A technique for measuring residual motion during the stagnation phase of an indirectly driven inertial confinement experiment has been implemented. This method infers a velocity from spatially and temporally resolved images of the X-ray emission from two orthogonal lines of sight. This work investigates the accuracy of recovering spatially resolved velocities from the X-ray emission data. A detailed analytical and numerical modeling of the X-ray emission measurement shows that the accuracy of this method increases as the displacement that results from a residual velocity increase. For the typical experimental configuration, signal-to-noise ratios, and duration of X-ray emission, it is estimated that the fractional error in the inferred velocity rises above 50% as the velocity of emission falls below 24 μm/ns. By inputting measured parameters into this model, error estimates of the residual velocity as inferred from the X-ray emission measurements are now able to be generated for experimental data. Details of this analysis are presented for an implosion experiment conducted with an unintentional radiation flux asymmetry. The analysis shows a bright localized region of emission that moves through the larger emitting volume at a relatively higher velocity towards the location of the imposed flux deficit. This technique allows for the possibility of spatially resolving velocity flows within the so-called central hot spot of an implosion. This information would help to refine our interpretation of the thermal temperature inferred from the neutron time of flight detectors and the effect of localized hydrodynamic instabilities during the stagnation phase. Across several experiments, along a single line of sight, the average difference in magnitude and direction of the measured residual velocity as inferred from the X-ray and neutron time of flight detectors was found to be ∼13 μm/ns and ∼14°, respectively.

One of the primary goals of experiments conducted at the National Ignition Facility (NIF)1 is to ignite a deuterium-tritium (DT) fuel layer within a spherical fusion target.2–4 Achieving ignition on the NIF requires that the DT fuel is accelerated to tremendous velocities in a spherical implosion. This fuel then undergoes a dramatic deceleration as it implodes on itself, coming nearly to rest in the process called “stagnation.” Under the right stagnation conditions, the fuel strongly compresses the central hot spot, producing enough areal density and temperature that self-heat by alpha particles from the DT fusion reactions heat the fuel to ignition. However, if the implosion is not sufficiently spherical and uniform, the stagnation process will be too inefficient, preventing adequate transfer of energy from the imploding shell into the hot spot and therefore preventing ignition. To date, NIF implosions have demonstrated a stagnation phase efficient enough to double the neutron yield due to alpha particle self heating.5 However, inefficiencies in the stagnation process, mainly due to implosion asymmetry, are thought to be limiting factors for capsule performance.6–8 The NIF inertial confinement fusion (ICF) program is focused on understanding and improving the stagnation phase on the path to ignition. The current efforts are focused on improving the symmetry of the radiation drive produced by the laser-heated hohlraum. One-sided asymmetries, or mode 1 asymmetries, are shown by simulation to be particularly damaging to stagnation. These asymmetries are characterized by high radiation drive on the north pole, for example, with low drive on the south pole.9 They produce a net translation of the implosion and an associated jet that transits the central hot spot. These residual flows disrupt the stagnation process, reduce hot spot compression, and prevent the conversion of kinetic energy to usable internal energy. The calculations suggest that conditions necessary for ignition cannot be reached at NIF if the stagnation asymmetry is enough to give the mass of the remaining ablator, fuel, and reacting hot spot a velocity above 35 μm/ns.10 Diagnosing the residual residual flows near stagnation is therefore an important measurement to build understanding and motivate improvements in the implosion.

There are currently two complementary and independent methods of measuring residual hot spot motion at the NIF. One method uses the arrival time at three different neutron time of flight detectors11,12 (NTOF) to infer a velocity of the neutron emitting fluid. This technique produces a resultant velocity vector weighted by neutrons produced in the central hot spot over the nuclear burn phase.

This paper focuses on the alternative method which uses the temporally and spatially resolved X-ray emission from the hot spot to determine the residual velocity vector of the implosion within the image plane. There has yet to be a bench marking process for this technique, and until now, only simple estimates for the error and accuracy were developed. The aim of this work is to use analytical and numerical modeling to quantify the accuracy and sensitivity of the inferred residual implosion velocity. It is found that the accuracy depends on a multitude of variables and is dependent on both the physical properties the X-ray self-emission as well as to variables associated with the measurement of the X-ray emission. For typical conditions, the fractional error in the inferred emission velocity increases beyond 50% as the velocity along a given line of sight falls below ∼24 μm/ns. When examining the data, this technique was also found to be able to differentiate between the velocity of the entire emitting volume and the velocity of a smaller emitting feature moving through the interior of the emission. This should allow for new insights into the origins and potential impacts of such emission features that occur during the stagnation phase of an ICF implosion.

The remainder of this paper is organized in the following manner. Section II will give a brief overview of the experimental measurement and describe in detail the methodology used to measure the X-ray velocity. Section III assesses how the accuracy of the method is affected by signal-to-noise, magnitude of the imparted velocity, and details the effects of different experimental configurations. Section IV will apply this methodology to an implosion experiment conducted by a DT fuel layer. In this experiment, the capsule experienced an unintentional radiation drive asymmetry. A comparison of the inferred residual implosion velocity of X-ray emission and neutron time of flight measurements is made. Additionally, a method to compare the emissivity profiles from the X-ray and neutron images is detailed in order to ascertain the species composition of the localized fast moving emission observed during stagnation. A summary, including conclusions and future work, will be given in Section V.

The residual velocity of the implosion is found by minimizing the difference between the observed center of X-ray emission and the emission center calculated for a test object for a given residual velocity and magnitude of image transformations associated with the magnification, translation, and rotation.13 To determine the accuracy of this method, synthetic emission data with a set of specified properties were created and analyzed to recover a residual velocity using the same processes used on real data. The difference between the specified velocity and the recovered velocity was examined as the magnitude of velocity, the duration of emission, the area of emission, and the noise were varied.

The setup is shown in Fig. 1, where a synthetic emission object is imaged by a pinhole array onto a four strip micro-channel plate detector (MCP). Each pinhole images the object at different spatial locations at the plane of the MCP denoted in Fig. 1 by the black points. The gain of each strip is temporally gated by a separate and independently timed voltage pulse that imparts an exposure time of τ. The voltage pulse travels down the length of the strip (∼35 mm) at a speed of ∼c/2, where c is the speed of light in vacuum. For each strip, this results in temporal measurement extent of ∼235 ps. Figure 1 shows a typical experimental configuration where the strips are exposed sequentially in time from left to right, creating a continuous record of emission. Pinhole images produced by the array at different spatial locations are thereby recorded at different times. If the emission has no transnational velocity, for the given field of view, then the expected location of the imaged emission would be centered at the projected pinhole locations. However, if the emission has a non-radial velocity component, then the center of imaged emission will not coincide with the location of the projected pinhole locations. In the example depicted in Fig. 1, the emitting object was given a constant residual velocity of 75 μm/ns in the +y direction. Over time, this results in an increasing discrepancy between the image emission center and the center of emission expected for a stationary object, denoted by the black dots. In addition to residual velocity, the location at which the emission is imaged is also a function of the relative position in x, y, and z, and the rotation ϕ of the pinhole array. The location of each pinhole in the array is determined from metrology to sub-micron accuracy in the object plane, and this uncertainty is not thought to appreciably contribute to the uncertainty in the recovered velocity. The algorithm varies the pinhole location and rotation, as well as the object's velocity to create hypothetical emission center locations. By minimizing the difference between the measured and the expected emission centers for a moving object, a residual velocity can be found.

