Plasma-based beam combiner for very high fluence and energy

Abstract

Extreme optical fluences, much beyond the damage threshold of conventional optics, are of interest for a range of high-energy-density physics applications. Nonlinear interactions of multiple beams in plasmas have the potential to produce optics that operate at much higher intensity and fluence than is possible in solids. In inertial confinement fusion experiments indirectly driven with lasers, many beams overlap in the plasma inside a hohlraum, and cross-beam energy transfer by Brillouin scattering has been employed to redistribute energy between laser beams within the target. Here, we show that in a hot, under-dense plasma the energy of many input beams can be combined into a single well-collimated beam. The emerging beam has an energy of 4 kJ (over 1 ns) that is more than triple that of any incident beam, and a fluence that is more than double. Because the optic produced is plasma, and is diffractive, it is inherently capable of generating higher fluences in a single beam than solid-state refractive or reflective optics.

Full text

ARTICLES
PUBLISHED ONLINE: 2 OCTOBER 2017 | DOI: 10.1038/NPHYS4271
Plasma-based beam combiner for very high
fluence and energy
R. K. Kirkwood1*, D. P. Turnbull1,2, T. Chapman1, S. C. Wilks1, M. D. Rosen1, R. A. London1,
L. A. Pickworth1, W. H. Dunlop1, J. D. Moody1, D. J. Strozzi1, P. A. Michel1, L. Divol1, O. L. Landen1,
B. J. MacGowan1, B. M. Van Wonterghem1, K. B. Fournier1and B. E. Blue1
Extreme optical fluences, much beyond the damage threshold of conventional optics, are of interest for a range of high-energy-
density physics applications. Nonlinear interactions of multiple beams in plasmas have the potential to produce optics that
operate at much higher intensity and fluence than is possible in solids. In inertial confinement fusion experiments indirectly
driven with lasers, many beams overlap in the plasma inside a hohlraum, and cross-beam energy transfer by Brillouin scattering
has been employed to redistribute energy between laser beams within the target. Here, we show that in a hot, under-dense
plasma the energy of many input beams can be combined into a single well-collimated beam. The emerging beam has an
energy of 4 kJ (over 1ns) that is more than triple that of any incident beam, and a fluence that is more than double. Because
the optic produced is plasma, and is diractive, it is inherently capable of generating higher fluences in a single beam than
solid-state refractive or reflective optics.
Extreme optical fluences, much beyond the damage threshold of
conventional optics, are of interest for a range of high-energy-
density physics (HEDP) applications1. Existing techniques
maintain the fluence internal to the laser system below the damage
threshold by using large-area solid-state optics2,3, and subsequently
increase the fluence by focusing the beams to small spots as they
propagate through vacuum to the target4,5. Such techniques have
also been enhanced by using the nonlinear optical properties of
solids to allow operation at higher power and energy, including the
use of Raman scattering to combine multiple beams in damage-
resistant solid materials6.
Nonlinear interactions of beams in plasmas have the potential to
produce plasma-based optics that operate at much higher intensity
and fluence than is possible in solids. Accordingly, the application
of plasma optics to overcome the limitations of solid materials in
reaching extreme laser intensities has received considerable study in
recent years7–24. The phenomenon of stimulated scattering in plas-
mas, either Brillouin (SBS) or Raman (SRS), is known to produce
diffractive cells of plasma waves that can scatter light with high
spatial coherence to produce small angular regions of scattering that
have fluence and intensity well beyond what solid materials can
withstand. The seeding of these instabilities is being developed to
manipulate and control the scatter, with the preponderance of recent
attention being given to the resonant Raman backscattering mech-
anism9–11 because of its potential to create extremely short, high-
intensity pulses. A series of experiments with low-energy lasers have
already demonstrated both amplification and pulse compression
of high-intensity pulses with durations from a few picoseconds to
sub-picoseconds12–16, and limiting physical mechanisms have been
identified17. More recent efforts toward reaching ultrahigh laser
intensities have considered weakly and strongly coupled stimulated
Brillouin scattering in plasmas, both alone and in conjunction with
Raman scattering18–23.
