In a National Ignition Facility (NIF) cylindrical hohlraum, any specular reflection (“glint”) off the wall from the outer cone (incident angle of 50° and 44° relative to the surface of the wall) laser beam will irradiate the capsule poles. If the glint power is sufficiently large during the picket (early time) of the laser pulse, it may seed high-mode perturbations on the capsule surface that can grow during the implosion. To quantify the glint power on the capsule during the picket by the outer beams, we performed dedicated experiments on NIF using a flat witness foil as a surrogate for the capsule in a half-hohlraum target. We found that the measured glint power is approximately comparable to simulations using a nominal electron conduction flux limiter of f = 0.15, and over an order of magnitude lower than that predicted using f = 0.03 in the wall. Based on our current understanding, we conclude that the glint from the outer beams plays an insignificant role in capsule drive asymmetry.

It has recently been found that the predictions of position and electron temperature of the Au bubble produced by the outer cone beams in a NIF cylindrical hohlraum are sensitive to the heat flux model.1–4 For example, using a standard, nearly unrestrictive (f = 0.15) flux limiter, the models predict a bubble which is colder, and its motion slower compared with models using a restricted heat flux limiter in the wall (f = 0.03), which provides better agreement with experimental data.3–5 However, simulations suggest that this restricted heat flux model (f = 0.03) gives rise to a significant specular reflection (glint) from the outer beams onto the capsule. This is illustrated in Fig. 1, where the specular reflection of the outer cone (incident angle of 50° and 44° relative to the hohlraum axis) laser beams from the inner surface of a typical NIF cylindrical hohlraum is shown to impinge onto the central pellet with a near normal incident angle to the capsule surface.

FIG. 1.

Illustration of specular reflection (glint) in an NIF cylindrical hohlraum in a typical laser pointing setup of an ICF experiment for a quad of 50° and 45° outer beams. The geometry is cylindrically symmetric and up–down symmetric about the target mid-plane. The glint of inner beams exits the hohlraum through the laser entrance hole(s), while the outer beams glint onto the surface of the fuel capsule.

FIG. 1.

Illustration of specular reflection (glint) in an NIF cylindrical hohlraum in a typical laser pointing setup of an ICF experiment for a quad of 50° and 45° outer beams. The geometry is cylindrically symmetric and up–down symmetric about the target mid-plane. The glint of inner beams exits the hohlraum through the laser entrance hole(s), while the outer beams glint onto the surface of the fuel capsule.

Close modal

While the possible explanation for a restricted heat flux may be explained by azimuthal magnetic (B) fields, it is not expected that the B-field plays an important role at the early time—during the early part of the laser pulse (i.e., “picket”), the magnetic field is predicted to be very small, and thus cannot be the cause of a possible restricted heat conduction. Nonetheless, regardless of the source, the level of glint at an early time onto the capsule can be used to discriminate between the various heat flux limiter models. Furthermore, it may also assess the possible level of perturbations on the capsule due to azimuthal variations in ablation rates caused by the finite extent of the laser spots on the pellet surface.

The outer beam glint follows the same physics principle as that in the inner beam glint (Fig. 1),6 where the laser beam refracts as it reaches the turning point density = nc sin2θ of the plasma. The laser absorption and reflection can be estimated using the inverse bremsstrahlung (IB) absorption model,7–9 that is determined by the plasma density profile at the laser–plasma interaction region, as well as the electron–ion collision frequency which is related to plasma temperature and averaged ion charge states. These quantities are in turn determined by the plasma hydrodynamics that is influenced by heat transport models.1,2 A more restrictive heat flux multiplier keeps the laser deposition region hotter, thus, reducing IB ∼ 1/Te1.5 and is expected to produce higher glint levels.

Assuming a range of plasma scale lengths between 5 and 10 μm, temperatures between 0.5 and 1 keV, and average charge states of gold (as hohlraum material) between 20 and 40 (these parameter ranges represent the calculated plasma conditions for nominal ICF experiments using various heat flux limiters), the analytical estimate of the glint percentage out of total laser light ranges from ∼0.02% to ∼4% for the 50° and 44° beams, i.e., spanning over two orders of magnitude, as shown in Fig. 2.

FIG. 2.

Estimated fraction of glinted laser energy for laser intensity of 2 × 1013 W/cm2 as a function of incident laser angle to the gold target surface using an analytical method6,7 for two different plasma conditions.

FIG. 2.

Estimated fraction of glinted laser energy for laser intensity of 2 × 1013 W/cm2 as a function of incident laser angle to the gold target surface using an analytical method6,7 for two different plasma conditions.

Close modal

The glint fraction shown in Fig. 2 is in line with the predictions from our state-of-the-art radiation hydrodynamics codes. This is highly dependent on the plasma models used, particularly the heat transport models. The need for different heat transport models is addressed elsewhere1–4 and the correct model to use is still being investigated.10  Table I lists predictions using two heat transport models, and they are different by one–two orders of magnitudes in glint energy and intensity, supporting the analytical results shown in Fig. 2.

TABLE I.

Code predictions of glint power using heat flux limiters of f = 0.15 and f = 0.03.

Heat flux limiter Total energy (kJ) Glint energy (kJ) % glint energy Glint int. (W/cm2)
0.15  45  0.016  0.04  1012–1013 
0.03  45  1.0  2.2  1013–1014 
Heat flux limiter Total energy (kJ) Glint energy (kJ) % glint energy Glint int. (W/cm2)
0.15  45  0.016  0.04  1012–1013 
0.03  45  1.0  2.2  1013–1014 

At the high end of the estimated range, the glint power is sufficiently large during the early time picket of the laser pulse to cause imprints onto the capsule and seed high-mode (>8) perturbations in the capsule that can grow and degrade the implosion in the compression process. This is illustrated by a simulation (Fig. 3) with about 1 kJ of glint out of 45 kJ total laser energy for a representative NIF ICF shot (N210113 that had a nominal target design and laser pulse shape used for the ignition experiments), which resulted in an unacceptably large asymmetry: when the capsule is compressed to ∼150 μm radius (9.5 ns, Fig. 3 right), the P2 is about −15% and P4 about +20%, relative to <10% P2 and <5% P4 in nominal successful implosions.11 P2 and P4 refer to the Legendre modes of the capsule's spherical harmonic expansion. Note that at normal incident to the capsule, the outer beam glint can induce an artifact on the capsule that looks like a tent feature,12,13 which can lead to a localized disruption during compression. An additional effect due to the outer beam glint is that it may affect the shock merger, effectively altering the desired adiabat, thus, directly affecting compression. Conversely, the high flux limiter (f = 0.15) integrated hohlraum simulations indicate that the early time glint from normal ignition pulses do not appear to induce any significant perturbations to the capsule, producing smooth implosions free from high-mode features, unlike Fig. 3.

FIG. 3.

Simulated 8.9 keV x-ray backlit images of capsule during compression at the end of laser pulse (8.5 ns, left) and near the peak compression (9.5 ns, right). The scale is the ratio of transmission of the x ray relative to the source. The red contours indicate minimum transmission in the images. This simulation used f = 0.03 on a nominal implosion pulse shape from a “Hohlraum Scan Campaign”14,15 shot N210113.

FIG. 3.

Simulated 8.9 keV x-ray backlit images of capsule during compression at the end of laser pulse (8.5 ns, left) and near the peak compression (9.5 ns, right). The scale is the ratio of transmission of the x ray relative to the source. The red contours indicate minimum transmission in the images. This simulation used f = 0.03 on a nominal implosion pulse shape from a “Hohlraum Scan Campaign”14,15 shot N210113.

Close modal

Given the sensitivity of the glint power to various plasma models used in the code, we carried out a set of experiments to measure the outer beam glint on NIF at the relevant laser energy and pulse shape. We describe the experimental setup and experimental results and compare them to the code simulations using different flux limiters. The simulations were preformed using LASNEX code16 in the presence/absence of self-generated magnetic fields (MHD modeling17) unless specified otherwise.