FIG. 1.

Illustration of the technique used to measure the residual velocity of the X-ray emission. An object with a velocity v is imaged by a pinhole array onto a four strip micro-channel plate. The image location, orientation, and magnification are dependent on the translation in x, y, and z as well as the rotation, ϕ, of the pinhole array. Each strip of the micro channel plate is temporally gated by an individual voltage pulse. As illustrated by the red curve, each voltage pulse has a gain width τ ≈ 100 ps and vertically traverses each strip with a velocity of ∼c/2. The strips are typically triggered sequentially in time to form a quasi continuous record over a ∼1 ns duration. Here, the black dots denote the image center for a stationary object. A residual emission velocity is found by solving for the velocity of emission that in conjunction with the magnification, pinhole rotation, and translation, best fits the measured emission location.

FIG. 1.

Illustration of the technique used to measure the residual velocity of the X-ray emission. An object with a velocity v is imaged by a pinhole array onto a four strip micro-channel plate. The image location, orientation, and magnification are dependent on the translation in x, y, and z as well as the rotation, ϕ, of the pinhole array. Each strip of the micro channel plate is temporally gated by an individual voltage pulse. As illustrated by the red curve, each voltage pulse has a gain width τ ≈ 100 ps and vertically traverses each strip with a velocity of ∼c/2. The strips are typically triggered sequentially in time to form a quasi continuous record over a ∼1 ns duration. Here, the black dots denote the image center for a stationary object. A residual emission velocity is found by solving for the velocity of emission that in conjunction with the magnification, pinhole rotation, and translation, best fits the measured emission location.

Close modal

This returned velocity is the measured residual velocity from the experiment. This process depends on what is defined as the center of emission for each object. In this work, the center of emission is determined by calculating the intensity weighted center of the image, Ck=kI(k)dk/I(k)dk. Here, k is the axis along which the center of emission, Ck, is found, and I(k) is the intensity profile of the emission along this axis. The center of emission is calculated across a range of intensity thresholds. The intensity threshold is the value of intensity below which the emission is artificially set to zero. The typical range of intensity thresholds is between 20% and 80% and is set relative to the peak intensity of each individual image that is analyzed. This is done to reduce the impact of background noise on the determination of the center of emission, and to examine how residual velocities change as the threshold is increased.

A spatially and temporally resolved image of the object for each pinhole is created by convolving the emission object with a velocity, a temporal emission profile, and with the temporal/spatial gate width of the detector. In this work, the temporal emission profile was modeled after nominal layered implosion experiments using a Gaussian profile with a full-width half-maximum (FWHM) of 150 ps. The weighted intensity is given as

I=I0×e[4ln(2)(ttFWHM)2],
(1)

where t = 0 corresponds to peak emission and tFWHM is the full-width half-maximum of the emission. The gain associated with the gate of the MCP detector is modeled as a 1D Gaussian profile with a spatial FWHM of 15 mm, which corresponds to the 100 ps integration time.

An overview of the steps used to create each image is given in Fig. 2. Initially, as shown in Fig. 2(a), the object has a 2-D Gaussian spatial distribution. Figure 2(b) shows the change in emission shape from the convolution between the velocity of the object and the gate profile of the MCP. Here, the velocity of the object is moving at an angle of 45° with respect to the gate, leading to a broadening of the image in both the x- and y-directions. Additionally, changes in the detected emission shape due to the interplay between a residual velocity and the finite emission duration are also accounted for. As will be discussed in more detail, this shape can be analytically calculated. Next, steps (c) through (e) are performed numerically to account for hGXD14 instrument response. The hGXD detector comprised an array of channels which convert incident X-ray photons into electrons which are then amplified by the potential associated with the temporal gate. The electrons then strike a phosphor and populate unstable excited states. When these states decay, optical wavelength photons are emitted that are recorded onto either photographic film or arrays of charged coupled detectors. In this model, the channel structure of the MCP detector and the statistical nature of detecting incident X-ray photons were accounted for. Additionally, it was assumed that all the incident photons were converted into free electrons via the photoelectric effect at the same quantum efficiency. The signal was then amplified in a nonlinear manner to mimic the avalanche amplification of the free electrons by the potential of the temporal gate. The spatial blurring of the image associated with the spreading of the amplified electron signal and reflections between the MCP and phosphor was also modeled. Figure 2(f) shows the last step in the synthetic image creation in which spatially uniform noise with a Gaussian distribution is applied to the image to model noise associated with neutrons produced by the implosion interacting with the film. This process creates synthetic data with properties that can be systematically varied to study how changes in velocity, emission duration, and noise can affect the accuracy of the measurement. Figure 2(g) shows the data taken from a layered implosion experiment, and it is seen to qualitatively share many of the characteristics of the synthetic data. Details on the analytical calculation of the emission profile and subsequent numeric processes used to create the synthetic data will now be presented.

FIG. 2.

(a)–(f) Flowchart detailing each step taken to create synthetic data. All images are on the same spatial scale. (a) The original object is modeled as a 2-D Gaussian. (b) A velocity is imparted to the object at an angle of 45° with respect to the temporal MCP gate. Here, the width of the object is increased in both the x and y directions due to the convolution between the motion of the object and the MCP gate. The shape is also modified by the temporal emission profile. (c-i) To account for the response for the detector, the MCP pore pattern of the hGXD is modeled. Here, the detector pattern separates the continuous emission profile into finite spatial bins which can lead to an offset for x and y emission profiles. (c-ii) A magnified image of the MCP pore pattern showing the effect of the Possion photon statistics. (d) The emission signal is amplified in an exponential manner to model the response photo-multiplier tube and micro-Channel Plate components of the. Here, cross-talk effects between adjacent MCP pores are also included. (e) The image is spatially blurred to account for reflections between the MCP and phosphor elements of the hGXD detector. (f) Background Gaussian noise from neutrons is added which is not subject to the statistics of the hGXD imaging process. (g) Emission from a layered implosion experiment N160120 for comparison.

FIG. 2.

(a)–(f) Flowchart detailing each step taken to create synthetic data. All images are on the same spatial scale. (a) The original object is modeled as a 2-D Gaussian. (b) A velocity is imparted to the object at an angle of 45° with respect to the temporal MCP gate. Here, the width of the object is increased in both the x and y directions due to the convolution between the motion of the object and the MCP gate. The shape is also modified by the temporal emission profile. (c-i) To account for the response for the detector, the MCP pore pattern of the hGXD is modeled. Here, the detector pattern separates the continuous emission profile into finite spatial bins which can lead to an offset for x and y emission profiles. (c-ii) A magnified image of the MCP pore pattern showing the effect of the Possion photon statistics. (d) The emission signal is amplified in an exponential manner to model the response photo-multiplier tube and micro-Channel Plate components of the. Here, cross-talk effects between adjacent MCP pores are also included. (e) The image is spatially blurred to account for reflections between the MCP and phosphor elements of the hGXD detector. (f) Background Gaussian noise from neutrons is added which is not subject to the statistics of the hGXD imaging process. (g) Emission from a layered implosion experiment N160120 for comparison.