During inertial confinement fusion (ICF) experiments indirectly
driven with lasers, many laser beams overlap in plasma inside
a hohlraum. In such experiments, Brillouin scattering has been
employed to usefully redistribute energy between quads of laser
beams within the target on the nanosecond timescale to tune the
symmetry of the X-rays driving the implosion using a technique
known as cross-beam energy transfer (CBET)25–27. Use of CBET
has allowed the production of fusion energy to be increased and
models of alpha particle heating to be tested28,29, but hydrodynamic
evolution of plasma conditions and the resultant uncertainty
in interpreting measurements have made the properties of the
amplified beams difficult to diagnose. Further, the technique has
not previously been used to create an isolated plasma optic that
produces a single beam that emerges from the optic brighter than
the individual pumps and which can be incident on other targets.
In this work we show that CBET in a hot, under-dense plasma
can be used to transfer energy from multiple beams to a single
beam that emerges well-collimated and with a fluence and energy
that exceeds that of any of the individual beams incident on the
plasma in the same time period. Our observations are consistent
with an output beam radiance that is also higher than that of the
incident beams. Because the optic is plasma-based, the maximum
fluence and intensity it transmits is much higher than is possible
from solid-state optics. Furthermore, as a diffractive optic, it is not
subject to the limitations of refractive and reflective optics that must
conserve the etendue of a beam (the product of the area of the
spot at best focus and solid angle of the beam)30. As a result, the
optic we have produced reduces the total etendue of the incident
light (that is, it reduces the product of the area of the overlapping
spots at best focus and total solid angle of the beams) to produce
a high-radiance collimated beam with lower total etendue. CBET
produces the highest energy 1 ns pulse of ultraviolet light available
at the NIF and is directly scalable to larger numbers of beams to
produce a still higher single-beam fluence, radiance and energy.
Such a beam combiner holds promise to advance a range of HEDP
applications that require high energy and fluence in collimated
beams to access the interior of complex targets31 or to maintain the
1Lawrence Livermore National Laboratory, Livermore, California 94551, USA. 2Laboratory of Laser Energetics, University of Rochester, Rochester,
New York 14623, USA. *e-mail: kirkwood1@llnl.gov
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ARTICLES NATURE PHYSICS DOI: 10.1038/NPHYS4271
Pump
beams
Fiducial
beams
Ta witness plate
ab
Seed
beam
Gas-filled
balloon
2.5
2.0
1.5
Incident power/beam (TW)
1.0
0.5
0.0
012
Time (ns)
3
Extended heater case A
Heater, all cases
Pump case B, C
Seed case B, C
Seed case A
Figure 1 | Beam combiner target. a,b, The gas-filled balloon target (10mm in major diameter) shown in ais used to create a uniform plasma to amplify a
single seed beam (red) by combination of eight pumping beams (yellow), each with the incident power shown in b, via seeded SBS forward scatter. In
addition to the two groups of pumps crossing the seed at 14.7◦and 20.7◦, the gas is ionized and heated with forty heater beams at larger angle (not shown
in a). A witness plate is used to diagnose the red-shifted seed beam energy as it emerges from the plasma via the relative brightness of the X-ray spots
created by it and by a fiducial set of beams (green). The 1-TW fiducial beam power is not shown in band has the same shape as the seed beam power.
light intensity over long interaction distances, as needed for Raman
pulse compression9–23 to operate with long-duration pumps.
The design of the plasma beam combiner uses a C5H12 gas-filled
balloon target pre-heated by 40 NIF beams to produce a uniform,
nearly stationary plasma over a cylindrical volume approximately
7 mm in length and 2 mm in radius with an initial electron density of
2.5% of the critical density of the 351-nm pump and seed beams, and
a peak temperature of 1.8keV, according to rad-hydro simulations
(described later). These conditions allow the seed beam to propagate
along the axis of the target with minimal deleterious effects,
such as loss to inverse bremsstrahlung absorption or defocusing
by filamentation, while allowing up to eight pumping beams to
intersect the seed beam at similar angles (see Fig. 1) and maintain
nearly resonant interactions with the ion acoustic waves produced
in the plasma by the interference with the seed beam.