We found that the measured glint power is about an order of magnitude lower than that predicted by simulations using a flux limiter (f = 0.03) in the wall. The model using f = 0.15 (both with and without MHD) nominally agrees with the averaged measured glint intensity. However, the glint intensity in the model goes down vs time, while the experimental data show an upward trend. Overall, the data indicate that the glint from the outer beams play an insignificant role in capsule implosion dynamics and asymmetry.

The experiments reported here focus on measuring the glint power of outer beams from a standard NIF cylindrical hohlraum. For this purpose, we use, in particular, a designed target, diagnostics setup, and a shortened nominal ICF experimental laser pulse, as described below.

Since we are only concerned with the outer beam glint at an early time, when the plasma scale length is small, these experiments use only the picket portion of the laser pulse from the well-established nominal Hybrid-E (HyE) pulse shape (inset of Fig. 4).18 The actual laser pulse used in the experiments is shown in Fig. 4.

FIG. 4.

The total laser power history used in the experiment. The pulse is the picket section (highlighted region, inset figure) of nominal ignition pulse. Also marked on the laser pulse are the times where the measurement was made using the primary gated x-ray (GXD) diagnostic.

FIG. 4.

The total laser power history used in the experiment. The pulse is the picket section (highlighted region, inset figure) of nominal ignition pulse. Also marked on the laser pulse are the times where the measurement was made using the primary gated x-ray (GXD) diagnostic.

Close modal

Because only the top half of the NIF lasers are used (see below the target setup), the total laser power is about half of the nominal picket power. The laser beams and their energy and peak intensities on the target are listed in Table II. The laser wavelength for all beams was 3509 Å.

TABLE II.

Detailed laser beam setup used in the experiments.

Beam goal Beam ID Number of beams Total energy (kJ) Peak Int. (W/cm2)
Drive  50° beams  32  18–22  1 × 1014 
40° beams  32  18–22  1 × 1014 
30° beams  12  1.8–2.4  2.5 × 1013 
23° beams  16  2–2.8  2.5 × 1013 
Calibration/reference  B133  0.180–1.36  1 × 1013–2 × 1014 
B134  0.036–0.45  2.4 × 1012–5 × 1012 
Beam goal Beam ID Number of beams Total energy (kJ) Peak Int. (W/cm2)
Drive  50° beams  32  18–22  1 × 1014 
40° beams  32  18–22  1 × 1014 
30° beams  12  1.8–2.4  2.5 × 1013 
23° beams  16  2–2.8  2.5 × 1013 
Calibration/reference  B133  0.180–1.36  1 × 1013–2 × 1014 
B134  0.036–0.45  2.4 × 1012–5 × 1012 

Two beams of a 30° quad were used to irradiate the calibration plate (more in Sec. III). The laser intensity was chosen to bracket the simulated glint intensity as listed in Table I.

Due to the up–down symmetry, a half-hohlraum target is used with a witness plate as a back wall, at the location of the capsule. This is illustrated in Fig. 5. The outer beam glint is captured by the witness plate, and if its intensity is sufficiently high, it would ionize the witness plate material, producing measurable x-ray emission on the diagnostics. The witness material is chosen so that the x-ray emission is dominated by He-like line emission (He-α). To obtain in situ calibration of the emission from the irradiating glint light intensity, a calibration plate of the same material placed outside of the hohlraum is illuminated by two additional laser beams, each with a square pulse shape, 1 ns long but with two different laser intensities, to bracket the intensity range of the measured glint. Using characteristic x rays from a witness as a probe is a technique well-established from various NIF experiments.6,19–21

FIG. 5.

(a) The schematic of the target where a half-hohlraum (halfraum) is used. In the place of capsule, a witness plate is used to capture the glint light from the outer beams. The calibration plate is external to the halfraum. (b) The actual photo of the target for shot N220329. Various shieldings were needed to block the unconverted 1w light and the diagnostic line-of-sight. (c) The half-hohlraum dimension, gas fill pressure, and the line-of-sight of the diagnostics.

FIG. 5.

(a) The schematic of the target where a half-hohlraum (halfraum) is used. In the place of capsule, a witness plate is used to capture the glint light from the outer beams. The calibration plate is external to the halfraum. (b) The actual photo of the target for shot N220329. Various shieldings were needed to block the unconverted 1w light and the diagnostic line-of-sight. (c) The half-hohlraum dimension, gas fill pressure, and the line-of-sight of the diagnostics.

Close modal

To best match the experimental condition in ICF shots, these experiments used a 4He hohlraum fill at a pressure of 149.53 Torr (density of 0.3 mg/cc), and the target temperature was kept at 32 K (higher than the typical DT experiment at ∼18.7 K).

The expected combined glint intensity from all outer beams, ranges from 1012 to 1014 W/cm2, a range which is too large for one material (as witness plate) to cover given the limited dynamic range of the diagnostics. We used two materials instead. The first one is chlorine (Z = 17) provided by saran (C2H2Cl2, 5 um thick foil) that can cover a glint intensity range between 1013 and 1014 W/cm2. The second one is aluminum (Z = 13, 20 μm thick foil), which shows better response at lower intensities (between 1012 and 1013 W/cm2). The normalized intensity of He-α line emission from the two layers (saran and Al) as a function of laser intensity as estimated using LASNEX simulations is shown in Fig. 6.

FIG. 6.

Normalized He-alpha yield using 1D LASNEX simulation for saran (red) and Al (Blue) as witness plates as a function of incident laser intensity.

FIG. 6.

Normalized He-alpha yield using 1D LASNEX simulation for saran (red) and Al (Blue) as witness plates as a function of incident laser intensity.

Close modal

The primary diagnostics used for the experiments are the time-integrated x-ray spectrometer22 viewing the witness plate from below at 37° to the hohlraum axis and the gated x-ray imager (GXD)23 viewing the witness plate through the LEH from above along the hohlraum axis. Both diagnostics are used for the saran witness plate experiment (since saran foil is transparent to Cl He-alpha), while only the gated x-ray imager could be used for the Al witness foil experiment, which is opaque to its own He-alpha.

The predicted glint induced x-ray images from saran as seen from the pole are shown in Fig. 7 for the two heat flux models. A centrally peaked glint induced x-ray emission is evident from the low flux model (f = 0.03), while for the other model using f = 0.15 does not have a clear feature. In addition, in the center of the image the peak signal is more than an order of magnitude stronger in the low flux-limiter model (f = 0.03) compared with the high flux-limiter model (f = 0.15). The bright outer ring in the simulated images corresponds to the LEH lip lighting up by the thermal conduction of the heated LEH plasma.

FIG. 7.

Pre-shot simulated glint induced x-ray emission (GW/sr/cm2) image for N220329 which used a saran witness plate at t = 1.0 ns. (a) From restricted heat flux limiter f = 0.03, strongly centrally peaked due to strong glint. (b) From less restrictive f = 0.15 heat flux limiter showing almost no glint in the interior. (c) Horizontal lineouts at image center from (a) and (b). In the inset image, a blowup of the f = 0.15 simulation is shown which has only a small increase in intensity near the center due to a weak glint signal.

FIG. 7.

Pre-shot simulated glint induced x-ray emission (GW/sr/cm2) image for N220329 which used a saran witness plate at t = 1.0 ns. (a) From restricted heat flux limiter f = 0.03, strongly centrally peaked due to strong glint. (b) From less restrictive f = 0.15 heat flux limiter showing almost no glint in the interior. (c) Horizontal lineouts at image center from (a) and (b). In the inset image, a blowup of the f = 0.15 simulation is shown which has only a small increase in intensity near the center due to a weak glint signal.

Close modal

To capture the images, we used the hardened gated x-ray imager hGXD23 with a magnification of 1.5×. The pinhole array and detector setup is illustrated in Fig. 8. A 12-pinhole array (three rows of four pinholes of different diameters, see Fig. 8) was used to project the x-ray image of the witness plate onto four strips of the detector, providing a spatial resolution of about 250 and 500 μm, each for pinhole diameters of 150 and 300 μm, respectively. The gain was calibrated to an accuracy of about 25%.23 Each of the four strips was timed differently as illustrated in Fig. 4. One strip (#4 in Fig. 4) is for the calibration plate which is illuminated 3 ns before the main picket pulse. The three other strips capture the witness plate emission at three times. The multiple images at one time allowed differential filters to be applied on each pinhole, enabling us to isolate the Cl or Al He-α line through image subtraction. The timing accuracy of the diagnostic was about 50 ps and the gate temporal resolution was about 80 ps.

