Laser absorption, power transfer, and radiation symmetry during the first shock of ICF gas-filled hohlraum experiments

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1 Laser absorption, power transfer, and radiation symmetry during the first shock of ICF gas-filled hohlraum experiments A. Pak, 1 E. L. Dewald, 1 O. L. Landen, 1 J. Milovich, 1 D. J. Strozzi, 1 L. F. Berzak Hopkins, 1 D. K. Bradley, 1 L. Divol, 1 D. D. Ho, 1 A. J. MacKinnon, 1 N. B. Meezan, 1 P. Michel, 1 J. D. Moody, 1 A. S. Moore, 1 M. B. Schneider, 1 R. P. J. Town, 1 W. Hsing, 1 and M.J. Edwards 1 Lawrence Livermore National Laboratory, Livermore, CA, 9455, USA (Dated: 8 November 215) Temporally resolved measurements of the hohlraum radiation flux asymmetry incident onto a bismuth coated surrogate capsule have been made over the first two nanoseconds of ignition relevant laser pulses. Specifically, we study the P2 asymmetry of the incoming flux as a function of cone fraction, defined as the inner-to-total laser beam power ratio, for a variety of hohlraums with different scales and gas fills. This work was performed to understand the relevance of recent experiments, conducted in new reduced-scale neopentane gas filled hohlraums, to full scale helium filled ignition targets. Experimental measurements, matched by 3D view factor calculations are used to infer differences in symmetry, relative beam absorption and cross beam energy transfer (CBET) employing an analytic model. Despite differences in hohlraum dimensions and gas fill, as well as in laser beam pointing and power, we find that laser absorption, CBET and the cone fraction at which a symmetric flux is achieved, are similar to within 25% between experiments conducted in the reduced and full scale hohlraums. This work demonstrates a close surrogacy in the dynamics during the first shock between reduced-scale and full scale implosion experiments and is an important step in enabling the increased rate of study for physics associated with inertial confinement fusion. I. INTRODUCTION To optimize the performance from an indirectly driven inertial confinement fusion (ICF) implosion the symmetric compression 1 of the spherical fusion target is required. In the indirect drive approach being conducted at the National Ignition Facility (NIF), a spherical fusion capsule target is placed within a hollow gold lined cylinder called a

2 hohlraum 1,2. The 192 laser beams of the NIF irradiate the inner wall of the hohlraum producing an x-ray flux that ablates the surface of the capsule target outward and by conservation of momentum, drives the implosion inward. Ignition hohlraums are typically 6 mm in diameter and 1 mm long. Previously, hohlraums have been filled with helium gas at cryogenic temperatures to reduce wall motion for the duration of the laser pulse in order to maintain the uniformity of the x-ray flux around the capsule surface. The laser pulses consist typically of a carefully timed succession of 2-4 steps in power launching shocks that optimally compress the capsule. In this work, the interplay between hohlraum fill inverse Bremsstrahlung absorption, cross beam energy transfer (CBET) 3 and the incident radiation asymmetry at the capsule surface during the time period of the first shock will be examined. The discussion will focus on understanding these dynamics for experiments conducted in a new reducedscale, room temperature (293 K), neopentane gas filled hohlraum. In order to compare the amount of laser beam absorption, CBET and incident radiation asymmetry between reduced-scale and full scale hohlraums, a new model is developed that uses view factor calculations, experimental data and analytic relationships to infer the relative amount of laser beam absorption and CBET. The reduced-scale neopentane gas filled hohlraum, known colloquially as the warm subscale platform, has been developed to enable the rapid and comprehensive study of physics related to integrated ICF implosions, including the evolution of implosion symmetry with convergence, as well as the Rayleigh- Taylor instability growth of preimposed density perturbations 4. Compared to full-scale ignition experiments, the subscale platform uses smaller hohlraums and targets that are fielded at room temperature. This increases the number of available shot opportunities in three ways. First, these non-cryogenic targets are simpler than cryogenic targets and therefore can be made in less time and for a considerably smaller cost. Secondly by eliminating the 4-6 hours it takes for a target to cool and stabilize at cryogenic temperatures, more experiments can be performed in the same amount of time as a single full scale cryogenic experiment. Finally, the reducedscale allows for comparable hohlraum radiation temperatures as full scale targets while operating the laser at lower laser energies and powers, thereby significantly reducing the optical damage per experiment. This reduces the cost and the amount of time required to replace and refurbish optics that limits the number of high energy (>1 MJ) experiments that can be conducted. The increased number of warm subscale experiments will allow 2

3 testing of many different hypothesis. Concepts that are shown to improve the implosion performance will be scaled back up in laser energy and power and applied to cryogenic ignition relevant experiments. In order for this to be done efficiently, the warm subscale platform must be fully characterized and the surrogacy to experiments in the larger cryogenic hohlraums must be ascertained. This paper focuses on the symmetry of the x-ray flux at the capsule surface created between the first and second nanosecond of the radiation drive. This epoch of the radiation drive is known as the picket, and is very important in the dynamics of the implosion as it initializes the first shock symmetry and adiabat of the implosion. Due to the way in which the capsule is compressed by multiple coalescing shocks, asymmetries in the radiation flux during the picket persist and grow over time scales of 5 to 1 ns. Radiation hydrodynamic calculations suggest that the remaining residual momentum imparted by a picket radiation flux asymmetry reduces the central pressure and resulting nuclear performance of an implosion upon stagnation 5. The remainder of the paper is organized as follows. In section II details of the subscale hohlraum, laser pulse shape and experimental configuration used to measure the radiation flux symmetry will be given. Section III will detail how results from the experiment and view factor calculations are used as inputs into an analytic model that infers the amount of inner laser beam absorption and CBET. A comparison of these quantities and the resulting symmetry made in larger ignition scale helium filled hohlraums at cryogenic temperatures will also be made. In Section IV we will summarize our findings and discuss potential future work. II. EXPERIMENT The experiments were conducted at the NIF laser facility using subscale reemission type targets 6. A picture of the subscale reemission target and relevant dimensions are shown in Fig 1 a) and b), respectively. The hohlraum has a length of 8.26 mm, and an internal diameter of 4.26 mm. The hohlraum length and radius are reduced in scale by.816x from the dimensions of the extended length, so-called +7 µm, ignition scale hohlraum 7 used at the end of the National Ignition Campaign (NIC) 8. The hohlraum length was extended in order to accommodate an improved laser beam pointing configuration that reduces the x-ray flux asymmetry at the capsule. The target in these subscale reemission experiments is a plastic capsule that has been coated in bismuth to an outer radius of 8 µm. The outer bismuth 3