The seed and pump beams are all f/20 and are focused to elliptical
focal spots at the centre of the gas balloon4. Each of the pump
beam wavelengths is shifted by 3.0 or 3.5Å to the blue of the seed
beam wavelength to allow the ion waves produced by the stimulated
amplification of the seed beam to be nearly frequency matched to
each pump beam throughout the entire volume over which they
intersect. This facilitates CBET to the seed beam via SBS forward
scattering of each pump that grows over a <∼3.6 mm distance
in the direction of the seed beam. As described in the Methods,
simulations indicate maximum gain exponents of 0.76 and 1.6 for
the linear growth of seed power produced by each of the two quads
of pump beams32. The pump beams have a power of 4.4TW equally
split between orthogonal linear polarizations.
The pump and seed beams as shown schematically in Fig. 1
terminate at a witness plate, located 12 mm from the crossing point.
The high-Z (Ta) witness plate converts optical intensity to X-ray
emission with a significant number of photons with keV energy,
which is imaged onto X-ray framing cameras and image plates for
diagnosis of the seed beam intensity. Calibration of the optical to
X-ray conversion factor is facilitated by an additional fiducial spot
produced by a set of four 1.0-TW beams with the same pulse shape
and timing as the seed beam and which directly irradiate the plate.
The fiducial beams do not pass through the balloon target or plasma
before they overlap at a different point on the Ta plate, as also shown
in Fig. 1. Figure 2 shows time-integrated images of the X-ray spots
on the witness plate.
A series of three experiments was conducted to demonstrate
the amplification of the seed. The first experiment, described as
case A, used the same heater beam pulse as the later experiments
but did not have any resonant pumping beams. This allowed the
transmission of a seed beam through the target to be determined
when there was no amplification from crossing beams, as well as
allowing the transmission to be determined when there was only
a minimal amplification by non-resonant crossing beams. In this
experiment the additional plasma heating that was produced in
other experiments, which have up to eight additional resonant pump
beams, was emulated by extending the pulse of eight of the 40 heater
beams for an additional 0.5ns, as shown in Fig. 1.
The 2-TW seed pulse was also extended to 1.2 ns duration to
allow time-resolved measurements of X-ray brightness both during
the period when no crossing beams were present and when the
eight non-resonant crossing beams were present. As described in the
Methods, the time-resolved measurements indicated that the power
transmission of the seed with no crossing beams was 65 ±13%,
consistent with simulation values, and that the seed transmission
when only eight heater beams were crossing was 85 ±15%.
Although the latter is not significantly different from the former,
and possibly influenced by small changes in plasma absorption at
the earlier time, it is also consistent with as much as a 1.2×power
amplification by the non-resonant extended heater pulses in the
plasma, similar to expectations32.
Experimental case B differed from case A in several ways. The
duration of the pulses was reduced as shown in Fig. 1, the seed
incident power (energy) was reduced to 0.75TW (kJ) and four
resonant crossing pump beams were added in an ∼f/8 group with
the centre of the group intersecting the seed at 14.7◦at the target
centre. This experiment demonstrated the increase in the total
energy in the seed beam that was produced by the four pumps
using an analysis of the brightness of the time-integrated amplified
seed spot shown in the centre frame of Fig. 2. The brightness is
seen to approach the brightness of the 2.4kJ spot in case A, and,
as described in the Methods, corresponds to 1.54 ±0.3 kJ being
delivered to the witness plate. Hence, the four resonant pump beams
caused a ∼2×increase in seed beam energy relative to its incident
value. Experimental case C was a repeat of case B with the addition
of another four resonant pump beams in a second ∼f/8 group
intersecting the seed at 20.7◦(for a total of eight pump beams).
In case C, a substantial increase in seed spot X-ray brightness was
observed, shown in the right-hand frame of Fig. 2. Analysis indicates
that 4.2 ±1 kJ of energy was delivered to the witness plate by
the amplified seed beam, representing a ∼5.7×increase in the
seed beam energy. The fact that the amplified seed beam energy
is significantly greater than the largest energy (1.1 kJ) incident in
any of the pump or seed beams during the 1ns seed pulse is the
primary result of this article. The observed 5.7×amplification
2
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NATURE PHYSICS DOI: 10.1038/NPHYS4271 ARTICLES
Case A
No resonant pump beams
Case B
Four resonant pump beams
Case C
Eight resonant pump beams
X-ray brightness (relative)
1
22
3
11
3
2
Figure 2 | Time-integrated measure of beam brightness. Three time-integrated images of the X-ray spots produced on the witness plate by the seed (1),
fiducial (2) and pump (3) beams are shown. The colour scale on each image is adjusted to make the brightness of the fiducial beams spot the same in all
cases, which calibrates the images relatively and compensates for the slightly dierent pulse length in case A. Case A shows the brightness and spot size
produced by the seed beam with 2.4kJ in 1.2 ns in its incident pulse when resonant pumps were not present, case B shows the same image when the seed
beam incident pulse was reduced to 0.75 kJ in 1ns and four resonant pump beams interacted with it, while case C shows the brightness when the number
of resonant pumps was then increased to eight. The brightness of the seed energy is seen to increase with the number of resonant pumps between cases B
and C, becoming greater than that produced with no pumps even when the incident seed power is much higher in case A.