FIG. 8.

The target, pinhole, and gated imager setup for the gated x-ray imager. 12 pinholes are used in two pinhole sizes (150 and 300 μm in diameter, and the images are filtered by a pair of filters (details shown in Fig. 9). The strip number and timing are marked.

FIG. 8.

The target, pinhole, and gated imager setup for the gated x-ray imager. 12 pinholes are used in two pinhole sizes (150 and 300 μm in diameter, and the images are filtered by a pair of filters (details shown in Fig. 9). The strip number and timing are marked.

Close modal

The filters used in the experiments are shown in Fig. 9. Two thicknessed of saran foils (12.5 and 25 μm) were used to form a pair of differential filters for N220329 which used Cl as a witness element [Fig. 9(a)]. The ratio of their transmissions enables one to deduce the mean photon energy. For example, if the ratio from the two filters is about 2, the image would be mostly from Cl He-α. For the following shot that used Al as a witness element, a pair of filters isolate a narrow photon energy range around Al He-alpha (<0.5 keV). A similar technique has been used in previous experiments (e.g., Refs. 6 and 21). The filter transmission used is shown in Fig. 9(b). The thickness of the filters was selected to match their transmission to form a “Ross-pair.”24 The transmission of the two filters is nearly identical for energies below ∼1.5 keV and above ∼1.9 keV. Simulations suggest that when there is significant Al He-α emission, the subtraction of these two filter images primarily isolates the Al He-α complex.

FIG. 9.

(a) The transmission ratio of the two differential filters of saran (#1:25 μm and #2: 12.5 μm) used for N220329 with the transmission of each filter is shown in the inset. The Cl He-α line is marked in red. (b) The transmission of the Ross-pair filters (16.8 μm Al and 15 μm Si, together with the Be and polyimide filters used for detector protection) is shown, which are used in shots N230131 and N230517. The Al He-α line energy is marked in red.

FIG. 9.

(a) The transmission ratio of the two differential filters of saran (#1:25 μm and #2: 12.5 μm) used for N220329 with the transmission of each filter is shown in the inset. The Cl He-α line is marked in red. (b) The transmission of the Ross-pair filters (16.8 μm Al and 15 μm Si, together with the Be and polyimide filters used for detector protection) is shown, which are used in shots N230131 and N230517. The Al He-α line energy is marked in red.

Close modal

The experimental setup is shown in Table III. For each shot, we adjusted the experimental design slightly based on the best available information using both simulations and earlier experiments to achieve the campaign objectives. For example, we changed the witness plate material from saran to aluminum foil after the first shot (N220329) and simplified the target and diagnostic shielding requirement accordingly. In addition, we increased the picket laser power by 50% on shot (N230517) to ensure a measurable glint signal.

TABLE III.

Overview of laser parameters and targets for the glint experiments.

Shot numberN220329N230517
Laser power   
Witness plate Saran (C2H2CI2Al with PET Washer 
Ross-pair filter 25 μm–12.5 μm saran 15 μm Si–16.8 μm Al 
Reference laser intensity range 6 × 1013–2 × 1014 W/cm2 4 × 1012–9 × 1013 W/cm2 
Key observables Time-integrated spectrum and gated images of CI He-alpha via Ross-pair filters Gated images of Al He-alpha via Ross-pair filters 
Shot numberN220329N230517
Laser power   
Witness plate Saran (C2H2CI2Al with PET Washer 
Ross-pair filter 25 μm–12.5 μm saran 15 μm Si–16.8 μm Al 
Reference laser intensity range 6 × 1013–2 × 1014 W/cm2 4 × 1012–9 × 1013 W/cm2 
Key observables Time-integrated spectrum and gated images of CI He-alpha via Ross-pair filters Gated images of Al He-alpha via Ross-pair filters 

In the first shot (N220329), we geared the experiment toward the higher glint, low flux-limiter (f = 0.03) simulations. Consequently, we began with a layer of chlorine-doped saran (C2H2Cl2) foil as the witness plate and looked for the presence of Cl He-α emission.

The spectrum from Virgil in the range of 2.7–3.0 keV is shown in Fig. 10, As can be seen, there is no indication of Cl lines in the spectrum, which stands in stark contradiction to the predictions from the low flux-limiter model (f = 0.03) but does appear consistent with the high flux-limiter (f = 0.15) simulation.

FIG. 10.

Witness plate emission (in J/keV/sr) from Virgil spectrometer (a) and from simulation using two models (b). The inset shows that the Virgil viewed only the witness plate as the emission from the calibration plate was blocked by the shield as designed.

FIG. 10.

Witness plate emission (in J/keV/sr) from Virgil spectrometer (a) and from simulation using two models (b). The inset shows that the Virgil viewed only the witness plate as the emission from the calibration plate was blocked by the shield as designed.

Close modal

Consistently, there is also no signature of the Cl emission from the witness plate on the HGXD images. The ratio of the differentially filtered images indicated that the signal on the image was dominated by x rays with E < 2.5 keV, likely from the hohlraum wall emission. The x-ray emission from the reference plate was recorded on the GXD, and its photon energy corresponded to that of the Cl He-α (2.8 keV) with a filter transmission ratio of about 1.55 as expected from the differentially filtered images (Fig. 9).

Although this shot did not obtain a measurable glint signal, the results confirmed that the methodology worked as designed. More importantly, the fact that the Cl signal is essentially below the detection threshold appears to indicate that (1) the glint intensity is less than 1014 W/cm2, and (2) the restricted flux (f = 0.03) over predicts the glint intensity. In other words, the thermal conduction in the Au wall is not highly restricted during the picket drive, an important conclusion which is re-affirmed in the two subsequent glint shots.

The succeeding experiments used Al as a witness plate to increase the sensitivity to a lower glint intensity (as shown in Fig. 6), and the calibration plate was changed accordingly. On the target, we added a fiducial plastic (PET) washer on top of the witness aluminum foil in the hohlraum to isolate any volume emission background not related to glint. Also, the laser pulse energy was increased by 50% to better ensure a measurable glint signal.

While shot N230131 only obtained useful calibration data, shot N230517 measured glint induced x rays. The data images from both filters (Si and Al as referred above) at t = 1.4 ns [Fig. 11(a)] are shown in Fig. 11(c). The dark and bright outer ring signals clearly seen in the figure are from the PET washer and LEH, respectively. The signal from the glint in the central section is obtained from these image pairs. Horizontal lineouts across the center of the images are illustrated in Figs. 11(d)–11(f). The reference data from the external calibration plate is shown in Fig. 11(b).

FIG. 11.

(a) The laser pulse shape (blue trace) vs time and the GXD diagnostic timing (red marker) used in N230517. (b) The example GXD image of the calibration plate (inset, Si filter, the color scale was chosen to show the low intensity spot at which the high intensity spot was saturated) and the lineouts from each filter; (c) the example GXD images for t = 1.4 ns from Si and Al filters. The feature from the PET washer and upper LEH are marked. The x-ray signal is at the center region. The lineouts were taken at the mid-section and the features from the images are marked with arrows onto the lineout. (d)–(f) The lineouts at three times from both filters.

FIG. 11.

(a) The laser pulse shape (blue trace) vs time and the GXD diagnostic timing (red marker) used in N230517. (b) The example GXD image of the calibration plate (inset, Si filter, the color scale was chosen to show the low intensity spot at which the high intensity spot was saturated) and the lineouts from each filter; (c) the example GXD images for t = 1.4 ns from Si and Al filters. The feature from the PET washer and upper LEH are marked. The x-ray signal is at the center region. The lineouts were taken at the mid-section and the features from the images are marked with arrows onto the lineout. (d)–(f) The lineouts at three times from both filters.