Close modal

The emission profile I(r) that is produced by each individual pinhole results from a temporal convolution of the original object with its associated velocity, the temporal emission history, and the gate profile of the MCP gain. Assuming that each of these quantities can be described by a Gaussian profile, I(r) can be written in the following manner:

I(r)=|Σp̃Σg̃Σt|1/2π5/2et2Σte(rrpvpt)TΣp̃(rrpvpt)e(rrgvgt)TΣg̃(rrgvgt)dt,
(2)

where Σg̃=[1σgx2001σgy2] and Σp̃=[1σpx2001σpy2] are the 2-D variances, σg and σp are of the gate profile and the projected profile of the image, respectively. The term Σt=12σt2 is the variance of the time (burn) profile, r is the position of a point in the image space, rp and rg are the locations of the emission projections and gate, respectively. Similarly, vp and vg are the velocities of the projections and gate, respectively. Combining similar temporal terms in the exponent, Eq. (2) can be rewritten and solved in the following manner:

I(r)=Aeat2+2b(r)t+c(r)dt=πaAe[b(r)]2a+c(r),
(3)

where A, a, b(r), and c(r) are given by

A=|Σp̃Σg̃Σt|1/2π5/2,
(4)
a=(vpTΣp̃vp+vgTΣg̃vg+Σt),
(5)
b(r)=(rTΣp̃vprpTΣp̃vp+vpTΣp̃rvpTΣp̃rp+rTΣg̃vgrgTΣg̃vg+vgTΣg̃rvgTΣg̃rg),
(6)
c(r)=(rpTΣp̃r+rTΣp̃rp+rpTΣp̃rrpTΣp̃rp+rgTΣg̃r+rTΣg̃rg+rgTΣg̃rrgTΣg̃rg).
(7)

As shown in Fig. 2(b), this analytic description for the shape of the imaged object is still Gaussian but has increased x and y variances, which arise from the velocity of the object, in this example, moving at an angle of 45° with respect to the MCP gate profile.

To model the hGXD instrument response, the structure of the MCP was first considered. The MCP comprised an array of pores or channels. The channels on the detector are about 1/5 the pixel area of typical images, so there are multiple channels per pixel. In the simulated data, an interpolation is first used to resolve the individual channels. The interaction between the photons from the emitting object and the finite sized MCP channels is shown in Fig. 2(c-i and ii). Here, the continuous emission from the object is discretely sampled by the array of channels of the MCP. The photon statistics and gain are computed for each channel independently.

The signal level of each channel is determined by sampling a Poisson distribution associated with the amplitude of the incident signal onto each channel independently. Here, the magnitude of the noise increases as N, where N is the number of photons. The signal-to-noise ratio is therefore proportional to 1/N. The resulting detected signal corresponds to frame (c-ii) in Fig. 2. The image resulting from the nonlinear amplification of the detected photons by the multi channel plate is shown in Fig. 2(d). The gain of the detector is statistical in nature and has an exponential form given by λeλx, where x is the incident signal level and λ is the gain of the detector. The final aspect of the detector that affects the image is a blurring that occurs due to the photo-multiplied electrons falling on the emitting phosphor material, and their potential to scatter, and be incident in a different location. The blurring function is approximately Gaussian towards the peak and has a long exponential tail that results in cross-talk between not only adjacent channels, but potentially even non-adjacent channels. The result of this blurring can be seen in Fig. 2(e). The final process in the creation of the synthetic emission data is to add a uniform background noise obtained from a Gaussian distribution. This noise is due to energetic neutrons produced by the implosion interacting directly with the detector film. This noise is added in Fig. 2(f) and results in the synthetic X-ray emission image that is analyzed. Figure 2(g) gives an example of the actual data for comparison to the simulated image. As previously discussed, Eq. (2) can be used to analytically express the shape of the emission imaged by a pinhole array as a function of time and space across the MCP detector. After applying the numerical models to account for the statistics associated with signal detection, amplification, and the instrument response, a synthetic data set containing the spatially and temporally resolved emission history in a format that approximates that of actual data is obtained. In this manner, emission can be modeled and the following parameters can be adjusted to match a desired experimental configuration.

  • Gate shape

  • Gate width

  • Original emission shape

  • Emission burn width

  • Geometry of system (magnification of pinholes)

  • Velocity of object

  • Rotation of pinhole array

  • Signal-to-noise ratio

  • Timing of film strips (position of images on strips)

  • Jitter between timing of strips

  • Size of strips

  • Number of strips

While discussing simulation findings, the fractional velocity error will be used and is defined as the fractional difference of the returned velocity from the input velocity. That is

error=|vinputvoutput|vinput.
(8)

The constants associated with Poisson photon detection statics and exponential MCP gain were adjusted to best match the observed data and held fixed throughout the parameter scans of the simulations. When noise levels are discussed, they pertain to the level of Gaussian background noise.

Synthetic data sets were created and examined to determine the sensitivity that different variables had on the recovery of a known input residual velocity. Since there are random components associated with detected photon statistics and the gain of the MCP detector, the results are based on an average over a series of 10 trials within a specified variance.

The first trial examined the accuracy of the technique as the signal-to-noise ratio and intensity threshold applied to the synthetic emission were varied. This trial used typical values for the emission duration and detector configuration:

  • Burn width = 150 ps with Gaussian profile

  • Gate width = 100 ps with Gaussian profile along strips and infinite profile across strips

  • Gate speed = c/2

  • Data strips timed back to back.

The trial also used a 100 μm/ns velocity at a 45° angle, i.e., equal x and y magnitudes. Above a threshold level of ∼20%, there is a little change in the accuracy with regard to the threshold used.

The total signal-to-noise ratio is a product of the background Gaussian noise as well as the statistical noise associated with Poisson detection statistics and the exponential gain of the detector. Figure 3 shows profiles across an emission object with four specified signal-to-noise ratios. The signal-to-noise ratio was changed by adjusting the level of Gaussian noise. In these line profiles, it is observed that above the signal-to-noise level of ∼20, the effect of the Gaussian noise is suppressed relative to the other statistics (Poisson and exponential) producing a stable threshold performance above this level. Below this level as can be seen in Fig. 3, the dominant source of noise is the Gaussian component. In this range of signal-to-noise ratios, the inferred velocity becomes more sensitive to the selected emission threshold.

FIG. 3.

Lineouts in x (blue) and y (red) across a simulated emission object for varying levels of signal-to-noise: 10, 15, 20, and 30. Note that 20 and 30 look very similar, and it appears other sources of noise dominate above the signal-to-noise level of 20 while below that level Gaussian background noise dominates.

FIG. 3.

Lineouts in x (blue) and y (red) across a simulated emission object for varying levels of signal-to-noise: 10, 15, 20, and 30. Note that 20 and 30 look very similar, and it appears other sources of noise dominate above the signal-to-noise level of 20 while below that level Gaussian background noise dominates.

Close modal

Next, the accuracy of the routine to recover the correct input velocity was examined as the magnitude of the input velocity was varied. As shown in Fig. 4, it was found that the fractional error in the recovered velocity decreases, as the magnitude of the velocity increases. Errors in the recovered velocity arise from differences between the actual center of emission and the measured center of emission. Differences between the actual and measured centers of emission result from the noise of the measurement and the statistical nature of the photon detection and the subsequent amplification. As the velocity increases the total displacement of the emission from the expected stationary centers of emission increases while the level of statistically induced variation between the measured and actual emission center stays constant. Therefore, at larger separation distances, the fractional error in the recovered velocity is expected to decrease as errors in determining that emission centers have relatively less of an impact. The synthetic data shown in Fig. 4 were generated by varying the input velocity while keeping all other simulation inputs constant. The simulations were all set up in the same manner, with a full-width half-maximum emission duration of 150 ps, back to back MCP strip timings, and a signal-to-noise ratio of 30. The emission velocity was set to an angle of 45° with respect to the MCP gate. The measured center of emission was found for each image using the relative 55% threshold of the maximum signal.