100 µm
0.05
Case B
(PF3D simulation)
Case B
(measured)
Case C
(measured)
−0.05
0.00
0.05 0.100.00
x (cm)
−0.05−0.10 −0.10
x (cm)
y (cm)
0.05
0.00
−0.05
y (cm)
0.05
0.00
−0.05
y (cm)
0.05 0.100.00 −0.05
x (cm)
0.05 0.100.00
Figure 3 | Measured and simulated beam fluence. The measured X-ray brightness images are interpreted with simulations to produce a measured fluence
image of the amplified beams at the image plate as observed from the camera location as described in the Methods, and shown in comparison with the
spot shape of the unamplified beam (dotted ellipses). Also shown is a pF3D simulation of the shift produced in the spot centre when there is a single quad
of pump beams, asymmetrically crossing and amplifying the seed beam for comparison with observations in case B. The measured seed spot shown for
case C contains 4 ±1 kJ of energy in 1ns, when each of the eight resonant pumping beams delivered only 1.1 kJ in the same period, demonstrating the
creation of a brighter beam by plasma combination.
is a large fraction of the maximum amplification of ∼10×that
would be expected for growth of a linear wave in the presence of
the eight resonant pumps if the ion wave resonance is perfectly
matched throughout the volume and the polarizations of the beams
are optimally aligned, according to linear fluid theory32.
The amplified seed laser intensity incident on the witness plate is
inferred from the X-ray images and shown in Fig. 3 for cases B and
C. In case B, it is apparent that the brightest region of the seed beam
is shifted from the centre of the half-maximum contour that would
be produced by the incident, unamplified, beam (shown as the white
dashed lines). The shift is most prominent in this case because there
is only a single quad of pumping beams incident from one side of the
seed. The shift in case B is captured by simulations using the code
pF3D (ref. 33), where the experimental setup is reproduced with
plasma conditions obtained from separate HYDRA34 simulations
shown in Fig. 4 and described in the Methods. The simulations with
pF3D use NIF phase plates and resolve the resulting laser speckles.
The simulated amplified seed spot projected onto the witness plate
is shown in Fig. 3. Diagnosis of these simulations strongly indicates
that the observed shift is caused primarily by depletion of the pump
beams as they cross the seed, and to a lesser extent by the differing
gains associated with each pump beam resulting from simple polar-
ization and geometrical considerations. Our simulations produce a
2.3×amplification of the seed for case B. The small difference from
the experimentally measured value of 2.0×is likely attributable to
uncertainty in the inverse bremsstrahlung absorption occurring in
the balloon membrane.
The seed beam is observed to become better centred relative to
the spot of the unamplified beam in case C, where there were two
quads of pumping beams crossing the seed more symmetrically. The
size of the laser spot shown in Fig. 3 is estimated from the area within
an ellipse that best fits the half-maximum contour. This allows a
more accurate estimate of the fluence that the beam produced at
the witness plate; results are included in Table 1 and the technique
is described further in the Methods.
The observation of the size of the amplified spot on the witness
plate also gives an indication that the radiance of the amplified
beams is high, since the observed spots are not larger than the
incident spots after travelling a distance of ∼12mm from the focal
plane to the witness plate surface. Although precise determination
of the solid angle occupied by the amplified beam would require
more data on the spot size at a range of locations, simulations
indicate that the plasma and amplification effects do not move the
amplified beam waist from the centre of the amplification region.
