1. INTRODUCTION
Interferometry using optical wavelength laser beams was established as
a powerful technique to probe dense plasmas within a few years of the
invention of the laser (Alpher & White,
1965). Further development of the technique including utilizing a
shorter wavelength, 4ω harmonic at 266 nm wavelength, and short
duration, 15 ps, for the probe beam, was important to determine the
electron density profile steepening at high laser intensities for
laser-produced plasmas (Attwood et al.,
1978). The short pulse duration was essential for probing close to
the target surface to freeze plasma motion. This trend to produce shorter
wavelength probes was extended mainly to allow access to large plasmas at
high density with less deleterious effects of absorption and refraction
that strongly limit the applicability of visible or UV probes. The first
soft X-ray laser interferometer was demonstrated by Da Silva et
al. (1995) using the Nova high power
laser-generated 15.5 nm Ne-like Y laser with a multi-layer coated beam
splitter Mach-Zehnder interferometer. Large 1-mm-scale plasmas were probed
to an electron density as high as 2 × 1021
cm−3 to within 25 μm of the initial target
surface.
Recently, Rocca et al. (1999)
established the 46.9 nm Ne-like Ar capillary discharge X-ray laser as a
tabletop interferometer tool using at first Lloyd's mirror and then
Mach-Zehnder diffraction grating instrumentation (Rocca
et al., 1999; Filevich et al.,
2000). Further benefits can be achieved by going to shorter
wavelengths if this can be combined with short pulse duration. The
transient gain X-ray lasers have been shown to operate with small tabletop
lasers of less than 10 J pump energy. It is possible to produce Ni-like
ion 4d–4p transition, 14.7 nm wavelength X-ray lasers in the
saturation regime with greater than 10 μJ output energy, and at a high
repetition rate of 1 shot per 4 minutes (Dunn et
al., 2000). This is sufficient output for applying tabletop,
picosecond X-ray laser interferometer to laser-produced plasmas (Smith et al., 2002; Filevich et al., 2004). At this wavelength
the critical density ncrit is 5.1 ×
1024 cm−3 and so allows the probe to access
much higher density plasmas. Further progress in expanding the technique
to different plasmas together with a better understanding of the X-ray
source characteristics are reported in this paper.
2. DESCRIPTION
Details of the techniques to generate this X-ray laser (XRL) source on
the LLNL compact multipulse terawatt (COMET) laser can be found elsewhere
(Dunn et al., 2000; Smith et al., 2002). For these experiments,
the short pulse pumping conditions are optimized to give both strong
output, and 5 ps X-ray layer pulse duration by using a 6.7 ps laser
pumping pulse (Dunn et al., 2003). The
pulse duration of the X-ray laser probe takes a snapshot image of the
plasma to be probed and determines the temporal resolution for the
interferometer. The Mach-Zehnder type interferometer for the 14.7 nm,
picosecond duration X-ray laser, uses diffraction gratings as
beam-splitters to generate and recombine the two beams (Filevich et
al., 2000, 2004).
The gratings diffracting the X-ray laser at grazing incidence angles use
well-established technology, have high throughput and are robust. This
makes the diffraction grating interferometer (DGI) well matched to soft
X-ray laser lines over a broad spectral range, including the Ni-like ion
Pd 4d–4p X-ray laser at 14.7 nm wavelength. The X-ray laser output
is relay imaged to the plasma (to be probed) using two high reflectivity
Mo:Si multilayer coated mirrors. A normal incidence spherical mirror and a
45° flat mirror controlled by a stepper motor are used to align the
beam under vacuum to the instrument. This has two advantages: it maximizes
the X-ray laser fluence at the plasma and minimizes the steering of the
beam due to variations in the XRL deflection angle as it exits the plasma.
One major difference between this work and earlier X-ray laser
interferometer (Da Silva et al., 1995)
is that with the 100× lower output available here, a substantial
fraction of the X-ray laser beam is used to probe the plasma. One
consequence is that this produces more constraints to the degree of
overlap of the beams and spatial coherence of the source for the
experiments reported here.
The first Au-coated grating G1, with 900 l/mm groove spacing,
splits the XRL into a 0th order (plasma probe) arm and a 1st order
(reference) arm, Figure 1. The grating blaze
angle and geometry have been designed to give equal reflectivity of
∼25% in each arm. The two orders are reflected by the long Au-coated
mirrors L1 and L2 to overlap the arms onto the second grating G2. The
plasma to be probed is placed in the 0th order beam at the position
between G2 and L1. The spherical multilayer mirror IM with 25 cm focal
length, after G2, images the plasma and relays the beam via the output
Au-coated mirror L3 to the back-thinned charge-coupled device (CCD)
camera. The total throughput of the instrument before the imaging optic IM
is ∼12%.
Experimental setup showing soft X-ray Diffraction Grating
Interferometer. X-ray laser enters and exits from right. CCD camera not
shown is positioned approximately 5 meters from instrument.