4 ϕ 3.1 mm 9 9 / mm 1mm a) 8.26 mm 1.6 mm 4.69 mm b) Laser Intensity (a.u.) Orientation (θ / ϕ) / z Outer cone Inner cone Outer cone c) FIG. 1. (Color online) a) A picture of the subscale reemission target during construction. Here the two halves of the hohrlaum are being joined vertically together. The silver band with the circular hole, through which the target is seen is part of the fixture that is used to assemble and metrologize the targets and is not part of the target itself. b) The dimensions and orientation of the hohlraum and capsule from orthogonal lines of sight. Here the orientation is described by the polar, θ, and azimuthal, φ, angles. The upper panel shows the target orientated along the hohlraum axis with the capsule visible through the 3.1 mm diameter LEH window. The shaded inset in the upper panel shows the azimuthal angle orientation. The lower panel views the target along the gated x-ray imager line of sight where the 1.6 mm diameter Bi coated capsule, is visible through the 2.35 mm diameter diagnostic window. c) VISRAD calculation showing the incident laser intensity at the hohlraum surface as seen from 9 /78. Here the 192 beams of the NIF laser are arranged to irradiate the hohlraum in three azimuthal rings positioned at 3 different z locations along the hohlraum axis. The false color on the capsule shows the resulting incident radiation flux. layer is 12 µm thick and is used to efficiently diagnostic holes are covered by a 1 µm thick reradiate the incident x-ray flux to infer the polyimide window to allow the hohlraum to uniformity (symmetry) around the capsule by be filled with gas, while still allowing for the soft x-ray imaging. To view the reemission of transmission of x-rays of energy 8 ev x-rays from the capsule, two diagnostic holes, to the gated x-ray detector9 (GXD) located each 2.35 mm in diameter have been made along the line of sight. The rear diagalong the equatorial axis at an azimuthal an- nostic window at minimizes the emisgle of and , respectively. The sion from the hohlraum wall which can com4

5 promise the reemission signal. The upper and lower laser entrance holes (LEH s) are 3.1 mm in diameter and are each covered by a 5 nm thick polyimide window to allow for the hohlraum to be filled with gas. In an analogous manner to cryogenic hohlraums, the warm subscale hohlraum is filled with gas to improve the control of radiation flux symmetry by impeding hohlraum wall motion that is triggered by laser ablation. In the NIC, implosions were performed at temperatures ranging between 18 and 24 K, and the hohlraum was filled with helium gas to a density of.96 mg/cm 3 ( torr). This density would exceed the pressure that can be contained by the LEH windows using helium gas at the initial subscale hohlraum temperature of 293 K. In order to reduce the fill pressure, the neutral particle density was reduced in the warm subscale hohlraum by using neopentane (C 5 H 12 ) gas. Neopentane has an average atomic mass of 4.24 and when fully ionized has an average charge state of These values are both comparable to those of the helium gas fill used in cryogenic implosions. The gas fill density of the subscale neopentane filled hohlraum experiments was chosen to be.824 mg/cm 3, to create the same average electron density of cm 3 that is obtained in the full scale helium gas filled hohlraum experiments. In these experiments, all of the 192 laser beams of NIF irradiate the hohlraum and create the x-ray radiation drive. The 192 beams are grouped into 48 quads, with each quad consisting of 4 beams. As shown in Fig. 1 c), the quads of the NIF laser are arranged to form three laser cones, two outer cones and one inner cone. Each cone consists of 16 quads and irradiates an azimuthal ring at three different longitudinal locations along the axis of the hohlraum. Defining the midplane of the hohlraum to be z=, in the subscale hohlraum the laser beams are nominally pointed such that the peak intensity of the outer laser rings occurs at a z = ±2.26 mm, while the inner ring intensity peaks at z= mm. The inner cone consists of quads which enter the hohlraum through the upper and lower LEH at angles of 23.5 (156.5 ) and 3 (15 ), with respect to the hohlraum axis. In these experiments a separation between the wavelengths of the outer beams and the inner beams was used to control cross-beam energy transfer. The outer beam wavelength was nm, the 23.5 (156.5 ) wavelength was nm and the 3 (15 ) wavelength was nm. Figure 2 a) shows the laser pulse shape configuration used in the reemission experiments. In these experiments, the power and duration of the laser pulse was chosen to create a similar first shock strength as used during the NIC campaign. The outer cone pulse 5

6 Power (TW) Temperature (ev) s 1 s 2 s 3 s 4 Inner Outer Truncated Inner b) Time (ns) a) Power (TW) Power (TW) Power (TW) Inner Outer Equivalent C.F. c) Inner Outer Equivalent C.F. d) Time (ns) Cone Fraction Cone Fration FIG. 2. (Color online) a) Requested laser power vs. time for the subscale reemission experiment N b) The measured radiation temperature vs. time (solid line) plotted with the temporal history of the total laser power (dashed line). The rectangles labeled S 1 4 denote the time at which the symmetry measurement is made on the four strips of the imaging detector. c) and d) show the temporal evolution of the inner and outer cone laser power and cone fraction with time for the two experiments, N14528 and N14525, respectively. The truncated inner beams were also used in these experiments (Fig. 2 a)) but are not shown in c) and d) for clarity. shape represents the combined laser power time history of the upper and lower outer cones. The inner cone is comprised of two pulse shapes. The inner pulse shape curve in Fig. 2 a) represents time dependent power of 1 of the inner cone quads, while the truncated inner pulse shape represents the shape and power of 6 of the inner cone quads. These 6 quads are truncated in reemission experiments because they strike portions of the two diagnostic windows. This can create sources of x-ray emission that overlap the reemission signal and reduce the fidelity of the measurement. To reduce background levels and increase the signal to noise ratio, these 6 quads are turned off 8 ps before the symmetry measurement is performed. This approach assures that the plasma conditions in the LEH region (where CBET occurs) are similar to those in implosion experiments. Keeping these conditions similar is important as they dictate the amount of CBET that occurs. Energy is transferred from the outer to inner beams where they spatially and tempo- 6