Close modal

The calibration data from N230131 and N230517 is plotted in Fig. 12 as a function of laser intensity (I). There are two laser spots for each calibration plate, thus there are two points per shot. The experimental data were taken at the peak of the x-ray image corresponding to the peak laser intensity on target. The error in the intensity is small (<10%) and is calculated from the uncertainties in the laser energy (∼5%) and the area of illumination from the measured image (5%–8%). The best fit to the data point gives I2.8+/%-0.4 dependence. The error refers to the standard deviation normalized by the square root of the number of data points. The data in Fig. 12 are slightly steeper than that reported by Lemos et al.6 

FIG. 12.

In situ calibration data on GXD counts/pixel (right axis) from Al calibration plate as a function of laser intensity from N230131 (red squares with error bar) and N230517 (blue circle with error bar). The fit to the data is shown as the dashed line. The modeled normalized signal (left axis) vs laser intensity is shown as the black line.

FIG. 12.

In situ calibration data on GXD counts/pixel (right axis) from Al calibration plate as a function of laser intensity from N230131 (red squares with error bar) and N230517 (blue circle with error bar). The fit to the data is shown as the dashed line. The modeled normalized signal (left axis) vs laser intensity is shown as the black line.

Close modal

Using the in situ calibration, which seemed to bracket the data well, we were able to obtain the glint intensity from the Ross-pair subtracted witness plate data. This is summarized in Table IV. Also listed is the inferred glint intensity using Fig. 12. The error includes the uncertainty in the calibration fit and the standard deviation in the signal counts. The data indicate the glint intensity increases with time from 0.8 to 1.4 ns.

TABLE IV.

Measured glint signal strength extracted from the Ross filter pair for N230517.

t (ns) Ave. counts/pix Error counts/pix Inferred glint int. (W/cm2) Error glint int. (W/cm2)
0.8  380  320  3.5 × 1012  1.2 × 1012 
1.1  1800  350  6.4 × 1012  1.4 × 1012 
1.4  3350  430  8.8 × 1012  0.8 × 1012 
t (ns) Ave. counts/pix Error counts/pix Inferred glint int. (W/cm2) Error glint int. (W/cm2)
0.8  380  320  3.5 × 1012  1.2 × 1012 
1.1  1800  350  6.4 × 1012  1.4 × 1012 
1.4  3350  430  8.8 × 1012  0.8 × 1012 

In order to compare with the modeling, we compute in the simulations the average laser intensity which has reflected off the hohlraum wall and impinged on a roughly 0.5 mm diameter region of the interior Al witness plate. Those results are shown in Fig. 13 for the restricted heat flux model (f = 0.03) and the nearly unrestricted heat flux (f = 0.15), including a simulation with MHD turned on. In comparison with modeling, the measurement agrees better with f = 0.15, both with or without including MHD, while strongly disagrees with the f = 0.03 model, which predicted over an order of magnitude higher glint power. This observation is consistent with that found from the first Cl experiments.

FIG. 13.

Glint intensity (left axis) vs time from measurement (red squares with error bar) and simulations from models using f = 0.03 (canyon triangle with line, no MHD), and f = 0.15 without MHD (blue circle with line) and with MHD (pink diamond with line), referenced by the picket laser power (right axis).

FIG. 13.

Glint intensity (left axis) vs time from measurement (red squares with error bar) and simulations from models using f = 0.03 (canyon triangle with line, no MHD), and f = 0.15 without MHD (blue circle with line) and with MHD (pink diamond with line), referenced by the picket laser power (right axis).

Close modal

In the simulations, a mass weighted average of the laser intensity is used to convert the 1D (radial) laser intensities into a single point for the plot. Averaging over the entire Al plate shows basically the same trend in time but lower values that are generally smaller by roughly less than a factor of 2. The simulated data are extended up to 2 ns as a guide. Note that although the glint induced x-ray emission can be computed at later time (>1.5 ns), it might not be valid to be compared to experiments. This is because the x rays from the hohlraum wall will heat the witness plate and produce x rays, and this contribution increases with time, making it indistinguishable from the x rays from the glint light.

We note that although the magnitude of the glint is approximately consistent with the f = 0.15 model, the time behavior does not seem to agree. Simulations suggest the glint is rapidly declining with time, while the experimental data suggest a slight increase in glint. There is a possibility that the interpretation at late times (t = 1.4 ns) of the Al witness plate emission being due solely to glint may not be correct. The x rays from the hohlraum wall and thermal conduction from the laser heated spots will, eventually, heat the Al witness plate sufficiently, creating re-emission and thus confusing our interpretation. To check this hypothesis, we were able to turn off glint in the simulations by preventing the laser rays from interacting with the witness plate once they reflect. In this case, we found that the Al witness plate is considerably dimmer up to times close to 2 ns, even for f = 0.15 simulations. Thus, we believe that x-ray contamination is not important at these early times and that the disagreement in the time behavior of the glint is real.

In this section, several aspects of the data-model comparisons and their implications for understanding hohlraum physics are discussed, including the spatial distribution of the glint and background signals. Additionally, we also discuss the comparison between data and simulations of the laser entrance holes self-emission. While this does not directly impact the glint results discussed above, it offers information that may help improve the current hohlraum models.

If the hohlraum is hot enough, it could radiatively, or by thermal conduction, heat up the witness plate and give rise to x-ray self-emission. To understand the level of such potential “background” emission, simulations were performed where the light reflections off the wall were “turned off.” The results evaluating the background contribution to the signal are shown in Fig. 14 for models using f = 0.15 without [Figs. 14(a) and 14(b)], and with [Fig. 14(c)] MHD17 included.

FIG. 14.

Peak emission as a function of time at the center of the simulated glint image using f = 0.15 from (a) No-MHD models with glint on (solid lines) and off (dashed lines) for both filters, and the difference of the two filters (red colored traces); (b) No-MHD models with LEH window on (solid lines) and off (dashed lines) for both filters and their difference; and (c) comparison of MHD, No-MHD, and background (glint off) with LEH window (solid lines) and LEH window off (dashed lines).

FIG. 14.

Peak emission as a function of time at the center of the simulated glint image using f = 0.15 from (a) No-MHD models with glint on (solid lines) and off (dashed lines) for both filters, and the difference of the two filters (red colored traces); (b) No-MHD models with LEH window on (solid lines) and off (dashed lines) for both filters and their difference; and (c) comparison of MHD, No-MHD, and background (glint off) with LEH window (solid lines) and LEH window off (dashed lines).

Close modal

Simulations show that the glint has a much larger signal on the Si Filter image than for the one filtered with Al [Fig. 14(a)], with both images showing a significant self-emission from the lip of the LEH window early in time (<2 ns). However, the subtraction of the two images produces an image that is free from LEH window effects [Fig. 14(b)].

One can see that the hohlraum background on both the Si- and Al-filtered channels are smaller than the corresponding signal [Fig. 14(a)], but the fraction of the background is higher in the Al-filtered data [Fig. 14(a)]. As the hohlraum heats up at later times (>2 ns), the background emission increases. However, this does not affect the glint results because we confined the measurements to times less than 2 ns.

Interestingly, simulations also show [Fig. 14(c)] in the Si–Al filter subtraction that the f = 0.15 No-MHD model has considerable signal early in time compared with the No-glint model. Also, we see that for MHD, No-MHD (f = 0.15), and the No-glint models there is basically no impact from the LEH window in the Si–Al filter. Although this might indicate that MHD plays an important role on the LEH region, further study needs to be done to confirm it.

In addition to the discrepancy in time-history of the glint strength, another important discrepancy between data and simulation is the spatial distribution of the glint signal: while the model predicts a central peaked shape (Fig. 15), the data have an approximately flat profile (as shown in Fig. 15 inset). It is unclear on what is the exact cause for this difference, it is worth pointing out that the model is 2D, whereas in experiments, the plasmas from the wall at the outer beam region are 3D in their spatial profile in electron temperature and density25—the 3D effect to the glint should be addressed with further simulations.

FIG. 15.

LASNEX simulated witness plate glint emission (lines) and background (dashed lines) profile at the three times. The inset is the experimental data at the same three times in the same color scheme.