FIG. 4.

Solid blue curve represents the fractional difference in input velocity value as a function of the input velocity. Also shown by the dashed green curve is the absolute difference in measured velocity as a function of input velocity for the same data set. The data set used a constant signal-to-noise ratio of 30. The horizontal dashed line represents the vertical origin for the absolute velocity difference shown on the right hand side vertical axis. At a velocity of ∼24 μm/ns, the fractional and absolute error in velocity is approximately 50% and 12 μm/ns, respectively.

FIG. 4.

Solid blue curve represents the fractional difference in input velocity value as a function of the input velocity. Also shown by the dashed green curve is the absolute difference in measured velocity as a function of input velocity for the same data set. The data set used a constant signal-to-noise ratio of 30. The horizontal dashed line represents the vertical origin for the absolute velocity difference shown on the right hand side vertical axis. At a velocity of ∼24 μm/ns, the fractional and absolute error in velocity is approximately 50% and 12 μm/ns, respectively.

Close modal

As seen in Fig. 4, velocities below 24 μm/ns have a greater than 50% error in the recovered velocity. An estimate of the minimum velocity which can be measured with this technique can be made by estimating the minimum velocity required to move the emission center by the detector resolution element in the image plane.

vδMΔ.
(9)

Here, v is the velocity of emission, δ is the pixel size, M is the image magnification, and Δ is the temporal emission duration. In the absence of any measurement uncertainty, Eq. (9) indicates that the minimum resolvable velocity would be equal to ∼11 μm/ns for an experiment with a total emission duration of 150 ps and the standard pixel size and magnification of δ = 20 μm and M = 12×, respectively. Creating synthetic data with typical experimental noise levels to mimic the measurement uncertainty, it was observed that the variance in the emission center location was typically no more than 5δ from the actual emission center. Therefore, emission velocities ≳55 μm/ns would translate the center of emission a distance greater than or equal to the noise induced variance over a 150 ps emission duration. It is thought that this is the reason that, as seen in Fig. 4, the expected error in the velocity measurement is seen to stay relatively constant for emission velocities >50 μm/ns. Velocities in the range between 15 μm/ns and 50 μm/ns are able to be measured as the time period of emission from the first image to the last is usually close to 300 ps for a temporal emission profile with a full-width half-maximum of ∼150 ps. As Eq. (9) and Fig. 2 indicate, the minimum velocity and the error associated with the velocity measurement will decrease as the displacement of the emission center over the duration of the measurement increases. This can be accomplished by either an increase in the emission duration, or an increase in the emission velocity.

The final trial presented here was to determine the effect of the number of data points on the accuracy of the analysis algorithm. This trial was run with a 50 μm/ns velocity once again at a 45° angle, with equal x and y components. The signal-to-noise level was set to 50:1, a very high level, and an infinite emission duration was used. This ensured that every synthetic image had the same intensity profile before the statistical amplitude variations from noise and detector gain were applied. A 50% threshold level was used for all trials. This setup is unphysical so the absolute level of errors is not a good measure, but the error from one trial to another is important in determining how the configuration of the data affects the accuracy of the method. The relative error in velocity as the number of synthetic data points and the subsequent area over which the data were spread onto the micro-channel plate was increased is shown in Fig. 5. The synthetic images were spatially distributed onto the detector in a manner consistent with the acquisition of actual data. This means that emission data are first collected vertically along the length of a micro-channel plate strip. After the data have covered the vertical extent of a strip, the emission data are then applied in the same vertical manner to the horizontally adjacent strip. It can be seen that there is a steep drop in the fractional error as the data points move onto the second strip, from the first but after that, the accuracy stays relatively constant as more emission data points are added across the larger detector area. Shot data from NIF are usually established in a way that provides data across two strips. It also shows that if the data are only on one strip, a sizeable 3–4× increase in error in the recovered velocity is expected.

FIG. 5.

Fractional difference in the recovered velocity as a function of the number of images (blue dots) used in the recovery algorithm. Each blue data point is a separate analysis. The dashed red curve is a fit to the data trend. The solid vertical lines indicate when the data points moved onto a different strip, representing an increased temporal and spatial domain for the algorithm.

FIG. 5.

Fractional difference in the recovered velocity as a function of the number of images (blue dots) used in the recovery algorithm. Each blue data point is a separate analysis. The dashed red curve is a fit to the data trend. The solid vertical lines indicate when the data points moved onto a different strip, representing an increased temporal and spatial domain for the algorithm.

Close modal

With the methodology outlined above, the residual velocity and the uncertainty in this velocity for x-ray emission data can be estimated in the following manner. First, a normalized intensity threshold is chosen. Then, the intensity weighted center of emission above this threshold is found for each emission image. From the difference between the measured emission centers and the emission centers for a stationary object, a residual emission velocity can be inferred.13 Synthetic data are then created with the measured emission duration, spatial extent, signal-to-noise, and inferred velocity. To account for uncertainty in the registration of the pinhole array, the routine is initialized with an offset of 1° in rotation and a ±0.25× variance in magnification. Additionally, an uncertainty in the timing of each strip with a variance of 10 ps is included to account for the measured uncertainty in the reported timing. The routine is then run ten times and the variance in the inferred velocity that results from the random noise, interstrip timing fluctuation, and uncertainty in rotation and magnification is used as the error bar on the inferred velocity.

This analysis and comparison with the neutron time of flight measurements are presented in detail for experiment N140225. Figure 6 shows an overview of the pertinent details of this experiment. This includes the orientations from which the temporally and spatially resolved X-ray emission is measured, details of an unintentional capsule drive deficit, and time integrated images of the neutron and x-ray emission. This experiment was conducted using a gold hohlraum with an initial diameter of 5.75 mm and length of 9.43 mm, which was filled with helium gas to a pressure of 1.6 mg/cm3. The spherical capsule target had an initial radius of 1.112 mm and an ablator thickness of 177.2 μm and a deuterium tritium ice thickness of 68.9 μm. In the indirectly driven implosion experiments at the NIF, 192 laser beams are arranged into 48 separate laser quads which irradiate the inner surface of the hohlraum target in three azimuthally symmetric cones. Each of the three cones consists of 16 quads. The two so-called outer cones create rings of X-ray emission centered at z = ±2.26 mm, while the X-ray emission from the inner cone is centered around the hohlraum mid-plane at z = 0 mm. The absolute and relative amounts of power in the inner and outer laser cones are varied in time to create a radiation drive that symmetrically compresses the fusion capsule target while minimizing the adiabat of the DT fuel. In experiment N140225, the so-called high foot laser pulse shape was used.15 The requested energy and peak power of the laser pulse were 1.63 MJ and 350 TW, respectively. Unfortunately, as shown in Figs. 6(b) and 6(c), two inner laser quads, denoted as bundle 42 (B42), delivered low in laser power and energy with respect to the other inner laser beams. Three-dimensional view factor calculations indicate that this created an azimuthal radiation asymmetry centered at a θ=90°,ϕ=315°. Before the peak of the laser pulse, the power in B42 was on average ∼14% of the average power delivered by the 14 other inner quads. During the time period of peak laser power, B42 reached on average only ∼30% of the power of other inner laser quads. The azimuthal imbalance of the laser power is expected to result in the bulk motion of the implosion for this experiment. A simple estimate of the magnitude of the flux asymmetry that results from the lower amount of power delivered to B42 was made using 3D view factor calculations. These calculations were made using the VISRAD program.16 In these calculations, the effects of cross beam energy transfer17 and beam absorption through the hohlraum were not accounted for directly. Instead, the laser cone fraction was first adjusted to create a symmetric radiation drive at the capsule. Then, the power of the beams in B42 was reduced to 30% of the other inner cone laser beams. The reduction in laser power of B42 was chosen to match the observed reduction during the time period of peak laser power, as the majority of the laser energy is delivered during the time period of peak laser power. These calculations suggest that the reduction in peak power of B42 results in a flux asymmetry along the equator of the capsule, with a peak to valley flux difference of ∼1.8%. Despite this flux asymmetry, N140225 still achieved a primary DT neutron yield of 2.8 × 1015, and the ion temperatures from the average width of the DT and DD neutron spectrum were inferred to be 4.51 and 3.94 keV, respectively.