7 rally overlap as they cross one another in the region around the two hohlraum LEH s. The ponderomotive force from the beating of interfering lasers drives an ion acoustic wave. This acts as a Bragg grating, and transfers energy from the higher frequency outer beams to the lower frequency inner beams in the plasma rest frame. On NIF, an imposed wavelength shift between the inner and outer beams is used to control the amount of energy transferred. As power is transferred through an ion acoustic wave, the increase in inner beam power depends on the laser and plasma conditions with the approximate magnitude following the proportionality given by, where P inner P inner P outerp inner n e λ T e (1) is the change in inner beam power, n e is the electron density, T e is the electron temperature, λ = λ inners λ outers is the wavelength difference between the inner and outer laser cones, P outer and P inner are the incident outer and inner beam powers, respectively. In gas filled hohlraum experiments, at the peak of the laser power, CBET is used to control the incident radiation flux symmetry 3. Furthermore, this process has been shown to be present during the picket of the laser pulse where it also modifies the symmetry of the x-ray flux by transferring power from the outer to inner laser cones 1. The cone fraction is defined as, CF = P I P I + P O (2) and is ratio of the inner cone power, P I, to the total laser power, P T = P I + P O with P O being the outer cone power. In this work we will refer to a single cone fraction value for each experiment specified by the mean value of the cone fraction between the times of.6 to 1 ns. By varying the incident cone fraction of the laser, the symmetry of the capsule radiation flux can be varied 11,12. In the two experiments, N14525 and N14528, the change in the symmetry of x-ray flux at the capsule surface has been measured at two different incident laser cone fractions. In previous work, as the cone fraction was increased from.15 to.3, a linear decrease in the second Legendre moment amplitude of the incident x-ray flux was observed 1. Therefore, the cone fraction at which this asymmetry is minimized in the reduced scale hohlraum can be found by linearly interpolating between the two observations. The temporal history of the radiation temperature within the hohlraum that results from the NIF laser irradiation is measured by the DANTE 13 soft x-ray power detectors and is shown for experiment N14525 in Fig. 2 b). The magnitude of the radiation temperature is observed to peak at t 1.3 ns at a value of 9.2 ± 5 ev. In Fig. 2 b), each rect- 7

8 angle, labeled S 1 4, corresponds to the temporal extent of a individual strip on the four strip GXD detector used to make the symmetry measurement. As shown in 2 b), the peak radiation temperature and subsequent flux at the capsule surface occurs later than the peak laser power at early times. The reason for this is, at the beginning of the laser pulse the LEH and hohlraum plasma is relatively cold and opaque and absorbs a significant fraction of the laser power. As the plasma temperature rises, the absorption of the laser power decreases and the fraction of laser power that propagates to the hohlraum wall increases. This burn through process is responsible for the delay between the rise in hohlraum temperature and laser power observed 2 b). In two reemission experiments, N14528 and N14525, the radiation symmetry was varied by changing the full NIF equivalent inner cone fraction from.21 to.4, respectively. The requested total energy and peak power of the laser pulse for the two experiments was kept constant at 14.3 kj and TW, respectively. Figure 2 c) and d), show the inner and outer laser cone powers and the so-called full NIF equivalent cone fraction of the two experiments. The full NIF equivalent cone fraction is found by scaling the inner cone power used on the reemission experiment to account for the truncated inner quads and is given 1.6P I1 /(1.6P I1 +P O ), where P I1 is the power in the 1 inner cone quads with the full temporal picket pulse shape. In addition to the laser cone fraction, the symmetry of the radiation flux at the capsule is also dependent on the location at which the laser deposits energy at the hohlraum wall. In reemission experiments the upper static x-ray imager (SXI) diagnostic 14 observes the location of x-ray emission produced by the laser irradiating the hohlraum wall. The upper SXI images the hohlraum wall through the upper LEH window along the line of sight as shown in Fig. 3 a). The upper SXI diagnostic is temporally integrated and filtered by 2 µm of copper and 1 µm of polyimide which in this work limits the detected x-ray energies to below 93 ev. Figure 3 b) shows the VISRAD 15 calculation of the total deposited laser intensity for a cone fraction of.4. Figure 3 c) shows the upper SXI data recorded on experiment N14525 which was conducted with a cone fraction of.4. The location of a portion of the lower outer cone and central inner cone can be observed by the upper SXI diagnostic. Using the measured z location of the inner and outer ring, view factor calculations can be performed to determine the symmetry of the radiation flux at the capsule. These calculations will enable an estimation of the integrated laser absorp- 8

9 2 Inner Cone 2 ( mm ) 1-1 ( mm ) 1-1 Inner Outer Lower Outer Cone a) b) ( mm ) c) ( mm ) Intensity (a.u.) FIG. 3. (Color online) a) An illustration of hohlraum from the perspective of the upper SXI diagnostic line of sight. The SXI measures x-ray emission from the hohlraum wall through the upper LEH, which is denoted here by the dashed circle. b) VISRAD calculations of the deposited laser power for a cone fraction of.4. The upper SXI diagnostic observes emission from a portion of the inner and lower outer cone. The two dashed lines denote the location of the inner and lower outer cones at the hohlraum wall. c) The upper SXI data from experiment N14525 showing the position and relative intensity of a portion of the inner and outer cone. Here the scale refers to space in the plane of the LEH. tion by the hohlraum plasma and CBET that has occurred. The x-rays that are re-radiated by the bismuth capsule are temporally and spatially resolved by using a pinhole array to image the emission onto the GXD 9. Images at two different central photon energies are created by simultaneously varying the pinhole diameter and filter. The diameter and filtering alternates from 5 µm diameter pinholes paired with 2.5 µm of aluminum filtering and 1 µm diameter pinholes combined with 6 µm aluminum filtering. This filtering shifts the peak spectral intensity of the detected x-rays to higher energies than the peak spectral intensity that irradiates the capsule. This is done to increase the sensitivity of the measurement to relatively small (few percent) radiation flux asymmetries. The amplitude of the measured asymmetry of the remitted radiation is then reduced in scale by this sensitivity correction to infer the incident spectrally integrated radiation flux symmetry. Assuming the reemission spectrum follows a black body spectral shape, the incident symmetry is then given by the measured reemission symmetry divided by hν/4kt Remit as described in reference 12, where hν is the 9

10 a) Incident Laser Cone Fraction = b) Incident Laser Cone Fraction = Time = 1.35 ns Time = 1.48 ns Time = 1.7 ns Time = 1.83 ns FIG. 4. Spatially and temporally resolved images of the x-ray reemission from experiments N14525 (a) and N14528 (b), respectively. Here the x-ray reemission from the capsule is observed along the equatorial axis of the hohlraum from an azimuthal angle of 78. In this view the hohlraum axis and the poles of the capsule are orientated in up and down direction. The central ring of emission is the reemission from the capsule and is observed to be limb brightened. The outer ring of emission is residual emission from the hohlraum wall that can be seen through the diagnostic window. The images have been spatially blurred by spatial resolution of the pinhole ( 5µm) and temporally blurred over 1 ps by the gain width of the MCP detector. These images were filtered by 2.5 µm of aluminum, which places the peak of the transmitted x-ray spectrum at an energy of 66 ev. central energy at which the reemission measurement is made, T Remit is the corresponding to the temperature of reemission, and k is Planck s constant. The temperature is inferred from the ratio of signal levels between the 2.5 µm and 6 µm channels. For experi- 1