FIG. 15.

LASNEX simulated witness plate glint emission (lines) and background (dashed lines) profile at the three times. The inset is the experimental data at the same three times in the same color scheme.

Close modal

The x-ray images of the witness plates show extensive details, including those from two different sized pinholes and filters. This is shown in Fig. 16(a) for a gate time of 1.4 ns. In the following, we attempt to use this image to evaluate the maximum spatial variation of the glint signal from the data and estimate its impact on the capsule implosion.

FIG. 16.

(a) HGXD data from N230517, overlaid with 40 × 40 pixel regions of interest of uniform background (A–F) vs glint (G and H). (b) Zoom-in on region G where the plowshare pattern artifact from the film scanner can be seen. (c) The variance-to-signal ratio in the two regions of interest where glint is captured (G and H) is comparable to the one in regions A–F where the input to the detector is uncorrelated Poisson noise, which constrains the maximum amplitude of the glint speckle (see main text for details).

FIG. 16.

(a) HGXD data from N230517, overlaid with 40 × 40 pixel regions of interest of uniform background (A–F) vs glint (G and H). (b) Zoom-in on region G where the plowshare pattern artifact from the film scanner can be seen. (c) The variance-to-signal ratio in the two regions of interest where glint is captured (G and H) is comparable to the one in regions A–F where the input to the detector is uncorrelated Poisson noise, which constrains the maximum amplitude of the glint speckle (see main text for details).

Close modal

In the regions where the signal on the detector is uniform, the input noise should follow uncorrelated Poisson statistics, and, since the detector is a linear system, we expect the variance of the output signal will be proportional to its average. If the regions exhibiting glint had a spatial structure with a scale length larger than the 200 μm resolution of the imaging system, then the variance-to-signal ratio in these regions would be increased compared to the regions of uniform illumination. In Fig. 16(c), we plot the variance-to-signal average ratio for different regions of interest. The raw data have been corrected for gain variations in the camera,23 and for the contribution of the intrinsic film noise (granularity) measured on the light exposure calibration wedge imprinted on the film before the shot. As can be seen on Fig. 16, the uniform regions have variance-to-signal ratios between 38 and 55. We attribute these variations to imperfections in the camera (fixed-pattern noise, defects in the micro-channel plate (MCP) and the film, etc.) as well as errors in gain calibration measurements, reportedly as high as 25%.23 The glint regions of interest, G and H, have variance-to-signal ratios of 31 and 50, respectively. While region H's ratio is bounded by the values obtained for the various background regions, region G exhibits a lower-than-expected variance compared to these reference regions. We surmise that this might be due to a combination of different instrumental effects, such as the intensity-dependent horizontal plowshare pattern artifact present in region G [Fig. 16(b)] associated with the raster scanning process of the microdensitometer used to digitize the film, which is smoothing the data, or the onset of a sub-linear response from the MCP for this region with the highest signal intensity of all. In any case, both glint regions G and H do not exhibit excess variance based on these considerations, which means that any speckling in the glinted beam must have an amplitude significantly smaller than the statistical noise in the measurement.

At the 200 μm scale of the imaging system, the glint induced x-ray images showed a noise level (defined as the ratio of the standard deviation to mean) of about 5%. Using the relationship between x-ray and laser intensity established using the external calibration plate, we can infer that the laser intensity variation over the 200 μm spatial scale would be less than 2% or so deduced from the measurement.

To assess the effect of the measurement on the current Hybrid-E implosions,18 we compared 1D HYDRA26 capsule only simulations with and without glint for shot N210808.27–29 To drive the capsule the simulations used a frequency-dependent-source (FDS) obtained from a detailed integrated simulation using the delivered laser pulse (i.e., all features of the pulse are included).

For a typical NIF hohlraum and capsule geometry (Fig. 1), the outer beams hit predominantly at 45° from the poles, near normal incidence, and as separate quads onto the capsule of about 1 mm radius. A total of 16 quads of lasers from 45° and 50° cones glint at 45° on a capsule with a perimeter of about 2π cos 45 × 1 = 4.5 mm and a width of about cos 45° × 2 mm (projecting the 2 mm size glint on the witness plate to the capsule surface), which gives an area of about 6 mm2. So, whether the outer quad glint is focused or not by the cylindrical shape of hohlraum, the average intensity on the capsule surface would be about the area on the witness plate ∼3 mm2 [Fig. 11(c)]/6 mm2 ∼ ½ of that measured on the witness plate.

In Table V, we listed the glint intensity measured from the enhanced picket power on the witness plate location (Col. 2), and the inferred intensity on the capsule (Col. 3) taking into account the reduction factor of 1/2 discussed above. In Cols. 4–6, we listed the simulated, maximum glint intensity on the capsule surface using f = 0.15.

TABLE V.

Outer beam glint intensity in W/cm2 from measurement and simulation at the witness plate or capsule surface.

t (ns) Measured at the witness plate Inferred on the capsule Simulated at the witness plate Simulated (f = 0.15) on the capsule Simulated (f = 0.15) on the capsule
At increased picket power, N230517 (see Table III and Fig. 13) At nominal picket power
0.8  3.5 × 1012  1.75 × 1012  9 × 1012  3 × 1012  1 × 1012 
1.1  6.4 × 1012  3.2 × 1012  5 × 1011  2 × 1011  9 × 1010 
1.4  8.8 × 1012  4.4 × 1012  8 × 1010  3 × 1010  1 × 1010 
t (ns) Measured at the witness plate Inferred on the capsule Simulated at the witness plate Simulated (f = 0.15) on the capsule Simulated (f = 0.15) on the capsule
At increased picket power, N230517 (see Table III and Fig. 13) At nominal picket power
0.8  3.5 × 1012  1.75 × 1012  9 × 1012  3 × 1012  1 × 1012 
1.1  6.4 × 1012  3.2 × 1012  5 × 1011  2 × 1011  9 × 1010 
1.4  8.8 × 1012  4.4 × 1012  8 × 1010  3 × 1010  1 × 1010 

Note that the glint intensity was measured with an enhanced picket power, which gives about a factor of three higher in glint intensity than that from the normal picket power (Col. 5 and Col. 6). Therefore, the expected glint intensity on the capsule should be further reduced by a factor of three from Col. 3, giving the intensity range between 6 × 1011 and 1.5 × 1012 W/cm2.

The capsule simulations using a peak glint intensity of 1.5 × 1012 W/cm2 show that the effect in shock merger timing is less than ∼10 ps, smaller than the temporal resolution element of 20 ps or the 50 ps asynchrony threshold on shock symmetry.30 Therefore, we conclude that at the measured level, the outer beam glint has little impact on the zeroth order implosion dynamics.

However, the simulations show that the glint introduces an additional seed to the mode l = 4 that may enhance its impact on the capsule performance. Calculations indicate that this level of glint intensity may add an additional seed corresponding to ∼30 nm peak-to-valley (or an amplitude of 15 nm) for mode l = 4, this represents about 60% of the current capsule smoothness requirement of 25 nm in amplitude.31 Assessing the impact of this additional seed is currently being investigated in the context of the Hybrid-E implosions.

It is worth mentioning that an earlier experiment by Pickworth et al.32 found unexplained structures when analyzing the capsule self-backlighting image. A reasonable assumption is that if the glint intensity is sufficiently high and long33 it might be the cause of those measured signatures, but more work will be required to ascertain this possibility.

Additionally, the presence of glint introduces the possibility of seeding a broadband spectrum of perturbations onto the outer surface of the capsule due to the inherent inhomogeneities of the laser beam. This process was studied earlier in the context of direct drive33 and found that significant perturbations may be seeded by beam mistiming. The NIF consistently measures mistiming which is in the range of 30–40 ps, a value which is calculated to be within tolerable levels. Thus, it is expected that short wavelength perturbations will be stabilized by the smoothing effect of the hohlraum x-ray drive. However, mid-wavelength modes could still be problematic. To ascertain the effect of glint on these modes, we use the theory from Ref. 33. where the separation between the ablation and absorption surfaces ( D a c) provides a measure of the decoupling of imprinted perturbations and modulations at the ablation front. Specifically, as the implosion proceeds, the separation between the ablation front and laser deposition surface increases, thus, for a given mode ( λ) when 2 π D a c ( t ) / λ 1, perturbation seeded by the glint begins to smooth out. Our model indicates that for λ 60 μ m (calculated to be the fastest growing mode) the decoupling occurs mid-way through the picket of the laser pulse. With the success of shot N221204 (achieving ignition) additional experiments are needed to ascertain the actual impact of glint on Hybrid-E implosion performance.