Using this result with the properties of partially coherent beams35
allows the measured spot size at the witness plate in case C to put
an upper bound on the amplified beam etendue (spot size ×solid
angle) of 4 ×10−3mm2-steradians. This compares with a value of
3×10−3mm2-steradians for the incident f/20 seed, and allows an
estimate that the transmitted amplified beam has a radiance at least
2.7×greater than that of the incident seed or pump beams. Fur-
thermore, these accomplishments using CBET due to SBS forward
scatter are achieved without producing any measurable undesired
SBS backscatter (<100 J/beam) and negligible SRS backscatter.
These results have demonstrated a plasma optic technique for
generating high-energy and high-fluence optical beams. A 4 kJ, 1 ns,
high-f-number transmitted beam of ultraviolet light was formed
by combining nine beams that were frequency-tuned to resonantly
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ARTICLES NATURE PHYSICS DOI: 10.1038/NPHYS4271
C5H12 gas fill
log(ne)
(cm−3)
Temperature
(keV)
22
−4
Heater cones Pump cone
Seed beam
0 4 mm
21
20
19
2.0
1.5
ne
1.0
0.5
0.0
−4
Temperature
a
b
04 mm
Figure 4 | Target detail and simulated conditions. a, Balloon target and the plasma conditions produced in it by all incident beams. The C5H12 gas is
contained at the desired density by a thin membrane balloon mounted on a washer. b, Plots of the density and temperature predicted by two-dimensional
simulations at a time of t=2.0 ns near the end of the pulse of the 40 heater beams which intersected in the target. The plasma temperature and density
produced within ±1 mm of the axis of the seed beam are suciently uniform that eight frequency-shifted pump beams are all brought close to resonance
with the stimulated ion waves that are produced by beating with the amplified seed beam throughout the interaction volume.
Table 1 | Table of measured seed properties.
Seed properties
(shot number)
Incident energy
(kJ)
Transmitted energy
(kJ)
Transmitted energy
increase
Incident fluence
(kJ mm−2)
Transmitted fluence
(kJ mm−2)
Fluence
increase
Case A, no resonant
pumps (160905-002)
2.35 ±0.1 2.90 ±0.6 1.2×1.54 ±0.1 2.71 ±0.8 1.76×
Case B, 4 resonant
pumps (160208-002)
0.75 ±0.1 1.54 ±0.3 2.0×0.49 ±0.03 2.3 ±0.6 4.7×
Case C 8 resonant
pumps (160905-001)
0.74 ±0.1 4.2 ±1 5.7×0.48 ±0.03 3.7 ±1 7.7×
The table summarizes the fluence and energy of the seed beam both when it is incident on the plasma combiner and when it emerges onto the witness plate, and showsamplification factors of both
quantities in each of the three cases studied.
transfer energy to a single beam by CBET in a uniform plasma.
When deposited on a witness plate the resulting amplified seed
beam had higher fluence and intensity than any of the incident
beams and is also consistent with simulations. Our results indicate
a higher transmitted beam radiance than would be achievable with
conventional refractive solid-state optics. Furthermore, this plasma
beam combiner has produced a transmitted beam with nearly twice
the energy of any f/20 beam with a 1 ns duration that is available if
only the conventional optics of the NIF laser facility are used. Our
results pave the way for combining much more of the 40TW of
resonant pump power and 80+TW of non-resonant pump power
that is available at the NIF.
Methods
Methods, including statements of data availability and any
associated accession codes and references, are available in the
online version of this paper.
Received 15 May 2017; accepted 23 August 2017;
published online 2 October 2017
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Acknowledgements
The authors are indebted to the staff of the NIF laser facility for carrying out these
experiments and insuring that a large number of detailed requirements of the
experiments were met, as well as to B. Wallin and K. Budil for their encouragement of
this work. R.K.K. gratefully acknowledges the contributions of R. L. Berger in performing
the kinetic calculations of the parameters in used in equation (1), and the help of
M. M. Marinak in carrying out the Hydra simulations shown in Fig. 4.
Author contributions
The concept for the beam combiner design we describe was formulated and its design
carried out by R.K.K., R.A.L., S.C.W., K.B.F., D.P.T. and W.H.D. The development of the
technique to measure the transmitted beam properties was done by R.K.K., D.P.T., L.A.P.,
O.L.L., J.D.M. and M.D.R. The final phase of implementation and integration with the
NIF laser facility was carried out by R.K.K., S.C.W., D.P.T., L.A.P., T.C., L.D., P.A.M.,
J.D.M., O.L.L., D.J.S., B.J.M., B.M.V.W. and B.E.B., which included assessments of likely
output beam performance for its impact on the facility and optimally integrating the
experimental requirements with other facility demands. Actual execution of experiments
was carried out by D.P.T., R.K.K. and L.A.P. Post experimental pF3D simulations were
carried out by T.C., L.D. and P.A.M., and final revisions of the manuscript were
considered by all authors.