11 ments N14525 and N14528 T Remit was inferred to be 66 ± 5 ev. Figure 4 a) and b) shows the measured x-ray reemission images from the bismuth coated capsule at a central energy of 66 ev for experiment N14525 and N14528 with a cone fraction of.4 and.21, respectively. For each experiment, Fig. 4 shows four frames of emission data taken between 1.35 ns and 1.83 ns in time, with the reemission flux amplitude reaching a maximum at 1.45 ns, similar to the measured hohlraum flux in Fig. 2 b). The emission from the capsule is limb brightened and the symmetry of the radiation flux is measured by decomposing the angular variation of the emission amplitude along the limb into Legendre modes. This emission changes from being brighter along the waist of the capsule to being brighter at the poles of the capsule as the cone fraction was changed from.4 on N14525 to a cone fraction of.21 on N Around the capsule, emission from the hohlraum wall opposite of the GXD diagnostic can be observed through the diagnostic window. This emission changes in time due to slightly different viewing angle and parallax associated with the location of the pinhole which images the capsule at each time. Incident P2/P (%) FIG C.F. =.21 C.F.= Time (ns) (Color online) The amplitude of the incident x-ray flux symmetry as a function of time for incident cone fractions of.21 and.4. P2/P is the relative amplitude of the 2nd Legendre mode. The shaded grey band corresponds to the time of peak incident flux at the capsule. III. RESULTS The inferred temporal evolution of the x- ray flux asymmetry, expressed here as the relative amplitude of the 2nd Legendre mode (P2/P) is shown for both N14525 and N14528 in Fig. 5. In both experiments the asymmetry is dominated by the second Legendre mode. Positive values of P2/P indicate a relatively larger x-ray flux incident at the poles of the capsule, while negative values indicate a larger flux along the equator of the capsule. As the cone fraction was varied from.21 to.4 the inferred incident P2/P at the peak of the picket flux, denoted in Fig. 5 as the shaded gray band, was observed to change from 4.3±1.3% to -24.3±1.2%, respectively. In both experiments the ampli- 11

12 Incident P2/P (%) Incident P2/P (%) a) Equivalent Cone Fraction 2 Data 1 3D View factor 1 2 Data Neopentane reduced scale HYDRA Neopentane reduced scale HDYDRA Helium full scale b) Wall Cone Fraction FIG. 6. (Color online) a) The inferred magnitude of the incident x-ray P2/P asymmetry vs. the incident laser cone fraction. The red circles represent the experimental data. The blue squares and green dashed and dotted line represent 3D calculation results from HYDRA for the neopentane reduced scale and helium filled full scale +7 hohlraums, respectively. b) The inferred magnitude of the incident x-ray P2/P asymmetry now plotted vs. laser cone fraction at the hohlraum wall. The red crosses are the approximate time integrated x-ray cone fraction inferred from the SXI data and the green diamonds represent results from the 3D view factor calculations. tude of P2/P decreases over time. The amplitude of the P4/P mode at the peak of the picket x-ray drive was observed to be 3.3±1.3% and 6.7 ±2.2% for a cone fraction of.21 and.4, respectively. Figure 6 a) compares the inferred incident P2/P flux asymmetry at the peak of the x- ray flux to the predicted asymmetry from 3- D radiation hydrodynamic calculations performed using the code HYDRA 16. These calculations include inverse Bremsstrahlung absorption and estimate the amount of power transferred via CBET to the inner laser cone. The calculations also include the effect of the diagnostic windows on the radiation asymmetry. Here the flux asymmetry is plotted versus the incident laser cone fraction. While the slope of P2/P flux asymmetry is approximately the same in the data and calculations, the observed P2/P flux asymmetry magnitude is offset below the calculations by approximately 26 %. This indicates that the calculations are underestimating the relative power of the inner laser cone that reaches the hohlraum wall. Assuming the decrease in inner cone power was entirely due to under predicting the magnitude of CBET, the difference between the calculations and data could be accounted for by increasing the power transferred by CBET from the outer to inner cone by 1.8X. This discrepancy is not yet understood, and as discussed in IV will be addressed in future work. Figure 6 a) also shows the predicted radiation flux asymmetry for the full scale extended length he- 12

13 lium gas filled hohlraum. Again it is observed that the calculated rate of change in the P2 flux asymmetry with cone fraction is similar to both the data and the calculations of the neopentane filled reduced scale hohlraum. This is reassuring and expected as the reduced scale hohlraum size and length were derived directly from the full scale +7 µm hohlraum. While the relative response of the radiation flux asymmetry to changes in the cone fraction appear to be similar, the large offset in the magnitude in the P2 radiation flux asymmetry between the calculations performed in neopentane and those conducted with helium again point to issues with correctly calculating the amount of CBET and potentially absorption that is occurring in the neopentane gas filled hohlraum. Proceeding from here, a model based on data, view factor calculations, and analytic relations will be developed to assess and compare the symmetry, relative CBET and absorption present in the reduced and full scale gas filled hohlraum experiments. To model the incident flux symmetry at the bismuth capsule, 3-D view factor calculations computed by the VISRAD program 15 are used. The view factor calculation accounts for the geometry of the hohlraum and capsule, and uses the measured cone pointing at the wall as measured by the SXI diagnostic. SXI data indicates the the outer and inner cone are both shifted outwards away from z = by 615 µm and 86 µm, respectively. View factor calculations indicate that the observed shift in outer cone location increases the amplitude of P2/P by 6.5% from the nominal cone location. The change in inner cone location from the nominal pointing has a small 1% effect on the P2/P asymmetry. From the measured hohlraum radiation temperature (Fig. 2 b)), the albedo of the hohlraum and bismuth capsule in the VISRAD calculation is set to.55 which is consistent with previous work 1. The view factor calculation does not account for cross beam energy transfer or absorption of the laser through the hohlraum plasma. Therefore the cone fraction specified in the view factor calculation is the ratio of inner cone to total laser power at the hohlraum wall after CBET, and laser absorption has occurred. The cone fraction at the hohlraum wall can be estimated from the time integrated SXI data that measures the magnitude of x-ray emission from inner and outer quads. Equation 2 can be rewritten in terms of the cone fraction at the hohlraum wall and in terms of the power associated with individual laser quads as, CF w = 1 (3) P OQ P IQ here P OQ and P IQ represent the power of a single outer and inner quad at the hohlraum 13

