunability
of the technique by showing maps of equivalent width for various
wavelength detunings from the 46.7 nm resonance peak. The data were
taken at a time delay Δτ of 200 ns using
50-μm/50-μm entrance/exit slits, giving a VUV probe
bandwidth of 0.05 nm. The asymmetry in the image densities is simply a
reflection of the complex and asymmetric shape of the resonance
structure itself (see Fig. 4, top panel). For
cases where integrated column densities NL =
∫n(l)dl are so high as to cause
saturation (and where, simultaneously, weaker resonances free from
overlap with transitions from neighboring ion stages are not
available), such off-resonance detuning should prove to be an effective
solution.
Maps of equivalent width recorded at different wavelength settings
and at an interlaser delay of 200 ns. Insert: the absolute
photoionization cross section of Ba+ (Lyon
et al., 1987). The bandwidth of the VUV probe beam was
0.05 nm.
To simulate the plasma expansion dynamics, or, more particularly, the
plasma plume expansion velocity, we have used a rather simple model
(Singh & Narayan, 1990). This model
distinguishes three phases in the laser-plasma life cycle: the laser
interaction with the target material, the laser interaction with the
evaporated material, and finally adiabatic expansion in vacuum after
termination of the laser pulse. Here we are only concerned with the
last phase because all measurements are made after termination of the
laser pulse. The equation describing the expansion is
where X0, Y0, and
Z0 are the initial plasma dimensions at the end of
the laser pulse, X(t), Y(t), and
Z(t) are the dimensions of the plasma,
T0 is the temperature at the end of the laser
pulse, M is the atomic mass, and γ is the specific heat
capacity ratio. Equation (3) shows that the plasma expansion depends on
the initial dimensions of the plasma plume, the initial temperature,
and the atomic mass of the species considered. In Figure 5 we compare the size of the measured plasma
plume in the direction of the laser pulse with the simulated dimensions
from the expansion code. The results were obtained for an initial
temperature of 10 eV and initial plasma dimensions of length 3 mm and
width 0.1 mm. The initial plasma temperature of 10 eV was computed
using Eq. (22) of Colombant and Tonon (1973)
for our laser wavelength (1064 nm) and on target irradiance of ∼7
GW·cm−2.
Comparison between the measured front plasma plume velocity and the
calculated velocity using the laser–plasma plume expansion model
of Singh and Narayan (1990).
The plasma plume dimensions were obtained by taking as a reference
point the position at which the absorption signal dropped by 50% and
following this point with time. Although the measured values lie above
the computed curve (Fig. 5), we observe the
same linear increase in the plasma dimension with time. Both lines have
similar slopes and the velocity of 5.7 × 105 cm
s−1 measured experimentally compares well with the
simulated value of 5.9 × 105 cm s−1.
However, it must be emphasized that the measured images are both charge
and electronic state selective and the model used concerns the whole
plume expansion. Hence it is rather fortuitous that they agree so well
and is most likely a reflection that the plume is predominantly
composed of Ba+ at the times probed here. The result points
to a need for more sophisticated simulations, encompassing
hydrodynamics, kinetics, and atomic physics in an (ideally)
self-consistent single simulation (or at least in a sequential
postprocessing fashion) for the low temperature plasma plumes of
currently significant interest to the pulsed laser deposition
community.
4. SUMMARY
We have demonstrated the use of a vacuum-UV photoabsorption facility
providing a pulsed, wavelength-tuneable, and collimated VUV beam to
probe the expansion dynamics of Ba+ in an expanding Ba
plasma plume. Time-resolved equivalent width and integrated column
density (NL) maps of single ionized barium after the
termination of the plasma-producing laser pulse have been extracted and
presented. NL for Ba+ drops by an order of
magnitude or so over the time period sampled here of 100 ns–500
ns and an expansion velocity of 5.7 ± 0.5 × 105
cm·s−1.
Although only a small number of measured absolute photoionization
cross sections (including resonances) were available in the literature
until recently, a number of new experiments based on merged ion and
synchrotron beams at, for example, the Advanced Light Source (ALS) in
Berkeley and at the ASTRID storage ring in Aarhus are already producing
copious absolute data (West, 2002). Hence the
applicability of resonant photoionization imaging is set to widen to
many other ion species over the coming years. Future applications that
involve probing the interaction region of two colliding plasmas or of a
plasma with a surface are planned. For the case of two interpenetrating
plasmas, we should be able to effectively perform novel atomic
collisions type experiments with full space and time resolution.
Because we have charge and state of excitation selectivity, permitting
us to track the depletion (and even the filling) of ion electronic
states during the interaction, we will obtain fuller information than
that obtained in traditional beam–beam collisions. Although
experiments on imaging the fragments from collision events are now
appearing (Schulz et al., 2003), to our
knowledge such experiments have not been performed in the past even with
traditional ion beams, much less with more practical cases like plasmas.
We will also combine ICCD emission imaging and spectroscopy with
photoabsorption imaging to correlate our absorption with emission data
(e.g., Geohegan 1993) already available in
the literature for low temperature PLD plumes.
ACKNOWLEDGMENTS
We are grateful to Dr. Jean Paul Mosnier for a number of useful
discussions during the course of this work and to Dr. Wil Whitty for the
use of a code based on the Singh and Narayan (1990)
plume expansion model. Kevin Kavanagh acknowledges scholarship funding from
the Irish Research Council for Science, Engineering and Technology (IRCSET).
John Hirsch is funded by the EU under contract no. HPRI-CT-1999-50099. Work
supported by Irish Government National Development Plan including the
HEA-PRTLI Scheme and the Basic Research Grants Scheme as administered
by SFI, IRCSET and Enterprise Irland.