Additional information
Reprints and permissions information is available online at www.nature.com/reprints.
Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in
published maps and institutional affiliations. Correspondence and requests for materials
should be addressed to R.K.K.
Competing financial interests
The authors declare no competing financial interests.
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5

ARTICLES NATURE PHYSICS DOI: 10.1038/NPHYS4271
Methods
The beam combiner creates a nearly stationary plasma in which pumping beams
cross the seed beam and produce ion waves with a wavevector that is the difference
of the incident pump and seed beam wavevectors32. In a stationary plasma, these
ion waves will then be driven close to their resonant frequency when the frequency
difference between each pump and the seed beam is equal to the sound speed times
the ion wave’s wavenumber, which will depend only on the polar angle with which
each pump crosses the seed. As a result, identical-frequency pumps that cross the
seed from any direction will resonantly drive ion waves in the same region of
plasma if the angle they subtend with the seed beam is the same, and beams with
different crossing angles can drive waves resonantly with adjustments to each of
their wavelengths, allowing multiple pumps to be resonant to amplify the same
seed by SBS36. A similar geometry has also been described as beneficial for
amplification and compression by Raman backscatter24 and, when used for
Brillouin forward scatter by a cone of pumps crossing the seed at a small angle in a
plasma with little flow, keeps the frequency shifts required for resonance small and
similar for all pump beams.
The geometry of the beams at the NIF facility allows for four same-wavelength
pump beams to cross the seed with angles near 14.7◦(±3.1◦) and another four
with a different wavelength to cross at angles near 20.7◦(±2.4◦). The wavelengths
of these two groups of pump beams are shifted relative to the 351-nm seed beam by
0.1 nm and 0.12nm, respectively, to keep them near resonance in the expected
plasma conditions. Additional beams are used at crossing angles >∼40◦, which do
not resonantly drive ion waves and are used primarily to pre-heat the plasma. The
incident power time history and pointing of the 40 heater beams are designed to
produce a plasma with a temperature and density that allow the pumps to amplify
the seed with a sufficient linear gain rate of CBET32 while avoiding the
filamentation instability37, and to also produce a high enough electron temperature
that absorption of the beams by inverse bremsstrahlung is minimized.
The theoretical models used to describe the response of the plasma density to
the electromagnetic waves in this design32,38,39 have been validated with
experimental observations for cases where the wave amplitudes are small26,40,41.
However, the models are also known to over-predict wave amplitudes and scattered
power in many cases with large wave amplitudes where nonlinear wave saturation
becomes evident25,42–45. A key feature of this application of amplification of a seed
by multiple pumps via CBET is that a linear wave response allows a single
undepleted pump to produce a growth of the seed beam that is exponential in
space, with the total growth rate of the seed described by the sum of the growth
rates of the individual pump beams. Linear theory32 can be applied to small beam
crossing angles and the plasma materials used here to obtain the gain exponent G
for the expected spatial power growth exponent of the power of a weak seed beam
when it is resonant with many pumping beams given by equation (1).
G=1/8Σj(ωpe/ωo)2(vosc,j /ve)2(ωr,iaw,j /ωi,iaw,j)Ljωo,j /c(1)
Here, vosc,j =(e Ej/ωom)is the quiver velocity of the electrons due to the
component of the field of the jth pump beam that is aligned to the field of the seed
(Ej), ωr,iaw,j is the real part of the ion wave frequency driven by the jth pump
interacting with the seed beam, which has a wavenumber that is the difference of
the two electromagnetic wavenumbers, and ωi,iaw,j is the imaginary part of that
frequency. Further, ωpe is the electron plasma frequency, veis the thermal velocity
of the electrons, ωo,j is the frequency of the jth pump, Ljis the distance the seed
beam propagates while interacting with the jth pump, and cis the speed of light.