14 wall, respectively. The total laser power of an individual quad can be estimated by taking the peak SXI signal level measured on an outer and inner quad, and multiplying it by the projected spot area on the hohlraum wall. This assumes that the x-ray SXI signal follows the same linear proportionality on the outer and inner quads and averages over the spatial distribution of intensity within the laser spot. The error in determining the wall cone fraction arises from signal to noise ratio of the measurement. At lower cone fractions, the signal from the inner cone is relatively weak and leads to relatively larger uncertainties in the inferred cone fraction. A comparison between the observed and calculated incident P2/P radiation flux asymmetry at the capsule versus laser cone fraction at the hohlraum wall is shown in Fig 6 b). In general the view factor calculation is in agreement with the observed symmetry and wall cone fraction data. This result indicates that the view factor calculations can indeed be used to model the radiation flux asymmetry at the capsule for these experiments. Through the matching of the observed symmetry, view factor calculations can be used to estimate the laser cone fraction at the hohlraum wall. This in turn will allow for an estimate of the magnitude of the cross beam energy transfer and inner beam absorption that occurs in different reemission experiments. These processes can be modeled analytically in two discrete and sequential steps, first allowing all of the power transfer to take place where the inner and outer beams overlap at the LEH and then estimating the amount of power absorbed due to inverse Bremsstrahlung. The resulting cone fraction at the hohlraum wall can be written, CF w = e κ IL I αp I e κ IL IαPI + e κ OL OβPO (4) here L O and L I refer to the path length from the LEH to the hohlraum wall for the outer and inner beams respectively. factor e κl The is the fraction of laser power that is transmitted through the hohlraum fill plasma. Laser power is absorbed through the inverse bremsstrahlung (IB) process 17. The average IB absorption coefficient κ has units of inverse length and can be expressed as, κ = ln(λ IB )Z eff n 2 e (1 n e n cr ) 1/2 n cr Te 3/2 (5) here κ has units of cm 1 and is a function of ln(λ IB ), the Coulomb logarithm associated with IB, the electron temperature T e in ev, the critical and electron plasma density n e and n cr, respectively in cm 3. To account for multiple species an effective charge state is used and defined by, Z eff = f j Zj 2 / f j Z j, j j where f j = n j / n j is the ion species fraction. For helium and neopentane, Z eff j equals 2 and 4.57, respectively. In Eqn. 4, α and β 14

15 represent the power multiplier resulting from CBET on the inner cone and outer cone, respectively. The relationship between the cone multipliers and the power after transfer is given by, αp I = P I (1 + ) = P I + (6a) P I βp O = P O (1 ) = P O (6b) P O where P I and P O are the incident inner and outer cone power, respectively, is the amount of power transferred from the outer beams to the inner beams. At the time at which the symmetry measurement is made, as a result of IB absorption, it is expected that the relative attenuation of the outer beams is less than the attenuation of the inner beams for two reasons. The first reason is that the path length of the outer beams to the hohlraum wall is 1.4X shorter than that of the inner beams. The second reason is that the electron temperature along the outer beams is calculated to be > 2X larger than the electron temperature along the inner beams. This results in an outer IB absorption coefficient that is much smaller for the outer beams than it is for the inner beams. The outer beam electron temperature is higher because the intensity of the outer beams, with their smaller beam diameter, is approximately 2.5X larger than for the inner beams. In the limit that the outer beam attenuation is small compared to the inner beam attenuation, and using the conservation relation for total power P T = αp I + βp O, with Eqn. 4, the inner beam multiplier α can be written as, α = CF w CF 1 [CF w + (1 CF w )e κ IL I] (7) where CF is the incident laser cone fraction given by Eqn. 2. This methodology was used to infer the attenuation and inner beam multiplier for a number of reemission experiments. Table I summarizes our findings. To test this approach, the incident symmetry of a near-vacuum hohlraum 18 (NVH) experiment, N14916, was first modeled. NVH experiments provide a good test of the model as they are conducted with a very low density gas fill,.3 mg/cm 3 He4, which minimizes the role of absorption. Additionally N14916 was performed with no wavelength separation between the inner and outer cones, which in conjunction with the lower electron density allows α 1. This experiment was conducted in a larger hohlraum, with a diameter of 6.72 mm, and a length of mm. The 3.9 mm diameter LEH of the larger NVH is covered with the same polyimide windows that are used in all other implosion experiments. The view factor model indicates that a wall cone fraction of.16, nearly equal to the incident cone fraction of.17, is required to match the observed radiation flux symme- 15

16 Exp. H D H L Gas Fill n e /n cr λ(3 /23 ) P T CF CF w P 2 P e κ IL I α N C 5 H / N C 5 H / N He / N He / N He.32 / N He / N He.1 / TABLE I. Parameters and results from several reemission experiments. Here Exp. denotes the experimental identification number, H D and H L are the hohlraum diameter and length in millimeters, respectively, the gas fill was varied between helium and neopentane, n e /n cr is the ratio of the electron density to the critical plasma density, λ is the wavelength separation in angstroms between the outer laser cone and the 3 and 23 inner laser cones, respectively, P T is the total laser power in TW, CF is the incident laser cone fraction, CF w is the inferred laser cone fraction at the hohlraum wall from VISRAD calculations, P 2 P denotes the magnitude of the incident flux asymmetry in the second Legendre mode, e κ IL I and α are the inferred the inner cone transmission and power multiplier coefficients, respectively. The uncertainty in α is found to be ±.1 and arises mainly from the uncertainty of the inferred incident P2/P flux asymmetry which is typically ±1% try. With this inferred wall cone fraction, Eqn. 7 can be rewritten to solve for e κ IL I, the transmission coefficient of the inner cone. For N14916, this transmission coefficient is inferred to be.92, which is consistent with the level of transmission expected for the low density hohlraum fill. We now move to modeling and comparing the relative CBET and IB absorption in gas filled hohlraums. For each scale hohlraum, the view factor calculations were used to determine the wall cone fraction that matched the observed capsule flux asymmetry. These calculations take into account the measured laser cone locations and dimensions of the different hohlraums and LEH s. Data from experiments N13111 and N11814 was used to infer the amount of attenuation and CBET that is occurring in the helium filled full scale 575 hohlraum. Using data from experiment N13111, in which the wavelength separation was set to zero, the transmission coefficient for the inner cone can be calculated in the same manner as discussed above and 16