Finally, at the early time ( 1 ns) of the experiment it is possible that the Landau–Darrieus instability34,35 might grow (e.g., mode 4), even though the glint intensity could be small (<1012 W/cm2). It is expected that during the initial ∼100s ps, the x-ray drive from the hohlraum would provide mitigation for this instability so it may not be a concern. However, more experiments and simulations are required to properly assess the actual growth because, at the present, at these low intensities, the simulation models are not sufficiently reliable.35 

The intensity of specular reflection (glint) of outer laser beams inside cylindrical hohlraums have been measured on the NIF experiments during the picket laser pulse. The comparison of the glint data with simulation shows that the averaged glint power is an order of magnitude less than that predicted by the model using the restricted heat flux limiter (f = 0.03), indicating this model is not applicable, and that the glint power is increasing in time in contrast to the best model (f = 0.15 with MHD) that shows a decrease in glint intensity over time. The evaluation of the impact of the measured glint on early capsule perturbations indicates that the glint has a negligible impact on instability development during the capsule implosion.

We thank Nick Aybar, Eugene Kur, Will Farmer, Steve MacLaren, Mike Rubery, and Art Pak for valuable discussion. This work was performed under the auspices of the U.S. Department of Energy by LLNS, LLC, under Contract No. DE-AC52- 07NA27344.

The authors have no conflicts to disclose.

Hui Chen: Conceptualization (equal); Formal analysis (equal); Writing – original draft (equal); Writing – review & editing (equal). Mike Hardy: Methodology (supporting). Nicholas Hash: Methodology (supporting). Denise Hinkel: Conceptualization (equal); Supervision (equal). Joe Pierce Holder: Data curation (equal). N. Izumi: Conceptualization (equal). Nathan Daniel Masters: Methodology (supporting). Weston Montgomery: Methodology (equal). John Douglas Moody: Conceptualization (equal); Writing – review & editing (equal). Katya Newman: Project administration (supporting). Sonja rogers: Project administration (supporting). Douglas Tod Woods: Conceptualization (equal); Formal analysis (equal); Writing – original draft (equal); Writing – review & editing (equal). James S. Ross: Supervision (equal). Vladimir Smalyuk: Conceptualization (equal); Writing – review & editing (equal). Christopher Weber: Conceptualization (equal). T. Zobrist: Methodology (supporting). Nuno Lemos: Conceptualization (equal); Formal analysis (equal); Writing – original draft (supporting); Writing – review & editing (supporting). Mordecai D. Rosen: Conceptualization (equal); Writing – review & editing (equal). Otto L. Landen: Conceptualization (equal); Formal analysis (equal); Supervision (equal); Writing – review & editing (equal). Jose L. Milovich: Conceptualization (equal); Formal analysis (equal); Writing – original draft (equal); Writing – review & editing (equal). Marilyn Schneider: Conceptualization (equal); Writing – review & editing (equal). Clement Trosseille: Formal analysis (equal); Writing – original draft (equal). Jared Craig Delora-Ellefson: Methodology (supporting).

The data that support the findings of this study are available from the corresponding author upon reasonable request.