Because the C5H12 material contains two ion types there are two acoustic modes
propagating in the plasma and equation (1) can describe the resonance of either
mode, by using the appropriate ωiaw,j to represent each mode. When using a fully
kinetic value of ωiaw,j (ref. 46) it is found that the Gvalues are numerically
approximately the same for both modes for this case, and that value is used to
calculate the gain exponents stated above. However, the situation is more
complicated for the evaluation of the wave resonance frequency, and the
wavelengths of the beams were selected considering the presence of both modes,
the expected plasma non-uniformity as well as facility limitations. Equation (1) is
consistent with simulations of CBET in hohlraums that showed more than one
pump can affect a beam’s amplification39 and has been specifically validated with
previous observations in experiments using multiple pumping beams40. Moreover,
there are both simulations and confirming experiments showing that a beam can
be amplified by interaction with more than one pump beam with separately tuned
wavelengths47,48. Equation (1) gives the maximum exponent of the seed beam
amplification that would be obtained if ion acoustic waves are resonant everywhere
and remain linear, and pumps do not deplete, and is useful as an upper bound
estimate of the performance of the multi-beam plasma combiner.
In these experiments the beams had the power pulse shapes shown in Fig. 1 and
were incident on a target that was a thin nearly spherical polyimide membrane
filled with C5H12 gas such that the electron density in the gas, once ionized, was
2.5 ×1020 cm−3. Eight heater beams were pointed to each of five points along the
axis of the seed, corresponding to z=0, ±1.5, ±3.0 mm, as shown schematically in
Fig. 4. The pump beams were also pointed to z=0 and were turned on well before
the seed so they pre-heat the plasma. All beams had phase plates that made their
spots elliptical at best focus, with radii ranging from 0.82 ×0.59 mm to
0.63 ×0.37 mm on each beam4. All heater and pump pulses began at low power to
allow the high-density material in the balloon membrane to be heated and expand
before ramping up to their peak power to reduce the possibility that SBS
backscatter would be produced.
Two-dimensional HYDRA simulations34 were carried out to determine the
plasma conditions. The heaters and pumps were modelled as cones of incident light
that are symmetric around the axis of the seed beam and intersect it at each of the
five pointing locations. The minimum cone thickness near best focus in the
simulation was adjusted to represent the appropriate minimum beam spot size.
This two-dimensional representation is sufficient to determine plasma conditions
in the region near the axis in which the seed beam propagates. The results of
simulations shown in Fig. 4 predict that by t=2ns a sufficiently uniform plasma
density and electron temperature is created so that the ion waves are driven near
resonance throughout most of the interaction volume. Maintaining the resonance
over this large region is desirable for efficient beam combination both because it
allows the seed to collect energy from all parts of the pump beam’s transverse
profile, and because spreading the energy transfer over a large volume keeps ion
acoustic wave amplitudes low, mitigating effects of the nonlinear wave saturation,
which would limit the efficiency of energy transfer41–44. The HYDRA simulations
further showed that these conditions would not produce significant deleterious
secondary instabilities such as filamentation, or Brillouin and Raman scatter, as the
threshold for ponderomotive filamentation37 remains >10×above the average
intensity of our amplified seed beam profile and the growth exponent for Brillouin
backscatter is ∼5, Raman backscatter ∼3, and Raman forward scatter still lower49.
The seed beam was applied at 2.1 ns with the rectangular pulse shape shown in
Fig. 1. The simulated plasma conditions for the duration of the seed beam and the
resonance conditions needed to maximize the gains in equation (1) determined the
optimum wavelengths for the two groups of pump beams to best maintain
resonance of all pumps throughout the spatial region and temporal period that the
pumps and seed pulse interacted.
The transmitted beam power and energy is ascertained from the images of the
X-rays emitted from the Ta witness plate placed 12 mm from target centre and
tipped to be near normal to the seed beam. Pinhole imaging in the equatorial plane
views the plate 58◦off-normal. The data shown in Fig. 2 are the time-integrated
images of the Ta witness plate obtained with an X-ray camera that used an image
plate detector that is sensitive to X-ray photons in the keV energy range, and was
filtered with 10-µm-thick Al (refs 50,51). The four bright spots were produced by
the elliptical spot of the seed beam at near normal incidence to the foil, each of two
groups of four pump beams that were imperfectly overlapped to produce two
structured pump spots, and a fourth large spot produced by the four fiducial beams
incident at 60 degrees from the foil normal and overlapping on the foil surface.