FIG. 6.

Details of the experimental geometry, laser delivery, and temporally integrated X-ray and neutron emission data for experiment N140225. (a) Illustration of the hohlraum with relevant dimensions from the equatorial θ = 90°, ϕ=78.75° line of sight. The dashed black line in (a) and (b) represents in initial capsule diameter, while the 100 μm diameter purple sphere represents the X-ray emission diameter at stagnation. (b) Illustration of the hohlraum from the polar θ = 0°, ϕ=0° line of sight. The red circle illustrates the impact to the inner laser cone azimuthal asymmetry that results from the reduced delivered power of the two quads in bundle 42 (B42). The wedge label B42 denotes the area over which the two quads of B42 irradiate the hohlraum. (c) The requested inner quad power vs. time denoted by the dashed curve is compared to the average delivered quad power of B42, shown here as the solid red curve, and with the average delivered power of the remaining 14 inner cone quads, indicated here by the solid blue curve. (d) and (e) Time integrated X-ray emission as seen from the equatorial θ = 90°, ϕ=78.75° and polar θ = 0°, ϕ=0° line of sight, respectively. (f) A temporally integrated image of the 13–15 MeV primary neutron emission as seen from the θ = 90°, ϕ=315° line of sight. The peak intensity of each image was used to individually normalize each piece of emission.

FIG. 6.

Details of the experimental geometry, laser delivery, and temporally integrated X-ray and neutron emission data for experiment N140225. (a) Illustration of the hohlraum with relevant dimensions from the equatorial θ = 90°, ϕ=78.75° line of sight. The dashed black line in (a) and (b) represents in initial capsule diameter, while the 100 μm diameter purple sphere represents the X-ray emission diameter at stagnation. (b) Illustration of the hohlraum from the polar θ = 0°, ϕ=0° line of sight. The red circle illustrates the impact to the inner laser cone azimuthal asymmetry that results from the reduced delivered power of the two quads in bundle 42 (B42). The wedge label B42 denotes the area over which the two quads of B42 irradiate the hohlraum. (c) The requested inner quad power vs. time denoted by the dashed curve is compared to the average delivered quad power of B42, shown here as the solid red curve, and with the average delivered power of the remaining 14 inner cone quads, indicated here by the solid blue curve. (d) and (e) Time integrated X-ray emission as seen from the equatorial θ = 90°, ϕ=78.75° and polar θ = 0°, ϕ=0° line of sight, respectively. (f) A temporally integrated image of the 13–15 MeV primary neutron emission as seen from the θ = 90°, ϕ=315° line of sight. The peak intensity of each image was used to individually normalize each piece of emission.

Close modal

Also shown in Figs. 6(a) and 6(b) are the views from which the equatorial and polar X-ray emission is observed, respectively. The equatorial line of sight views the X-ray self emission of the implosion at stagnation through a gold coated high density carbon window cut into the hohlraum at an azimuthal angle of ϕ=78.75°. The gold coated window in combination with the 2.5 mm of Kapton filtering covering the hGXD is expected to transmit X-ray with energies >8 keV along the equatorial line of sight. The polar hGXD is also filtered with the same amount of Kapton and detects X-rays >7.2 keV. For both detectors, images are created by an array of pinholes with a nominal spatial resolution of ∼10 μm. Each image is temporal integrated over ∼100 ps. In this experiment, X-ray emission images recorded on two separate strips over a total temporal duration of 250 ps were used to infer the velocity for both the equatorial and polar views.

In addition to the time resolved X-ray measurements, spatially resolved time integrated measurements of the X-ray emission are also made. The time integrated measurements are recorded onto an image plate detector. In different areas of this detector, separate filters made from aluminum, vanadium, copper, germanium, Kapton, and molybdenum are used.18 Due to the difference in the spectral transmission of the filters, one image can be subtracted from another, forming a so-called Ross pair, that results in an image with spectral content either between a band of energies, or above a certain photon energy. Figures 6(d) and 6(e) show the time integrated X-ray emission as seen from the equatorial and polar line of sight, respectively. Each of these time integrated images is imaged through 85 μm of aluminum and 1525 μm of Kapton, which yields a transmission of 10% at a photon energy of ∼8 keV. These images have been found to be largely representative of the shape of the time resolved emission at peak X-ray emission. In addition to separating the spectral content of the X-ray emission, these time integrated X-ray measurements are also quite useful for comparing to the temporally integrated neutron emission image. Figure 6(f) shows the neutron image as seen from the θ=90°,ϕ=315° line of sight measured using the neutron imaging diagnostic.19 As will be discussed in more detail, comparing the profiles of neutron and X-ray emission at different photon energies is one method being explored to better understand the dynamics that occur during the stagnation of the implosion.

Figure 7 shows the inferred velocity and uncertainty of the X-ray emission data as seen from the equatorial view. As shown in Fig. 6(a), from this line of sight, a velocity in the vertical direction z and a horizontal direction x is observed. Here, the residual motion is calculated across a range of intensity thresholds, from 25% to 80%. Figure 7(a) gives an example of how the x-ray emission shape and emission profile changes in time for three different intensity thresholds. Again, the threshold percentage of intensity is calculated with respect to the peak intensity for each image independently. Figure 7(b) shows the inferred velocity as a function of threshold level in the x and z directions. Also shown by the shaded blue and green bands are the reported velocities from the neutron time of flight detectors in the x and z directions, respectively. At threshold levels between 0.25 and 0.5, the inferred residual X-ray emission velocity is found to be in agreement with the velocity inferred from the neutron time of flight detectors. Across these contour levels, the average residual velocity was found to be −11.0 ± 11.3 μm/ns and 28.9 ± 13.9 μm/ns in the x and z directions, respectively. Comparatively, a velocity of 5.9 ± 15 in the x and 27.3 ± 15 μm/ns in the z direction was inferred from the emitted 14 MeV neutron spectrum measured by the neutron time of flight detectors. For this line of sight, the neutron velocities are within the error bars of the inferred X-ray emission velocity.

FIG. 7.