1.
M.
Rosen
,
H.
Scott
,
D.
Hinkel
,
E.
Williams
,
D.
Callahan
,
R.
Town
,
L.
Divol
,
P.
Michel
,
W.
Kruer
,
L.
Suter
,
R.
London
,
J.
Harte
, and
G.
Zimmerman
, “
The role of a detailed configuration accounting (DCA) atomic physics package in explaining the energy balance in ignition-scale hohlraums
,”
High Energy Density Phys.
7
,
180
(
2011
).
2.
O. S.
Jones
,
L. J.
Suter
,
H. A.
Scott
,
M. A.
Barrios
,
W. A.
Farmer
,
S. B.
Hansen
,
D. A.
Liedahl
,
C. W.
Mauche
,
A. S.
Moore
,
M. D.
Rosen
,
J. D.
Salmonson
,
D. J.
Strozzi
,
C. A.
Thomas
, and
D. P.
Turnbull
, “
Progress towards a more predictive model for hohlraum radiation drive and symmetry
,”
Phys. Plasmas
24
,
056312
(
2017
).
3.
N.
Izumi
,
D. T.
Woods
,
N. B.
Meezan
,
J. D.
Moody
,
O. L.
Landen
,
L.
Divol
,
H.
Chen
,
D. A.
Callahan
,
M.
Hohenberger
,
A. L.
Kritcher
,
D. T.
Casey
,
M. D.
Rosen
,
J. S.
Ross
,
M. B.
Schneider
,
M. J.
Edwards
, and
W. W.
Hsing
, “
Low mode implosion symmetry sensitivity in low gas-fill NIF cylindrical hohlraums
,”
Phys. Plasmas
28
,
022706
(
2021
).
4.
N. B.
Meezan
,
D. T.
Woods
,
N.
Izumi
,
H.
Chen
,
H. A.
Scott
,
M. B.
Schneider
,
D. A.
Liedahl
,
O. S.
Jones
,
G. B.
Zimmerman
,
J. D.
Moody
,
O. L.
Landen
, and
W. W.
Hsing
, “
Evidence of restricted heat transport in National Ignition Facility Hohlraums
,”
Phys. Plasmas
27
,
102704
(
2020
).
5.
H.
Chen
,
D. T.
Woods
,
O. S.
Jones
,
L. R.
Benedetti
,
E. L.
Dewald
,
N.
Izumi
,
S. A.
MacLaren
,
N. B.
Meezan
,
J. D.
Moody
,
N. E.
Palmer
,
M. B.
Schneider
, and
M.
Vandenboomgaerde
, “
Understanding ICF hohlraums using NIF gated laser-entrance-hole images
,”
Phys. Plasmas
27
,
022702
(
2020
).
6.
N.
Lemos
,
W. A.
Farmer
,
N.
Izumi
,
H.
Chen
,
E.
Kur
,
A.
Pak
,
B. B.
Pollock
,
J. D.
Moody
,
J. S.
Ross
,
D. E.
Hinkel
,
O. S.
Jones
,
T.
Chapman
,
N. B.
Meezan
,
P. A.
Michel
, and
O. L.
Landen
, “
Specular reflections (“glint”) of the inner beams in a gas-filled cylindrical hohlraum
,”
Phys. Plasmas
29
,
092704
(
2022
).
7.
W.
Kruer
,
The Physics of Laser Plasma Interactions
(
CRC Press
,
2003
).
8.
P.
Mora
, “
Theoretical model of absorption of laser light by a plasma
,”
Phys. Fluids
25
,
1051
(
1982
).
9.
E. L.
Dewald
,
O. S.
Jones
,
O. L.
Landen
,
L.
Suter
,
P.
Amendt
,
R. E.
Turner
, and
S.
Regan
, “
Hard x-ray imaging for measuring laser absorption spatial profiles on the National Ignition Facility
,”
Rev. Sci. Instrum.
77
,
10E310
(
2006
).
10.
D.
Hinkel
, “
Improving hohlraum predictive capability using focused experiments at the National Ignition Facility
,” in
Plenary Talk [PF1], International Conference on Inertial Fusion Sciences and Applications Conference
, Denver, CO, September 25–29,
2023
.
11.
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
, “
Metrics for long wavelength asymmetries in inertial confinement fusion implosions on the National Ignition Facility
,”
Phys. Plasmas
21
,
042708
(
2014
).
12.
S. R.
Nagel
,
S. W.
Haan
,
J. R.
Rygg
,
M.
Barrios
,
L. R.
Benedetti
,
D. K.
Bradley
,
J. E.
Field
,
B. A.
Hammel
,
N.
Izumi
,
O. S.
Jones
,
S. F.
Khan
,
T.
Ma
,
A. E.
Pak
,
R.
Tommasini
, and
R. P. J.
Town
,
Phys. Plasmas 
22
,
022704
(
2015
).
13.
R.
Tommasini
,
J. E.
Field
,
B. A.
Hammel
,
O. L.
Landen
,
S. W.
Haan
,
C.
Aracne-Ruddle
,
L. R.
Bendetti
,
D. K.
Bradley
,
D. A.
Callahan
,
E. L.
Dewald
,
T.
Döppner
,
M. J.
Edwards
,
O. A.
Hurricane
,
N.
Izumi
,
O. A.
Jones
,
T.
Ma
,
N. B.
Meezan
,
S. R.
Nagel
,
J. R.
Rygg
,
K. S.
Segraves
,
M.
Stadermann
,
R. J.
Strauser
, and
R. P. J.
Town
,
Phys. Plasmas
22
,
056315
(
2015
).
14.
D. A.
Callahan
,
O. A.
Hurricane
,
J. E.
Ralph
,
C. A.
Thomas
,
K. L.
Baker
,
L. R.
Benedetti
,
L. F.
Berzak Hopkins
,
D. T.
Casey
,
T.
Chapman
,
C. E.
Czajka
,
E. L.
Dewald
,
L.
Divol
,
T.
Döppner
,
D. E.
Hinkel
,
M.
Hohenberger
,
L. C.
Jarrott
,
S. F.
Khan
,
A. L.
Kritcher
,
O. L.
Landen
,
S.
LePape
,
S. A.
MacLaren
,
L. P.
Masse
,
N. B.
Meezan
,
A. E.
Pak
,
J. D.
Salmonson
,
D. T.
Woods
,
N.
Izumi
,
T.
Ma
,
D. A.
Mariscal
,
S. R.
Nagel
,
J. L.
Kline
,
G. A.
Kyrala
,
E. N.
Loomis
,
S. A.
Yi
,
A. B.
Zylstra
, and
S. H.
Batha
,
Phys. Plasmas
25
,
056305
(
2018
).
15.
J. E.
Ralph
,
O.
Landen
,
L.
Divol
,
A.
Pak
,
T.
Ma
,
D. A.
Callahan
,
A. L.
Kritcher
,
T.
Döppner
,
D. E.
Hinkel
,
C.
Jarrott
,
J. D.
Moody
,
B. B.
Pollock
,
O.
Hurricane
, and
M. J.
Edwards
,
Phys. Plasmas 
25
,
082701
(
2018
).
16.
G. B.
Zimmerman
and
W. L.
Kruer
,
Comments Plasma Phys. Controlled Fusion
2
,
51
(
1975
).
17.
W. A.
Farmer
,
J. M.
Koning
,
D. J.
Strozzi
,
D. E.
Hinkel
,
L. F.
Berzak Hopkins
,
O. S.
Jones
, and
M. D.
Rosen
,
Phys. Plasmas 
24
,
052703
(
2017
).
18.
A. L.
Kritcher
,
A. B.
Zylstra
,
D. A.
Callahan
,
O. A.
Hurricane
,
C.
Weber
,
J.
Ralph
,
D. T.
Casey
,
A.
Pak
,
K.
Baker
,
B.
Bachmann
,
S.
Bhandarkar
,
J.
Biener
,
R.
Bionta
,
T.
Braun
,
M.
Bruhn
,
C.
Choate
,
D.
Clark
,
J. M.
Di Nicola
,
L.
Divol
,
T.
Doeppner
,
V.
Geppert-Kleinrath
,
S.
Haan
,
J.
Heebner
,
V.
Hernandez
,
D.
Hinkel
,
M.
Hohenberger
,
H.
Huang
,
C.
Kong
,
S.
Le Pape
,
D.
Mariscal
,
E.
Marley
,
L.
Masse
,
K. D.
Meaney
,
M.
Millot
,
A.
Moore
,
K.
Newman
,
A.
Nikroo
,
P.
Patel
,
L.
Pelz
,
N.
Rice
,
H.
Robey
,
J. S.
Ross
,
M.
Rubery
,
J.
Salmonson
,
D.
Schlossberg
,
S.
Sepke
,
K.
Sequoia
,
M.
Stadermann
,
D.
Strozzi
,
R.
Tommasini
,
P.
Volegov
,
C.
Wild
,
S.
Yang
,
C.
Young
,
M. J.
Edwards
,
O.
Landen
,
R.
Town
, and
M.
Herrmann
, “
Achieving record hot spot energies with large HDC implosions on NIF in HYBRID-E
,”
Phys. Plasmas
28
,
072706
(
2021
).
19.
L.
Pickworth
,
M.
Rosen
,
M.
Schneider
,
D.
Hinkel
,
L.
Benedetti
,
R.
Kauffman
, and
S.
Wu
, “
Determination of the laser intensity applied to a Ta witness plate from the measured X-ray signal using a pulsed micro-channel plate detector
,”
High Energy Density Phys.
23
,
159
(
2017
).
20.
M. A.
Barrios
,
J. D.
Moody
,
L. J.
Suter
,
M.
Sherlock
,
H.
Chen
,
W.
Farmer
,
J.
Jaquez
,
O.
Jones
,
R. L.
Kauffman
,
J. D.
Kilkenny
,
J.
Kroll
,
O. L.
Landen
,
D. A.
Liedahl
,
S. A.
Maclaren
,
N. B.
Meezan
,
A.
Nikroo
,
M. B.
Schneider
,
D. B.
Thorn
,
K.
Widmann
, and
G.
Perez-Callejo
, “