A quantitative comparison of the brightness of the seed and fiducial spots is
simplified because they have the same pulse shape. In this geometry, the bright
central region of the X-ray spot produced by the 4TW in the fiducial beams has
nearly the same laser intensity incident on the foil surface as the seed beam would
with 2 TW of power, owing to the doubling of the fiducial spot area by its larger
incidence angle. The fiducial beam power is maintained constant for all
experiments, so a similar brightness in the peak of the seed and the fiducial spots in
the same image thus indicates when the seed power approaches the 2-TW level, as
is observed for example in both case A and B. Further, simulations of the X-ray
emission produced by a uniform spot on the plate50,52 show that when the seed
beam intensity is varied between 0.5×and 4×of the fiducial beam intensity the
X-ray power spectrum from 200 eV to 3keV of photon energy has little time
dependence for the 1 ns duration of the incident power and varies monotonically
with incident seed intensity. The simulated dependence of spot spectral brightness
versus incident intensity is then used to determine the incident light intensity in the
seed spot image at positions where its brightness is different from the brightness at
the centre of the fiducial spot by integrating the product of simulated X-ray spectra
and the known instrument spectral sensitivity function51 over photon energy. In so
doing, a simulated variation of camera brightness of 20:1 is produced over the
range of the intensities studied, similar to work described for time-resolved
instruments in ref. 50.
This analysis then allows the X-ray brightness shown in the X-ray images in
Fig. 2 to be interpreted as an absolute measure of incident laser fluence versus
position on the witness plate by calibrating the brightness measured at the centre of
the fiducial spot as representing the known laser fluence there, and all other
brightnesses measured in the seed spots as representing a correspondingly higher
or lower intensity using the simulated functional dependence of image brightness
on laser intensity50. The resulting fluence versus position on the image plate surface
as viewed from the imaging system is shown for cases B and C in Fig. 3.
Subsequently, an integral of this measured fluence over the observed seed spot
allows the total transmitted energy in the seed beam to be determined, which is
stated in Table 1 for each of the three cases. When performing the integral it is
recognized that the image noise floor and a rapidly decreasing X-ray brightness at
lower laser fluence can prevent accurate detection of fluence in the wings of the
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NATURE PHYSICS DOI: 10.1038/NPHYS4271 ARTICLES
laser spot profile, which, although low compared to the peak values, could persist
over much larger areas and introduce significant uncertainties in the total energy
values. Estimates of this effect are included in the uncertainties in the reported
energies listed in Table 1.
In addition to time-integrated measurements with the image plate,
time-resolved images, also filtered with 10µm of Al, were captured along the same
line of sight with an X-ray framing camera50. A series of six images of the plate are
obtained in each experiment at different times throughout the duration of the seed
pulse, each with a 40 ps gate duration. The time-resolved image of case A has
allowed the determination of the seed power (and therefore the transmission
through the target) at both 2.6 ns, when only the seed and the eight heater beams
with extended pulses were on, and at 3.3ns, when only the seed beam was on. The
analysis of these images produced measurements of the power in the seed beam in
each of these time periods, and proceeded in the same manner as for the
time-integrated data, with the simulated photon spectral emission being convolved
with the different spectral sensitivity of the time-resolved instrument to produce a
different image brightness versus laser intensity function. The power measured at
3.3 ns was 1.4TW with 2.1 TW incident in the seed beam at that time, indicating
the transmission value stated above. The power delivered to the plate at 3.3 ns is
alternatively determined from the incident power and accurate modelling of the
plasma absorption, and is found to be in good agreement with the 1.4TW
determined by analysis of the X-ray spots, which supports the estimated accuracy
of the X-ray measurements. The power measured at 2.6ns was 1.7 TW when
2.0 TW was in the incident beam, which again gives the transmission value of 85%
stated above. An analysis of the time-resolved images in experimental cases B and
C was limited by saturation of portions of the images, but confirmed that the seed
output power in six different time periods during the 1 ns did not vary by more
than a factor of two from its time averaged value in case C, consistent with models.
Data availability. The data that support the plots within this paper and other
findings of this study are available from the corresponding author upon
reasonable request.
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