17 was found to be.72. Using this value of the inner cone transmission in Eqn. 7, the inner cone multiplier, α, resulting from the CBET associated with the 1.83 Å wavelength separation between the inner and outer beams for experiments N11812 and N11814 was calculated to be 2 and 2.3, respectively. To estimate the relative difference in α that occurs in the subscale neopentane filled hohlraum, the inner cone transmission coefficient must first be estimated. This is required as no experiment was performed in the subscale neopentane filled hohlraum with λ =. In order estimate the transmission coefficient, κ must first be estimated using Eqn. 5. This in turn requires an estimate of T e C5 H 12, the plasma temperature along the inner beam path in the subscale neopentane hohlraum. This is done by first using the measured inner cone transmission coefficient for the helium filled hohlraum experiments together with the average inner cone path length of 5.28 mm and Eqn. 5 to infer T e He, the electron temperature of the helium plasma. From this method a T e He 1.25 kev was estimated. Using this temperature, an estimate for T e C5 H 12, can be found by accounting for the differences in the charge state and laser power used. For a laser heated plasma in steady state, the plasma electron temperature can be estimated by balancing the power absorbed by inverse bremsstrahlung with power lost to heat conduction 2,19, ( Z 2 eff ln(λ IB )ln(λ HC )( ne n T e = cr ) 2 P L 28λ 2 S(Z eff ) ) 1/5 (8) here T e is in units of kev, n cr is the critical density of the plasma, P L is in units of TW, λ is the laser wavelength in microns, S(Z eff ) is a Spitzer-Härm transport coefficient 2 that is a function of Z eff, ln(λ IB ) and ln(λ HC ) are the Coulomb logarithm associated with IB and heat conduction, respectively. As both the helium and neopentane filled hohlraum experiments had the same n e and were performed at the same laser wavelength, using Eqn. 8 the ratio of electron temperatures between the two experiments can be written as, T e C5 H 12 T e He = ( Z 2 eff C5 H 12 S(Z eff He )P L C5 H 12 Z 2 eff He S(Z eff C 5 H 12 )P L He ) 1/5 (9) here the approximations that the ratio of Coulomb logarithms was 1 and that P L CF w P T were used to calculate the temperature ratio between the two experiments. Using Eqn. 9, and the previously inferred value of T e He = 1.25 kev, T e C5 H 12 for N14525 and N14528 was estimated to be 1.6 and 1.8 kev, respectively. With an estimate of the plasma temperature in the neopentane filled hohlraum, Eqn. 5 can then be used to solve for the IB absorption coefficient. The transmission of the inner cone power through 17

18 4.63 mm of plasma in the neopentane filled subscale hohlraums was then estimated to be.62 and.66 for N14528 and N14525, respectively. As expected, it appears that the higher Z eff of the neopentane plasma allows for more laser energy to be absorbed, enabling higher electron temperatures to be reached compared to helium filled hohlraums. While the electron temperature is higher, the transmission of laser power on the inner cone, e κ IL I, is 7 14% smaller in the subscale neopentane hohlraum compared to larger full scale helium filled hohlraum experiments. Using the calculated inner cone transmission coefficient, the incident and inferred wall cone fraction, Eqn. 7 was evaluated to estimate an inner cone power multiplier for neopentane filled hohlraum experiments. An α of 1.8 and 1.5 was found for N14525 and N14528, respectively. Varying the simulated wall cone fraction, CF w, to encompass the uncertainty of the measured P2/P incident x-ray symmetry, varies α by ±.1. As the subscale experiments were performed with similar laser powers and average wavelength separations to the full scale helium filled hohlraum experiments N11812 and N11814 a relative comparison of CBET can be made. This analysis indicates an average relative decrease of 25% in the CBET induced inner beam power multiplier α between the subscale neopentane filled hohlraum and the nominal length full scale helium filled hohlraum experiments. While some of this decrease may arise from the higher expected plasma temperatures in the neopentane fill hohlraums, other factors such as the difference in laser beam pointing and overlap, may also play strong roles in the amount of CBET that occurs. For example, it is found that in experiment N13426, which was conducted in a helium filled full scale hohlraum that had been increased in length by 7 µm, that α = 1.7. Examining the proportionality of CBET given by Eqn. 1, a decrease in inner beam power transfer could be expected on N13426 compared to N11812 due to having a slightly lower wavelength separation however, the higher laser power should more than compensate for this effect. One difference between these two full scale experiments is the laser beam pointing. The change in inner and outer cone overlap could strongly effect the exact plasma conditions and interaction path length which in turn could modify the amount of CBET that takes place in these two experiments. Another interesting comparison that can be made between the different scale and gas filled hohlraums, is the incident picket cone fraction at which the P2/P x-ray flux asymmetry is minimized. To assess this, the surrogacy between a reemission target, with the 18

19 two large diagnostic windows, and a so-called ignition type hohlraum, without these windows, must first be made. As shown in Fig. 6 a), the data indicates that for the reemission target a symmetric (P2/P=) x-ray flux will be achieved at an incident laser cone fraction of.24. For ignition targets, there will be relatively more x-ray flux at the equator of the capsule at the same incident laser cone fraction compared to reemission targets. Using the view factor calculations, the offset in cone fraction to achieve the same incident P2/P symmetry between ignition and reemission hohlraums was found to be 4 %. This is consistent with 3D hydrodynamic calculations previously used to model the full scale reemission experiments 1. In this manner the incident picket cone fraction that produces a symmetric mode 2 x-ray flux in subscale neopentane filled hohlraum, using the picket pulse shape, peak power and wavelength separation discussed here, was found to be.2. As the reduced scale hohlraum dimensions were derived from the extended length ignition hohrlaum, it is of interest to compare the cone fraction at which a symmetric mode two radiation flux is achieved. From N13426, the reemission experiment conducted in the full scale extended length helium filled hohlraum, it was inferred that a incident picket cone fraction of.2 would produce a symmetric mode 2 radiation flux. Applying the view factor calculation offset to account for the diagnostic windows, it is expected that for a ignition hohlraum a cone fraction of.16 would produce a symmetric P2/P x-ray flux at the capsule surface. Since laser absorption and CBET between these two experiments were inferred to be within 1% of each other, we conclude that 25% increase in incident cone fraction arises from the differences in the cone pointing and relative LEH diameter. IV. CONCLUSIONS An overview of the reemission experiments used to determine the x-ray flux symmetry between the first and second nanosecond of implosion experiments conducted in the subscale neopentane filled hohlraum was presented. Three-dimensional view factor calculations, that accounted for the measured cone locations, were used to model the observed symmetry. Using the calculated laser cone fraction from view factor calculations in conjunction with analytic relationships, the relative amount of cross beam energy transfer and inner cone absorption across several gas filled hohlraum experiments was assessed. This model indicates that the experiments conducted in the reduced scale neopentane filled hohlraums had a relative reduction in transmitted inner cone power of 1% compared to the full scale helium filled 19