(a) Images of X-ray emission at energies >8 keV taken at three different times during the implosion. Here, time is with respect to the time of peak X-ray emission at t = 0. Each row shows the emission at three different times above a different intensity threshold. Here, each intensity threshold is a percentage of the peak intensity for a given frame. Qualitatively, at higher thresholds, the centroid position of the emission can be observed to translate a greater horizontal distance in the same amount of time as compared to the images at a lower threshold. (b) The inferred velocity of the X-ray emission in the x (blue circles) and z (green diamonds) direction (see Fig. 6(a)) as a function of emission threshold. As seen in (a), the inferred velocity in the x direction does indeed increase as the emission threshold increases. Also shown by the blue and green bands are the inferred neutron velocities in the x and z directions, respectively. The width of the bands denotes the ±15 μm/ns uncertainty associated with the measurement.

FIG. 7.

(a) Images of X-ray emission at energies >8 keV taken at three different times during the implosion. Here, time is with respect to the time of peak X-ray emission at t = 0. Each row shows the emission at three different times above a different intensity threshold. Here, each intensity threshold is a percentage of the peak intensity for a given frame. Qualitatively, at higher thresholds, the centroid position of the emission can be observed to translate a greater horizontal distance in the same amount of time as compared to the images at a lower threshold. (b) The inferred velocity of the X-ray emission in the x (blue circles) and z (green diamonds) direction (see Fig. 6(a)) as a function of emission threshold. As seen in (a), the inferred velocity in the x direction does indeed increase as the emission threshold increases. Also shown by the blue and green bands are the inferred neutron velocities in the x and z directions, respectively. The width of the bands denotes the ±15 μm/ns uncertainty associated with the measurement.

Close modal

It is observed that at contour levels above 0.5, the magnitude of the x component of the inferred X-ray velocity begins to rapidly rise and approach ∼−100 μm/ns. Examining the X-ray emission as the threshold value is changed from 25% to 75% as shown Fig. 7(a), it is observed that a bright localized source of emission within the larger emitting volume becomes the emission at higher threshold levels. The residual X-ray emission analysis therefore is indicating that a smaller, localized source of bright emission is moving at a relatively higher velocity through the larger, slowing moving volume of emitting plasma. This picture is entirely consistent with the calculations of mode 1 drive asymmetries, which show a smaller localized jet of faster material moving through the emitting plasma in the direction of the lower applied flux.10 As previously discussed in this experiment, the flux asymmetry was localized along the equatorial plane of the capsule at an azimuthal angle of 330°. Therefore, the motion from any localized jet should be more apparent from examining the X-ray emission as seen from the polar line of sight (Fig. 6(b)).

As with the equatorial emission data, when the analysis was performed on the time resolved polar X-ray emission, it was observed that the velocity remained fairly constant at lower contour levels and then increased rapidly at higher contour levels. Averaging over the X-ray emission contours from 0.19 to 0.43, an average residual velocity of 38.5 ± 11.7 μm/ns at a ϕ of 330.5 ± 20.4° is found. Similar to the equatorial view, the bright localized region of emission, seen from the polar view in Fig. 6(e) in the lower right portion of emission, is also observed to move at higher velocities. The average velocity of the localized bright source of emission was inferred to be 112 ± 13.0 μm/ns, as the threshold at which the velocity is measured is set above 0.43. The direction of the motion as the threshold level is raised stays relatively constant at θ = 90.4 ± 5.9° and ϕ=323.5±6.6°. This velocity is consistent with the expected direction of residual motion, along a ϕ of 315°, that was expected due to the reduction in laser power and lower radiation flux from this azimuth. Furthermore, the observation of a higher velocity localized region of emission that moves towards the region of lower flux is also consistent with the physical picture developed from the detailed hydrodynamic calculations.10 

Additionally, projecting the inferred velocity from the polar line of sight onto the x axis at a ϕ of 348.75° yields a vx=27.65±8.6μm/ns, which is consistent within the overlapping error bars with the velocity as measured from the equatorial X-ray emission measurement. The projected velocity components of the neutron time of flight measurements were reported to be vx = −5.9 ± 15 μm/ns and vy = −67.4 ± 15 μm/ns. The neutron velocity in the y direction is outside the standard deviation of the X-ray velocities measured in this direction. The X-ray and neutron velocity in the x-direction agree within the uncertainty of the two measurements. Compared to the inferred X-ray velocity, the resulting velocity of the neutron emission as inferred from the neutron time of flight detectors has a larger velocity and is orientated at a different azimuthal angle of ϕ=265°. Table I summarizes the X-ray and neutron velocity measurements. It is interesting to note that the agreement in the vertical (z) direction between the two measurements is fairly good, but in the x-y plane in which the capsule flux asymmetry was imposed, the agreement is not as good.

TABLE I.

Inferred components of the residual velocity vector as inferred from X-ray emission >7 keV and 14 MeV neutron emission from experiment N140225.

vx (μm/ns)vy (μm/ns)vz (μm/ns)v (μm/ns)θ (deg)ϕ(deg)
X-ray contour <0.5 28.2 ± 8.6 −16.0 ± 8.6 29.9 ± 13.9 44.1 ± 18.0 47.3 ± 21.2 330.5 ± 20.4 
Neutron −5.9 ± 15 −67.4 ± 15 27.3 ± 15 73.0 ± 26 68 ± 15 265 ± 14 
vx (μm/ns)vy (μm/ns)vz (μm/ns)v (μm/ns)θ (deg)ϕ(deg)
X-ray contour <0.5 28.2 ± 8.6 −16.0 ± 8.6 29.9 ± 13.9 44.1 ± 18.0 47.3 ± 21.2 330.5 ± 20.4 
Neutron −5.9 ± 15 −67.4 ± 15 27.3 ± 15 73.0 ± 26 68 ± 15 265 ± 14 

Along a single line of sight, for a data set of eight experiments, the standard deviation in the difference of the residual velocity and angle was found to be 13.3 μm/ns and 13.9°, respectively, between the X-ray emission and neutron time of flight measurements. These experiments consisted of both cryogenically layered and symmetry capsule targets with and without intentionally imposed asymmetries.

Understanding the composition and species of material that is emitting the X-rays would inform our understanding of how to interpret the X-ray and neutron motion. Here, the morphology of the time integrated X-ray and neutron emission are compared in an attempt to ascertain if the bright fast moving feature observed in the X-ray emission comprised neutron emitting DT plasma or if it corresponds to non-neutron emitting CH plasma. Differences in the line of sight between the X-ray and neutron detectors in this experiment lead to some ambiguity in the composition. However, the approach outlined below should be applicable to other experiments and can be implemented in a much more straight forward manner once the soon to be completed polar and equatorial common line of sight X-ray and neutron detectors are commissioned.

As the neutron image is not temporally resolved, to investigate the relationship between the neutron and X-ray images, the time integrated X-ray images are used. While not as distinct, the bright localized source of fast moving X-ray emission is still quite visible in the time integrated polar X-ray image (Fig. 6(e)). One advantage of using the time integrated X-ray measurements is that images at photon energies >20 keV can be used. This image should be largely insensitive to optical depth effects of the assembled fuel and ablator. Since the X-ray and neutron images are not taken along the same line of sight, a so-called common integrated profile (CIP)20 is performed in order to compare the 1-D profiles of the X-ray and neutron emission. In this method, the polar X-ray image is first rotated such that the vertical axis corresponds to the azimuthal angle of the neutron imager diagnostic of ϕ=315° as shown in Fig. 8(a). Once this rotation is performed, both the X-ray and neutron image are summed vertically to create 1-D profiles. In this work, the profiles are normalized to the peak intensity of each profile. A comparison of the time integrated normalized neutron and the X-ray profiles created from images recorded at photon energies >7 keV (dashed line) and >20 keV (solid line) are shown in Fig. 8(c). Qualitatively, the differences between the shape of the neutron profile (dotted curve) and X-ray profiles are small.