A second ruling of 16 l/mm is machined vertically offset on G1 and
G2 substrates so that the instrument can be pre-aligned with an 827 nm
infra-red (IR) diode laser. The IR laser has an estimated coherence length
of ∼300 μm which is similar to the ∼ 400 μm 1/e half
width longitudinal coherence recently measured for the X-ray laser using a
6.7 ps pumping pulse (Smith et al.,
2003). The IR laser is used to adjust various optics to make the
two arms equal in length, and for generating interference fringes. High
quality 14.7 nm soft X-ray interference fringes have been generated with
visibility exceeding 0.8. The magnification of the imaging system is set
to give high X-ray laser fluence on the detector, effective working area
at the plasma as well as good spatial resolution. The soft X-ray laser
beam at the target position is imaged onto a 1.33 × 1.33
cm2 CCD with 1024 × 1024 pixels of 13 × 13
μm2 dimensions. Magnification of 22 times is routinely used
which gives a field of view of the plasma of ∼600 × 600
μm2. The pixel-limited spatial resolution is 0.6 μm
with the overall spatial resolution of the instrument determined to be
1–2 μm.
3. RESULTS
We report results from several laser-produced plasma experiments that
demonstrate probing long plasma columns generated by line focus incident
on a 0.1 cm long Al slab target heated by the 600 ps full width at half
maximum (FWHM), 1054 nm laser of COMET. A maximum energy of 3 J was
available to produce a short line focus of 12 μm (FWHM) × 0.31
cm long using a combination of a cylindrical lens f = 200 cm and
an off-axis parabolic f = 30 cm. This corresponds to an incident
laser intensity of ∼1013 Wcm−2. The target
rotation angle was carefully adjusted to ensure that the interferometer
probe was parallel to the surface. The beams that form the X-ray laser and
the second plasma to be probed come from the same oscillator and are
synchronized. A delay line on the plasma-forming beam was adjusted for the
X-ray laser to probe the plasma at various times from Δt =
−0.5 to +3.0 ns, where Δt = 0 refers to the peak of the
heating pulse. The absolute timing of the heating and X-ray laser beams
was better than 100 ps while the X-ray laser pulse duration was ∼5
ps.
Figure 2(a) shows one of a sequence of X-ray
interferograms of the 0.1 cm long Al target recorded at +0.86 ns after the
peak of the laser heating pulse. The 0.1 cm dimension of the plasma column
is off the page in the direction of the X-ray laser probe. It should be
noted that there is very strong lateral expansion of the plasma along the
target, vertical axis in Fig. 2(a), that is
present almost immediately after the start of the laser pulse. So in
addition to the expected strong expansion perpendicular to the target
surface there is a very strong sideways component. A second feature is the
small on-axis dip close to the target surface that is also observed in
earlier time interferograms. This feature has not been seen on previous
experiments at our laboratory with a wider line focus. The ability of the
X-ray laser interferometry to probe close to the target surface allows
this feature to be clearly seen. Simulations with the LASNEX hydrodynamics
code (Zimmerman & Kruer, 1975) indicate that
this is formed early on during the rising edge of the laser pulse and may
be a result of the small line focus creating hot plasma conditions in a
very localized region close to the target surface. The extracted 2D
electron density profile from the interferogram is shown in Figure 2(b) and for comparison the 2D LASNEX
hydrodynamic simulations at +0.8 ns, Figure
2(c). The laser pulse shape and focal spot shape are used in the
simulations in order to model the experimental conditions as closely as
possible. The overall agreement is good with some small differences on the
sides of the plasma. Figure 3 shows an on-axis
lineout of the experimental data and simulations with generally good
agreement. The maximum electron density measured is 4 ×
1020 cm−3 close to the target surface where
the fringe visibility becomes difficult to observe in the last 10 μm.
It should be noted that at times later than +1 ns there is a reversal of
the fringe direction close to the target surface (Filevich et al., 2005; Nilsen & Scofield, 2004). This is understood to be
the contribution from the presence of low ionization stage bound electrons
that for aluminum plasmas change the sign of the gradient of the index of
refraction. This requires careful determination of the ionization of the
plasma to interpret the fringe shifts (at late times) in extracting the
electron density from the interferograms. It also makes the interferometry
a very sensitive tool for probing low temperature plasmas.
(a) Soft X-ray interferogram of 1 mm long Al target recorded
at +0.86 ns after the peak of the laser heating pulse. Initial focal spot
is 12 μm (FWHM) and laser intensity is ∼1013 W
cm−2. (b) Extracted 2D electron density profile
from interferogram. Electron density contour at 1020
cm−3 is indicated with the next two contours towards
surface are 2 × 1020 and 3 × 1020
cm−3 while the next two contours away from the target
surface are 9 × 1019 and 8 × 1019
cm−3, respectively. (c) 2-D LASNEX simulations
at +0.8 ns for the same laser plasma conditions.