20 hohlraum experiments. The observed reduction in transmission is expected due to the increased inverse bremsstrahlung absorption of neopentane plasma. The model also indicates a relative decrease in α, the CBET induced inner cone power multiplier, of 25% in the reduced scale neopentane hohlraum experiments compared to the α inferred for experiments in the helium filled nominal length (9.43 mm) hohlraum. Interestingly, the relative inner cone power multiplier observed in the subscale neopentane experiments was comparable to that observed in the extended length hohlraum (1.13 mm) from which the subscale hohlraum dimensions were derived. This was not necessarily expected as the laser beam pointing and overlap, total laser power and wavelength separation were not held constant between the two experiments. It was also found that the incident cone fraction at which the P2/P asymmetry is minimized is.2 and.16 for the subscale neopentane filled hohlraum and extended length helium filled hohlraum, respectively. As we infer similar amounts of CBET and absorption between these two experiments, the differences are thought to originate from the differences in laser beam pointing, and relative LEH area. The x-ray flux symmetry predicted using the CBET model coupled with the radiation hydrodynamic code HYDRA under estimated the amount of power transferred by 1.8X in the reduced-scale neopentane gas filled hohlraum experiments. This discrepancy is not yet understood, but could arise from differences between the actual and calculated plasma conditions at the the hohlraum LEH region. Specifically, a reduced CBET amplitude would be expected if the simulated plasma density or simulated electron temperature was lower or higher, respectively, than the actual density and temperature. Future modeling work will explore this possibility by increasing the number of simulation zones around the LEH region and calculating CBET inline in the hydrodynamic code. Experiments conducted with increased amounts of power driving the first shock, in hohlraums with higher gas fill densities have recently shown improved performance 2. Full scale reemission experiments have confirmed, that much higher amounts of CBET occur during the first shock epoch due to the increased laser power and plasma density. With our current level of understanding, dedicated experiments would need to be performed to understand if there is a significant change in CBET in reduced scaled neopentane hohlraums with higher laser powers and densities than were examined in this paper. Besides the species of gas used to fill the hohlraum, several differences between the subscale and full scale experiments, including 2

21 the exact wavelength separation, laser power, and beam pointing preclude an exact determination on the cause for the reduction of CBET. To more accurately assess the apparent reduction in CBET, a series of experiments using the same scale hohlraum, laser power and wavelength separation could be conducted. For example, the transmission coefficients could first be determined by conducting reemission experiments with λ = in warm neopentane gas and cold (18-24 K) helium gas filled subscale hohlraums. The difference in CBET could then be inferred by measuring the asymmetry of the x-ray flux in helium filled subscale reemission experiments with the same wavelength separation as N14528 and N This would allow one to determine if the CBET is reduced by differences in plasma conditions created in helium versus neopentane filled hohlraums, or if the reduction arises from differences in laser beam pointing and dimensions between the full and subscale hohlraums. The authors sincerely thank the NIF operations staff who supported this work. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-7NA REFERENCES 1 G. Miller, E. Moses, and C. Wuest, NU- CLEAR FUSION 44, S228 (24). 2 J. Lindl, Physics of Plasmas (1994-present) 2, 3933 (1995). 3 P. Michel, L. Divol, E. A. Williams, S. Weber, C. A. Thomas, D. A. Callahan, S. W. Haan, J. D. Salmonson, S. Dixit, D. E. Hinkel, M. J. Edwards, B. J. MacGowan, J. D. Lindl, S. H. Glenzer, and L. J. Suter, PHYSICAL REVIEW LETTERS 12 (29), 1.113/PhysRevLett K. S. Raman, V. A. Smalyuk, D. T. Casey, S. W. Haan, D. E. Hoover, O. A. Hurricane, J. J. Kroll, A. Nikroo, J. L. Peterson, B. A. Remington, H. F. Robey, D. S. Clark, B. A. Hammel, O. L. Landen, M. M. Marinak, D. H. Munro, K. J. Peterson, and J. Salmonson, PHYSICS OF PLASMAS 21 (214), 1.163/ A. L. Kritcher, R. Town, D. Bradley, D. Clark, B. Spears, O. Jones, S. Haan, P. T. Springer, J. Lindl, R. H. H. Scott, D. Callahan, M. J. Edwards, and O. L. Landen, PHYSICS OF PLASMAS 21 (214), 1.163/ E. L. Dewald, J. Milovich, C. Thomas, J. Kline, C. Sorce, S. Glenn, and O. L. Landen, PHYSICS OF PLASMAS 18 (211), 1.163/ J. R. Rygg, O. S. Jones, J. E. Field, M. A. 21

22 Barrios, L. R. Benedetti, G. W. Collins, D. C. Eder, M. J. Edwards, J. L. Kline, J. J. Kroll, O. L. Landen, T. Ma, A. Pak, J. L. Peterson, K. Raman, R. P. J. Town, and D. K. Bradley, Physical review letters 112, 1951 (214). 8 M. J. Edwards, P. K. Patel, J. D. Lindl, L. J. Atherton, S. H. Glenzer, S. W. Haan, J. D. Kilkenny, O. L. Landen, E. I. Moses, A. Nikroo, R. Petrasso, T. C. Sangster, P. T. Springer, S. Batha, R. Benedetti, L. Bernstein, R. Betti, D. L. Bleuel, T. R. Boehly, D. K. Bradley, J. A. Caggiano, D. A. Callahan, P. M. Celliers, C. J. Cerjan, K. C. Chen, D. S. Clark, G. W. Collins, E. L. Dewald, L. Divol, S. Dixit, T. Doeppner, D. H. Edgell, J. E. Fair, M. Farrell, R. J. Fortner, J. Frenje, M. G. G. Johnson, E. Giraldez, V. Y. Glebov, G. Grim, B. A. Hammel, A. V. Hamza, D. R. Harding, S. P. Hatchett, N. Hein, H. W. Herrmann, D. Hicks, D. E. Hinkel, M. Hoppe, W. W. Hsing, N. Izumi, B. Jacoby, O. S. Jones, D. Kalantar, R. Kauffman, J. L. Kline, J. P. Knauer, J. A. Koch, B. J. Kozioziemski, G. Kyrala, K. N. LaFortune, S. Le Pape, R. J. Leeper, R. Lerche, T. Ma, B. J. MacGowan, A. J. MacKinnon, A. Macphee, E. R. Mapoles, M. M. Marinak, M. Mauldin, P. W. McKenty, M. Meezan, P. A. Michel, J. Milovich, J. D. Moody, M. Moran, D. H. Munro, C. L. Olson, K. Opachich, A. E. Pak, T. Parham, H. S. Park, J. E. Ralph, S. P. Regan, B. Remington, H. Rinderknecht, H. F. Robey, M. Rosen, S. Ross, J. D. Salmonson, J. Sater, D. H. Schneider, F. H. Seguin, S. M. Sepke, D. A. Shaughnessy, V. A. Smalyuk, B. K. Spears, C. Stoeckl, W. Stoeffl, L. Suter, C. A. Thomas, R. Tommasini, R. P. Town, S. V. Weber, P. J. Wegner, K. Widman, M. Wilke, D. C. Wilson, C. B. Yeamans, and A. Zylstra, Physics of Plasmas (1994-present) 2, 751 (213). 9 S. Glenn, P. M. Bell, L. R. Benedetti, D. K. Bradley, J. Celeste, R. Heeter, C. Hagmann, J. Holder, N. Izumi, J. D. Kilkenny, J. Kimbrough, G. A. Kyrala, N. Simanovskaia, and R. Tommasini, in PENETRATING RADIATION SYSTEMS AND APPLICATIONS XII, Proceedings of SPIE, Vol. 8144, edited by Grim, GP and Schirato, RC (SPIE, 211) Conference on Penetrating Radiation Systems and Applications XII, San Diego, CA, AUG 21-24, E. L. Dewald, J. L. Milovich, P. Michel, O. L. Landen, J. L. Kline, S. Glenn, O. Jones, D. H. Kalantar, A. Pak, H. F. Robey, G. A. Kyrala, L. Divol, L. R. Benedetti, J. Holder, K. Widmann, A. Moore, M. B. Schneider, T. Doeppner, R. Tommasini, D. K. Bradley, P. Bell, B. Ehrlich, C. A. Thomas, M. Shaw, 22