FIG. 8.

(a) Time integrated polar X-ray emission at photon energies >20 keV obtained from the Ross pair X-ray technique. The image is rotated such that the vertical axis azimuthally aligns with the NIS line of sight. (b) Time integrated image of 14 MeV neutrons from the θ = 90°, ϕ=315°. (c) Normalized common integrated profiles of the polar X-ray emission at photon energies above 7 and 20 keV given by the dashed and solid curve, respectively. Also shown is the profile of the 14 MeV neutron emission (dotted curve). These emission profiles are all integrated along the same line of sight of ϕ=315°. (d) A synthetic asymmetric 1D temperature profile. (e) The normalized X-ray and neutron emissivity of the synthetic profile shown in (d). The black dashed outer curve and the solid blue inner curve are the normalized X-ray emission at energies greater than 7 and 20 keV, respectively. Here, opacity effects are not considered. The solid and dashed red central curves are the normalized neutron emissivity using the reactivity given by Eq. (12) and the Bosch–Hale formulas, respectively.

FIG. 8.

(a) Time integrated polar X-ray emission at photon energies >20 keV obtained from the Ross pair X-ray technique. The image is rotated such that the vertical axis azimuthally aligns with the NIS line of sight. (b) Time integrated image of 14 MeV neutrons from the θ = 90°, ϕ=315°. (c) Normalized common integrated profiles of the polar X-ray emission at photon energies above 7 and 20 keV given by the dashed and solid curve, respectively. Also shown is the profile of the 14 MeV neutron emission (dotted curve). These emission profiles are all integrated along the same line of sight of ϕ=315°. (d) A synthetic asymmetric 1D temperature profile. (e) The normalized X-ray and neutron emissivity of the synthetic profile shown in (d). The black dashed outer curve and the solid blue inner curve are the normalized X-ray emission at energies greater than 7 and 20 keV, respectively. Here, opacity effects are not considered. The solid and dashed red central curves are the normalized neutron emissivity using the reactivity given by Eq. (12) and the Bosch–Hale formulas, respectively.

Close modal

To better understand the expected relationship between the X-ray and neutron profiles, an asymmetric 1-D temperature profile was created and the resulting X-ray and neutron emissivities were calculated. The temperature profile is shown in Fig. 8(d). Here, the peak of the temperature profile was set to 4.5 keV to be similar to the measured width of the DT neutron spectrum on experiment N140225. The emissivities of X-ray and neutron emission are shown in Fig. 8(e) and were calculated in the following manner.

First, the magnitude of the energy emitted by X-rays from the hot spot at stagnation via free-free Bremsstrahlung above a photon cutoff energy was estimated using the proportionality given by

γxrayZ2neniTe1/2eEcTeVpτxray.
(10)

Here, Z is the average ionization state, ne and ni are the electron and ion density, respectively, Te is the electron temperature, Ec is the X-ray cutoff energy below which a negligible amount of signal is transmitted through the diagnostic filtering, Vp is the volume of emission, and τx-ray is the duration of the X-ray emission.

Next, the number of neutrons produced by the hot spot, γDT, can be written as

γDT=nDnTσvDTΔτDTVp,
(11)

where nD and nT are the deuterium and tritium ion density, respectively, τDT is the duration of emission, Vp is the volume of emission, and σvDT is the fusion reactivity probability21 given by,

σvDT=9.1×1016e0.572|lnTi64.2|2.13.
(12)

Here, Ti is the ion temperature. Equation (12) has been stated to be accurate to 10% for ion temperatures greater than 3 keV.

Using Eqs. (10)–(12), the ratio of X-ray to neutron emission can be written as,

γxrayγDTZ2neniTe1/2eEcTenDnTe0.572|lnTi64.2|2.13.
(13)

If the hot spot is only comprised an equal molar concentration of fully ionized deuterium and tritium ions, Z, the average ionization state can be set to 1 and neni can be rewritten as nDnT. Furthermore, under the assumption that Te ≈ Ti, Eq. (13) can be further reduced to only a dependence on temperature,

γxrayγDTT1/2eEcTe0.572|lnT64.2|2.13.
(14)

In these limits, the normalized profiles of the X-ray and neutron emission from pure DT plasma can be calculated and compared. Here, the opacity effects from the surrounding assembled fuel and ablator have not been included.

Figure 8(e) shows the resulting normalized neutron and X-ray profiles. In Fig. 8(e), the two red curves that are nearly overlapped with each other show the predicted relative neutron emission using Eq. (12) (solid) and the Bosch and Hale (dashed)22 reactivities, respectively. The dashed outer curve and solid inner curve in Fig. 8(e) are the normalized Bremsstrahlung emission curves with low energy photon cutoffs of 7 keV and 20 keV, respectively. In this example, the agreement between the shape of the normalized X-ray and neutron emission near the peak of the profile at higher temperatures is fairly good. However, at lower temperatures, near the edges of the profile, the agreement decreases with the shape of X-ray emission being slightly larger and slightly smaller at the lower 7 keV and higher 20 keV photon energy cutoff, respectively. Unlike the calculations shown in Fig. 8(e), in the data shown in Fig. 8(c), the X-ray profiles at >7 and >20 keV are of similar widths. This could be due to opacity effects which would be expected to affect images taken at lower photon energies more. Also, unlike our simple estimate of the emissivities, Fig. 8(c) shows that the width of the measured >20 keV profile is slightly larger than that of the neutron profile. Here, uncertainty in the magnification between the X-ray and neutron images could also be playing a role. If unrelated to a magnification uncertainty, the larger width may suggest that there is emission from the ablator material that is emitting around the edge of the larger hot spot from either ablation front feed through or from ablator-fuel mix. The difference in the X-ray and neutron profiles at the edges of the temperature profile could also be affected by the uncertainty in the neutron reactivity. As previously stated, the accuracy of the reactivity given by Eq. (12) decreases as the temperature drops below 3 keV. Additionally, the radiation hydrodynamic calculations indicate that local thermal equilibrium between Te and Ti does not exist for the entirety of the stagnation phase. This could also lead to differences in the profiles between X-ray and neutron emission.

Equation (13) would suggest that if the localized bright source of fast moving X-ray emission comprised CH, then the yield of that emission would scale as Z2neCHniCHeEc/TeCH. Here, the subscripts CH denote the temperature and density of the potential ablator material that has mixed into the hotspot. These quantities do not have to be equal to those of the surrounding DT plasma. If they are similar, then Eq. (13) would indicate a relative enhancement of the X-ray yield due to the Z2neni term, compared to the surrounding DT plasma.23 This would in turn narrow the normalized profile. This scenario is not well supported by the data, as the measured X-ray profile at photon energies >20 keV is actually slightly larger than the neutron profile. In this experiment, the inference of species composition by this technique alone is somewhat ambiguous. This is due to the way in which the local bright feature of X-ray emission is aligned with respect to the neutron emission, the CIP profile may not be very sensitive to composition of the local bright feature. However, the sensitivity of the CIP profile to the composition of the emitting plasma is expected to be higher in experiments, where localized features are aligned towards the edge of the neutron image. Taking into account the volume of emission and the inferred temperature from the width of the neutron spectra, the magnitude of the total X-ray emissivity was consistent with other unperturbed implosion experiments that used similar targets and radiation drives. This is thought to indicate that there was no appreciable additional mix of higher Z ablator material into the hot spot due to the radiation flux asymmetry and supports the CIP analysis that suggests that the bright localized faster moving emission is originating from DT rather than CH plasma.