On-axis electron density lineout from Fig. 2
showing experimental data points (diamonds) and 2D LASNEX simulations
(solid line).
A second run was carried out where a similar laser pulse was tightly
focused at the center of the bottom of an Al groove of dimensions 100
× 200 × 1000 μm3 (H × D × L)
machined by a diamond saw. This has the effect of confining the expansion
of the plasma. The long axis of the line focus is aligned along the groove
length. Figure 4, top image, shows the
interferogram inside the groove before the laser pulse. The lower image,
taken at +0.6 ns after the peak of the pulse, already shows a number of
processes occurring. The plasma has expanded and hit the groove walls
where there is now local heating in the corners and a plasma jet stream
out of the groove. At later times low density material comes from the
walls and plasma jet streams out of the groove. At ∼1 ns, the electron
density is determined to be 1.2 ×
1021cm−3 in the groove corners which is higher
than the critical density of the laser heating beam. It should be possible
to measure significantly higher electron densities with this technique by
heating more target mass using higher energy beams focused to high
intensity.
Groove target 100 × 200 × 1000 μm3 (H
× D × L) viewed along the long axis. Laser pulse incident from
right. Top image shows interferogram before the laser pulse. Lower image
is recorded at 0.6 ns after the peak of the laser pulse for line focus
plasma of 12 μm (FWHM) width × 0.31 cm at a laser intensity of
∼1013 W cm−2.
We have recently performed experiments to study long laser pulses
incident in a tight focal spot on small lollipop targets to complement the
lower intensity line focus plasma column experiments. Figure 5 shows two 14.7 nm soft X-ray interferograms
of a 50 μm diameter lollipop target irradiated with a 20 J, 5 ns, 1064
nm flat top pulse generated by the JANUS laser. This beam is focused to 20
μm (FWHM) diameter spot that corresponds to an intensity of
1015 W cm−2 on target. The target is
constructed by etching a Si wafer 50 μm thick then coating on both
sides with 7 μm parylene-C. The interferogram before the laser pulse
is shown in Figure 5(a). As in the previous
examples, the target is viewed from the side. Figure
5(b) at +4.8 ns, very close to the end of the laser pulse, shows
the laser beam is incident from the right with strong plasma self-emission
clearly visible on that side. The fringe shifts on the backside (left) of
the target indicate plasma formation. The interferometer has been setup so
that the plasma will induce fringe shifts toward the left. The lateral
plasma expansion on the back surface is slightly larger than 100 μm
with some indication that the target has disintegrated at the top. It is
interesting to note that the plasma appears on the backside at fairly
early times in the pulse, and is expected to be mainly produced by plasma
from the front surface streaming round the target, rather than back
surface release from laser-induced shock. While it would require Abel
inversion to de-convolve the electron density profile, an estimate of the
electron density can be deduced from the fringe shifts and plasma size. We
estimate that the electron density is in excess of 5 ×
1021 cm−3 for Figure
3(b) but a full analysis is required with a more symmetrical 2D
fringe pattern for more precise density measurements.
50 μm diameter lollipop target consisting of 50 μm thick Si
coated with 7 μm parylene–C on each side viewed from the edge.
(a) Interferogram of target before laser pulse. (b)
Interferogram recorded at +4.8 ns after the start of the pulse. Laser
pulse incident from right.
4. CONCLUSIONS
Picosecond X-ray laser interferometry at 14.7 nm of laser-produced
plasmas has been successfully demonstrated using a Mach-Zehnder
diffraction grating interferometer. The combination of short wavelength
and short pulse duration of the source and the high throughput of the
instrument presents a unique diagnostic capability to study large, hot,
dense plasmas. This technique can be applied to different target plasma
geometries and has the potential to benchmark 2D hydrodynamic simulations
codes under a wide range of conditions. In addition to extracting 2D
density information from the interferograms, the technique can also
quantify the degree of plasma ionization in low temperature aluminum
plasmas. Plasmas created with laser pulses over 100 J of energy, and
intensities up to 1015 W cm−2 have been
studied, and soft X-ray interferograms have been recorded with ∼1
μm spatial resolution close to the target surface. It is particularly
important to note that the source, technique and instrumentation can be
scaled to shorter wavelengths and can be applied to large plasmas
generated on the National Ignition Facility and other large-scale, very
dense plasmas. Further data analysis and simulations are in progress and
will be reported shortly.
ACKNOWLEDGMENTS
Work performed under the auspices of the US Department of Energy by
the University of California Lawrence Livermore National Laboratory under
Contract No. W-7405-Eng-48, through the Institute for Laser Science and
Applications and by the National Nuclear Security Administration under the
Stewardship Science Alliance Program through the US Department of Energy
grant No. DOE-FG03-02NA00062.