23 C. Widmayer, D. A. Callahan, N. B. Meezan, R. P. J. Town, A. Hamza, B. Dzenitis, A. Nikroo, K. Moreno, B. Van Wonterghem, A. J. Mackinnon, S. H. Glenzer, B. J. MacGowan, J. D. Kilkenny, M. J. Edwards, L. J. Atherton, and E. I. Moses, PHYSI- CAL REVIEW LETTERS 111 (213), 1.113/PhysRevLett N. Delamater, G. Magelssen, and A. Hauer, PHYSICAL REVIEW E 53, 524 (1996). 12 E. L. Dewald, C. Thomas, J. Milovich, J. Edwards, C. Sorce, R. Kirkwood, D. Meeker, O. Jones, N. Izumi, and O. L. Landen, REVIEW OF SCIEN- TIFIC INSTRUMENTS 79 (28), 1.163/ , 17th Topical Conference on High-Temperature Plasma Diagnostics, Albuquerque, NM, E. Dewald, K. Campbell, R. Turner, J. Holder, O. Landen, S. Glenzer, R. Kauffman, L. Suter, M. Landon, M. Rhodes, and D. Lee, REVIEW OF SCIENTIFIC INSTRUMENTS 75, 3759 (24), 15th Topical Conference on High-Temperature Plasma Diagnostics, San Diego, CA, APR 19-22, M. B. Schneider, O. S. Jones, N. B. Meezan, J. L. Milovich, R. P. Town, S. S. Alvarez, R. G. Beeler, D. K. Bradley, J. R. Celeste, S. N. Dixit, M. J. Edwards, M. J. Haugh, D. H. Kalantar, J. L. Kline, G. A. Kyrala, O. L. Landen, B. J. MacGowan, P. Michel, J. D. Moody, S. K. Oberhelman, K. W. Piston, M. J. Pivovaroff, L. J. Suter, A. T. Teruya, C. A. Thomas, S. P. Vernon, A. L. Warrick, K. Widmann, R. D. Wood, and B. K. Young, REVIEW OF SCIENTIFIC INSTRUMENTS 81 (21), 1.163/ , 18th Topical Conference on High-Temperature Plasma Diagnostics, Wildwood, NJ, MAY 16-2, J. MacFarlane, JOURNAL OF QUANTI- TATIVE SPECTROSCOPY & RADIA- TIVE TRANSFER 81, 287 (23). 16 M. M. Marinak, G. D. Kerbel, N. A. Gentile, O. Jones, D. Munro, S. Pollaine, T. R. Dittrich, and S. W. Haan, Phys. Plasmas 8, 2275 (21). 17 D. J. Strozzi, E. A. Williams, D. E. Hinkel, D. H. Froula, R. A. London, and D. A. Callahan, PHYSICS OF PLASMAS 15 (28), 1.163/ L. Berzak Hopkins, N. Meezan, S. Le Pape, L. Divol, A. Mackinnon, D. Ho, M. Hohenberger, O. Jones, G. Kyrala, J. Milovich, A. Pak, J. Ralph, J. Ross, L. Benedetti, J. Biener, R. Bionta, E. Bond, D. Bradley, J. Caggiano, D. Callahan, C. Cerjan, J. Church, D. Clark, T. Doppner, R. Dylla-Spears, M. Eckart, D. Edgell, J. Field, D. Fittinghoff, M. Gatu Johnson, G. Grim, N. Guler, S. Haan, A. Hamza, 23

24 E. Hartouni, R. Hatarik, H. Herrmann, D. Hinkel, D. Hoover, H. Huang, N. Izumi, S. Khan, B. Kozioziemski, J. Kroll, T. Ma, A. MacPhee, J. McNaney, F. Merrill, J. Moody, A. Nikroo, P. Patel, H. Robey, J. Rygg, J. Sater, D. Sayre, M. Schneider, S. Sepke, M. Stadermann, W. Stoeffl, C. Thomas, R. Town, P. Volegov, C. Wild, C. Wilde, E. Woerner, C. Yeamans, B. Yoxall, J. Kilkenny, O. Landen, W. Hsing, and M. Edwards, Physical Review Letters 114, 1751 (5 pp.) (215). 19 C. Back, J. Grun, C. Decker, L. Suter, J. Davis, O. Landen, R. Wallace, W. Hsing, J. Laming, U. Feldman, M. Miller, and C. Wuest, Physical Review Letters 87, 2753/1 (21). 2 O. A. Hurricane, D. A. Callahan, D. T. Casey, P. M. Celliers, C. Cerjan, E. L. Dewald, T. R. Dittrich, T. Doeppner, D. E. Hinkel, L. F. B. Hopkins, J. L. Kline, S. Le Pape, T. Ma, A. G. MacPhee, J. L. Milovich, A. Pak, H. S. Park, P. K. Patel, B. A. Remington, J. D. Salmonson, P. T. Springer, and R. Tommasini, NATURE 56, 343+ (214). 24

25 Orientation (θ / ϕ) / ϕ 9 9 / mm 2.35 mm 3.1 mm 8.26 mm Laser Intensity (a.u.) z Outer cone Inner cone Outer cone 1mm a) 4.69 mm b) c)

26 Power (TW) Temperature (ev) s 1 s 2 s 3 s 4 Inner Outer Truncated Inner b) Time (ns) a) Power (TW) Power (TW) Power (TW) Inner Outer Equivalent C.F. c) Inner Outer Equivalent C.F. d) Time (ns) Cone Fraction Cone Fration

27 2 Inner Cone 2 ( mm ) 1-1 ( mm ) 1-1 Inner Outer Lower Outer Cone a) b) ( mm ) c) ( mm ) Intensity (a.u.)

28 Time = 1.35 ns Time = 1.48 ns Time = 1.7 ns Time = 1.83 ns a) Incident Laser Cone Fraction = b) Incident Laser Cone Fraction =