The comparison between the X-ray and neutron detectors is expected to become more straightforward with added new common line of sight X-ray and neutron detectors. As the name implies, the images will be taken along the same line of sight, allowing a 2-D comparison of the neutron and X-ray emission. This will help to considerably reduce the ambiguity associated with comparing 1-D profiles along different lines of sight. Additionally, uncertainty in the magnification and registration of the X-ray and neutron images should decrease. If a 2-D spatially resolved fit to the X-ray emission can constrain the Te and ne of the image, then in the absence of ablator mix, ne = ni and using the emissivity values in absolute units, it should be possible to constrain the temporally averaged Ti of the implosion. This spatially resolved Ti measurement of the condition of the hot spot during stagnation would be quite interesting to compare with the spatially averaged temperature measurements from the neutron time of flight detectors. Furthermore, this approach would attempt to constrain the spatially resolved time averaged electron and ion temperature and density within the hot spot. This would greatly inform our understanding of the conditions that are reached during the stagnation phase of the inertially confined implosions.

This work has focused on developing a method to determine the accuracy at which the motion of X-ray emission throughout the stagnation phase of an ICF implosion can be measured using the gated X-ray detectors at the NIF. As the implosion stagnates, these detectors spatially and temporally resolve the X-ray emission at energies >7 keV produced from the hot, ∼2–5 keV, volume of reacting plasma over a time period of ∼±100 ps from peak pressure. In this work, it was found that the accuracy at which a velocity can be measured improves as the displacement associated with the velocity increases. This means for a fixed emission duration, the accuracy improves at higher velocities. Additionally, a detailed analytic and numeric modeling of the detected X-ray emission was performed in order to assess the accuracy of the technique used to infer the velocity. It was found that the accuracy of this technique is sufficient to resolve a residual velocity of 35 μm/ns, which calculations have suggested is the maximum residual velocity at which stagnation conditions that result in ignition can achieved at NIF.

This model was studied using synthetic data with a known velocity and provided a method to determine the impact that a given signal-to-noise ratio and the temporal uncertainties associated with the detection of data had on the accuracy of recovering the specified velocity. As shown in Fig. 4, for a synthetic data set with a peak signal-to-noise ratio and temporal emission duration that were set to approximate the conditions found in typical implosion experiments, it was found that error in the recovered velocity reached 50% at a velocity of 24 μm/ns. Additionally, as shown in Fig. 5, it was found that as the number of data points was increased and spread over a larger area (number of detector strips), the fractional error in the recovered velocity decreased 3–4 times. Spreading the data over a larger area helps to increase the sensitivity to the magnitudes of the magnification and rotation of the pinhole array and leads to a more accurate fit. To estimate the uncertainty in the recovered velocity for a given measurement, a synthetic data set was created for each individual experiment. The synthetic data used the measured locations of the emission centers, and used the observed signal-to-noise level and spatial distribution on the detector. The routine, which determines the emission velocity by minimizing the difference between the expected location of the emission using the metrologized pinhole locations and the observed emission locations, was then run 10 times, with the MCP strip timings each being allowed to vary by the temporal triggering jitter of ±10 ps. The variance in the recovered velocity was then used as an error bar.

Using this method, the residual implosion velocity for experiment N140225 was examined. For this experiment, which was an indirectly driven implosion with a DT fuel layer, the capsule experienced azimuthal decrease in flux due to an inner laser bundle only delivering approximately 30% of the laser power during the peak of the pulse. While unintentional, the asymmetric radiation drive in this experiment provided a well suited data set to evaluate the technique to determine the velocity of the X-ray emission. 3D view factor calculations indicate that the reduction in flux was centered along the equatorial plane (θ = 90°) at an azimuthal angle ϕ=315° and extended over a ±45° angular range. These calculations suggest that the reduction in the inner cone drive reduced the radiation flux over this localized area by ∼1.8% from the average azimuthal flux. The emission from this experiment was observed to have a brighter localized region of emission within the larger volume of X-ray emission. By applying an intensity dependent threshold to the data, the velocity of different emitting volumes was inferred. It was found that larger emitting volumes had an average emission velocity of 44 ± 18 μm/ns at a θ = 47.3 ± 21.2° and ϕ=330.5±20.4° at intensity thresholds between 20% and 50%. The azimuthal direction of this velocity is consistent with the direction at which the capsule experienced the flux deficit. Comparatively, the neutron time of flight detectors inferred a velocity of 73 ± 26 μm/ns at a θ = 68.3 ± 15° and ϕ=265±14°. While the agreement in the velocity in the vertical z direction between the X-ray and neutron measurements was good, in the horizontal plane, the neutron time of flight detector inferred a much higher velocity in the −y direction than the X-ray measurement. This leads to an overall higher inferred neutron velocity in an azimuthal ϕ direction that was not consistent with the inferred X-ray velocity.

The velocity of the bright localized region of X-ray emission was isolated by using intensity thresholds >0.5. The smaller localized bright region of emission was found to reach an average peak velocity of 112.8 ± 13.0 μm/ns at a θ = 90.4 ± 5.9° and a ϕ=323.5±6.6°. This perturbation is quite consistent with the direction of the calculated capsule flux deficit from the previously mentioned view factor calculations.

Finally, to compare the spatial X-ray and neutron emission profiles from different lines of sight, the common integrated profile method was employed. Here, the 1-D profiles of the neutron and X-ray emission from energies >20 keV appear to be in good agreement with each other. Due to the ambiguity associated with this method and with this particular experiment, it was difficult to reach a conclusion on whether the localized bright source of X-ray emission was composed of neutron emitting DT atoms or if it comprised higher Z CH from ablation front mix. Additionally, simple estimates of the emissivity predict that the width of X-ray profile at energies >20 keV should be slightly smaller than the profile of neutron emission for N140225. In this experiment, the width of X-ray emission was observed to be slightly larger. As discussed, this discrepancy could arise from several sources, some of which include the uncertainty in magnification of the two detectors used, as well as the assumption that Ti = Te and the uncertainty in the equations used to estimate the reactivity of neutron emission at temperatures lower than 3 keV.

Future work will focus on developing a more complete understanding of the temporal and spatial observables associated with residual motion from the X-ray and neutron diagnostics. This will be aided by the new common line of sight X-ray and neutron detectors that will be commissioned in the coming year. These detectors will yield 2-D images of X-ray and neutron emission along the same line of sight and with reduced uncertainty in the magnification. Of particular interest is a comparison of absolute emissivities of X-ray and neutron images to gain access to the species composition of the emitting plasma and potentially the spatial distribution of electron and ion temperatures. In addition to this work, experiments with more deliberate and controlled applied asymmetries to the radiation drive and DT ice layer thickness have been performed. Results from these experiments with modeling will be presented in detail in a future publication.

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 No. DE-AC52-07NA27344.

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