Developing an experimental basis for understanding transport in NIF hohlraum plasmas
,”
Phys. Rev. Lett.
121
,
095002
(
2018
).
21.
N.
Izumi
,
N. B.
Meezan
,
S.
Johnson
,
B. N.
Woodworth
,
T.
Woods
,
O. S.
Jones
,
O. L.
Landen
,
J. J.
Kroll
,
S.
Vonhof
,
A.
Nikroo
,
J.
Jaquez
,
K.
Kangas
,
C.
Bailey
,
M.
Hardy
,
R.
Ehrlich
,
J.
Ralph
,
R. P.
Town
,
D. K.
Bradley
,
D. E.
Hinkel
,
A. S.
Moore
,
L.
Divol
,
C.
Young
, and
J. D.
Moody
, “
Simultaneous visualization of wall motion, beam propagation, and implosion symmetry on the National Ignition Facility (invited)
,”
Rev. Sci. Instrum.
89
,
10K111
(
2018
).
22.
M. J.
May
,
J.
Weaver
,
K.
Widmann
,
G. E.
Kemp
,
D.
Thorn
,
J. D.
Colvin
,
M. B.
Schneider
,
A.
Moore
, and
B. E.
Blue
, “
Understanding reconstructed Dante spectra using high resolution spectroscopy
,”
Rev. Sci. Instrum.
87
,
11E330
(
2016
).
23.
L. R.
Benedetti
,
J. P.
Holder
,
M.
Perkins
,
C. G.
Brown
,
C. S.
Anderson
,
F. V.
Allen
,
R. B.
Petre
,
D.
Hargrove
,
S. M.
Glenn
,
N.
Simanovskaia
,
D. K.
Bradley
, and
P.
Bell
, “
Advances in x-ray framing cameras at the National Ignition Facility to improve quantitative precision in x-ray imaging
,”
Rev. Sci. Instrum.
87
,
023511
(
2016
).
24.
P. A.
Ross
,
J. Opt. Soc. Am.
16
,
433
(
1928
).
25.
M. B.
Schneider
,
S. A.
MacLaren
,
K.
Widmann
,
N. B.
Meezan
,
J. H.
Hammer
,
B. E.
Yoxall
,
P. M.
Bell
,
L. R.
Benedetti
,
D. K.
Bradley
,
D. A.
Callahan
,
E. L.
Dewald
,
T.
Döppner
,
D. C.
Eder
,
M. J.
Edwards
,
T. M.
Guymer
,
D. E.
Hinkel
,
M.
Hohenberger
,
W. W.
Hsing
,
M. L.
Kervin
,
J. D.
Kilkenny
,
O. L.
Landen
,
J. D.
Lindl
,
M. J.
May
,
P.
Michel
,
J. L.
Milovich
,
J. D.
Moody
,
A. S.
Moore
,
J. E.
Ralph
,
S. P.
Regan
,
C. A.
Thomas
, and
A. S.
Wan
, “
The size and structure of the laser entrance hole in gas-filled hohlraums at the National Ignition Facility
,”
Phys. Plasmas
22
,
122705
(
2015
).
26.
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
(
2001
).
27.
H.
Abu-Shawareb
,
R.
Acree
,
P.
Adams
,
J.
Adams
,
B.
Addis
,
R.
Aden
,
P.
Adrian
,
B. B.
Afeyan
,
M.
Aggleton
,
L.
Aghaian
et al, “
Lawson criterion for ignition exceeded in an inertial fusion experiment
,”
Phys. Rev. Lett.
129
,
075001
(
2022
).
28.
A. L.
Kritcher
,
A. B.
Zylstra
,
D. A.
Callahan
,
O. A.
Hurricane
,
C. R.
Weber
,
D. S.
Clark
,
C. V.
Young
,
J. E.
Ralph
,
D. T.
Casey
,
A.
Pak
,
O. L.
Landen
et al, “
Design of an inertial fusion experiment exceeding the Lawson criterion for ignition
,”
Phys. Rev. E
106
,
025201
(
2022
).
29.
A.
Zylstra
,
A. L.
Kritcher
,
O. A.
Hurricane
,
D. A.
Callahan
,
J. E.
Ralph
,
D. T.
Casey
,
A.
Pak
,
O. L.
Landen
,
B.
Bachmann
,
K. L.
Baker
et al, “
Experimental achievement and signatures of ignition at the National Ignition Facility
,”
Phys. Rev. E
106
,
025202
(
2022
).
30.
H. F.
Robey
,
T. R.
Boehly
,
P. M.
Celliers
,
J. H.
Eggert
,
D.
Hicks
,
R. F.
Smith
,
R.
Collins
,
M. W.
Bowers
,
K. G.
Krauter
,
P. S.
Datte
,
D. H.
Munro
,
J. L.
Milovich
,
O. S.
Jones
,
P. A.
Michel
,
C. A.
Thomas
,
R. E.
Olson
,
S.
Pollaine
,
R. P. J.
Town
,
S.
Haan
,
D.
Callahan
,
D.
Clark
,
J.
Edwards
,
J. L.
Kline
,
S.
Dixit
,
M. B.
Schneider
,
E. L.
Dewald
,
K.
Widmann
,
J. D.
Moody
,
T.
Döppner
,
H. B.
Radousky
,
A.
Throop
,
D.
Kalantar
,
P.
DiNicola
,
A.
Nikroo
,
J. J.
Kroll
,
A. V.
Hamza
,
J. B.
Horner
,
S. D.
Bhandarkar
,
E.
Dzenitis
,
E.
Alger
,
E.
Giraldez
,
C.
Castro
,
K.
Moreno
,
C.
Haynam
,
K. N.
LaFortune
,
C.
Widmayer
,
M.
Shaw
,
K.
Jancaitis
,
T.
Parham
,
D. M.
Holunga
,
C. F.
Walters
,
B.
Haid
,
E. R.
Mapoles
,
J.
Sater
,
C. R.
Gibson
,
T.
Malsbury
,
J.
Fair
,
D.
Trummer
,
K. R.
Coffee
,
B.
Burr
,
L. V.
Berzins
,
C.
Choate
,
S. J.
Brereton
,
S.
Azevedo
,
H.
Chandrasekaran
,
D. C.
Eder
,
N. D.
Masters
,
A. C.
Fisher
,
P. A.
Sterne
,
B. K.
Young
,
O. L.
Landen
,
B. M.
Van Wonterghem
,
B. J.
MacGowan
,
J.
Atherton
,
J. D.
Lindl
,
D. D.
Meyerhofer
, and
E.
Moses
, “
Shock timing experiments on the National Ignition Facility: Initial results and comparison with simulation
,”
Phys. Plasmas
19
,
042706
(
2012
).
31.
S. W.
Haan
,
J. D.
Lindl
,
D. A.
Callahan
,
D. S.
Clark
,
J. D.
Salmonson
,
B. A.
Hammel
,
L. J.
Atherton
,
R. C.
Cook
,
M. J.
Edwards
,
S.
Glenzer
,
A. V.
Hamza
,
S. P.
Hatchett
,
M. C.
Herrmann
,
D. E.
Hinkel
,
D. D.
Ho
,
H.
Huang
,
O. S.
Jones
,
J.
Kline
,
G.
Kyrala
,
O. L.
Landen
,
B. J.
MacGowan
,
M. M.
Marinak
,
D. D.
Meyerhofer
,
J. L.
Milovich
,
K. A.
Moreno
,
E. I.
Moses
,
D. H.
Munro
,
A.
Nikroo
,
R. E.
Olson
,
K.
Peterson
,
S. M.
Pollaine
,
J. E.
Ralph
,
H. F.
Robey
,
B. K.
Spears
,
P. T.
Springer
,
L. J.
Suter
,
C. A.
Thomas
,
R. P.
Town
,
R.
Vesey
,
S. V.
Weber
,
H. L.
Wilkens
, and
D. C.
Wilson
,
Phys. Plasmas
18
,
51001
(
2011
).
32.
L. A.
Pickworth
,
B. A.
Hammel
,
V. A.
Smalyuk
,
H. F.
Robey
,
R.
Tommasini
,
L. R.
Benedetti
,
L.
Berzak Hopkins
,
D. K.
Bradley
,
M.
Dayton
,
S.
Felker
,
J. E.
Field
,
S. W.
Haan
,
B.
Haid
,
R.
Hatarik
,
E.
Hartouni
,
D.
Holunga
,
M.
Hoppe
,
N.
Izumi
,
S.
Johnson
,
S.
Khan
,
T.
Kohut
,
B.
Lahmann
,
O. L.
Landen
,
S.
LePape
,
A. G.
MacPhee
,
E.
Marley
,
N. B.
Meezan
,
J.
Milovich
,
S. R.
Nagel
,
A.
Nikroo
,
A. E.
Pak
,
R.
Petrasso
,
B. A.
Remington
,
N. G.
Rice
,
H. A.
Scott
,
P. T.
Springer
,
M.
Stadermann
,
C.
Walters
,
K.
Widmann
, and
W. W.
Hsing
, “
Development of new platforms for hydrodynamic instability and asymmetry measurements in deceleration phase of indirectly driven implosions on NIF
,”
Phys. Plasmas
25
,
082705
(
2018
).
33.
V. A.
Smalyuk
,
V. N.
Goncharov
,
T. R.
Boehly
,
J. A.
Delettrez
,
D. Y.
Li
,
J. A.
Marozas
,
A. V.
Maximov
,
D. D.
Meyerhofer
,
S. P.
Regan
, and
T. C.
Sangster
, “
Measurements of laser-imprinting sensitivity to relative beam mistiming in planar plastic foils driven by multiple overlapping laser beams
,”
Phys. Plasmas
12
,
072703
(
2005
).
34.
P.
Clavin
and
L.
Masse
,
Phys. Plasmas
11
,
690
(
2004
).
35.
V. N.
Goncharov
,
O. V.
Gotchev
,
E.
Vianello
,
T. R.
Boehly
,
J. P.
Knauer
,
P. W.
McKenty
,
P. B.
Radha
,
S. P.
Regan
,
T. C.
Sangster
,
S.
Skupsky
,
V. A.
Smalyuk
,
R.
Betti
,
R. L.
McCrory
,
D. D.
Meyerhofer
, and
C.
Cherfils-Clérouin
,
Phys. Plasmas
13
,
012702
(
2006
).