A new generation of gated x-ray detectors at the National Ignition Facility has brought faster, enhanced imaging capabilities. Their performance is currently limited by the amount of signal they can be operated with before space charge effects in their electron tube start to compromise their temporal and spatial response. We present a technique to characterize this phenomenon and apply it to a prototype of such a system, the Single Line Of Sight camera. The results of this characterization are used to benchmark particle-in-cell simulations of the electrons drifting inside the detector, which are found to well reproduce the experimental data. These simulations are then employed to predict the optimum photon flux to the camera, with the goal to increase the quality of the images obtained on an experimental campaign while preventing the appearance of deleterious effects. They also offer some insights into some of the improvements that can be brought to the new pulse-dilation systems being built at Lawrence Livermore National Laboratory.

At the National Ignition Facility1 (NIF), the Single Line Of Sight (SLOS) camera2 is a part of a new generation of pulse-dilation-based detectors, first introduced with the DIlation X-ray Imager3 (DIXI) camera, which are increasingly relied upon to record x-ray emission or radiographs of imploding Inertial Confinement Fusion4 (ICF) capsules. Since it was commissioned in 2014, the DIXI camera has been used on more than 300 NIF shots to provide x-ray imaging with a temporal resolution of 10 ps, well below the ∼100 ps achieved by the MicroChannel Plate (MCP)-based Gated X-Ray Detectors5 (GXDs). While the SLOS camera only achieves 35 ps temporal resolution, it is able to record four consecutive frames from the same image projected on its photocathode (PC), allowing its use with advanced x-ray imaging optics such as the Crystal Backlighter Imager6 (CBI).

Both DIXI and SLOS rely on the same underlying scheme7 that consists in providing a time-varying acceleration to an electron bunch created by the x-ray interaction with a photocathode and letting it drift and stretch while magnetically focused for several nanoseconds toward an electron-sensitive “backend” detector that captures slices of the bunch corresponding to small amounts of time. The hybrid complementary metal–oxide–semiconductor (hCMOS) sensor used in SLOS was developed by Sandia National Laboratories.8 It is able to record up to four frames with integration times as short as 2 ns with a dead time of 2 ns. The reader can refer to Refs. 2 and 9 to learn about the SLOS camera working principle, technical challenges, and initial characterization and commissioning.

One anticipated2 limitation of the SLOS camera is its ability to perform optimally under high photon flux: as the photocurrent increases in the drift region, Coulomb repulsion starts to stretch the electron packet at an even larger rate than the one that was initially introduced in the acceleration region. While the imposed 0.6-T axial magnetic field prevents electrons from shifting in the transverse drift direction, stretching in the axial direction will occur. Because of this additional broadening, a short event of duration Δt at the photocathode, which should correspond to an axial length L of the electron bunch at the end of the drift region, will have a greater length L′ > L. In consequence, for the fixed hCMOS electronic shutter duration, the captured slice of the electron packet will be equivalent to a shorter amount of time than it would normally be. This modification of the temporal response of the camera can also be accompanied by changes to the effective experiment times recorded at the backend detector, and, more importantly, distortions in the recorded images if different regions are affected differently by this effect. Therefore, understanding how the camera performance is affected by both the x-ray image shape and intensity that is cast on its photocathode is of primary importance to trust the integrity of the recorded data.

Since it is impossible to measure how space-charge (SC) affects the propagation of the electron bunch for every possible illumination pattern and intensity, Particle-In-Cell (PIC) simulations of the electron dynamics in SLOS have been performed, with the goal to predict the impact of SC effects for any relevant illumination scenario. A dedicated PIC code has been developed to perform these simulations. It is a two-dimensional axisymmetric Graphics Processing Unit (GPU)-accelerated code featuring the widely used Boris10 method to solve the particle motion in a leap-frog manner and with the electrostatic potential computed using a V-shaped multigrid algorithm. Self-induced magnetic fields are ignored in these simulations, which is acceptable given the magnitude of the current density (0.1–1 A cm−2) at work in the drift tube of SLOS. In the axisymmetric space, the camera is simply modeled as an acceleration region composed of a circular conductive photocathode held at an arbitrary potential, facing a grounded anode mesh, and an adjacent drift space enclosed by a grounded cylindrical conductor. All conductors are assumed to be perfect.

Before using the code to determine what is the best trade-off between image integrity and signal-to-noise ratio (SNR), which scales with the square root of the photon fluence within one detector integration period, it is necessary to validate that the PIC simulations are able to reproduce experimental data. We set up an experimental campaign dedicated to the acquisition of such data in a controlled environment in one of NIF’s offline laser characterization facilities.

The setup is presented in Fig. 1. A picosecond Nd:YAG laser of 43-ps full width at half maximum (FWHM) duration at the fundamental wavelength of 1064 nm is frequency quintupled to deliver 5 mJ of 213 nm light. The laser goes through a series of beam-conditioning optics to create a uniform illumination on the SLOS photocathode (PC). Aperture masks of different shapes and dimensions are placed in front of the photocathode. For this work, circular apertures of 2 and 8 mm were used, whose geometry can be reproduced by the PIC simulations, as well as an 8-mm-square aperture, which corresponds to the shape of the image projected by CBI on NIF experiments (see Ref. 6). An energy meter is inserted periodically in front of the photocathode to make sure that there is no drift in the photon fluence reaching the camera. A triggering signal is emitted by the laser system every time it delivers a pulse, with an associated jitter of 22 ps rms. This signal is fed into a timing system that, in turn, triggers the hCMOS sensor at the back of the drift tube as well as the high-voltage (HV) pulse electronics, which generates (10-ps rms jitter) the HV pulse traveling across the photocathode. Appropriate delays are introduced by the timing system to have the laser arrival time on the photocathode precisely match the HV pulse and to have the backend detector capture the desired fraction of the drifting electron signal. The jitter introduced by the timing system is 25 ps rms on both trigger channels.

FIG. 1.

The experimental setup (a) allows for precise synchronization of the camera with the laser by means of low-jitter triggers and timing system as well as oscilloscope-recorded fiducial and monitor signals (b).

FIG. 1.

The experimental setup (a) allows for precise synchronization of the camera with the laser by means of low-jitter triggers and timing system as well as oscilloscope-recorded fiducial and monitor signals (b).

Close modal

The combined jitter of the laser and timing systems as well as the HV pulse electronics is such that it is necessary to have a method to determine when the laser pulse arrived on the PC after each shot. To do so, a laser fiducial signal, tied to the laser master oscillator (5-ps rms jitter), is recorded on one channel of a 12.5 GHz oscilloscope. It is compared to the arrival time of a photocathode ramp monitor that is picked off of the HV pulse before it travels through the PC. We have evaluated the uncertainty associated with determining the PC monitor arrival time from the oscilloscope trace to be 3–4 ps rms. The uncertainty on the determination of the relative timing of the laser arrival on the PC to the HV pulse is the combination of the laser fiducial jitter and PC monitor uncertainty and amounts to 6.4 ps rms. Also recorded is a monitor signal emitted by the hCMOS sensor at the start of integration. However, timing information derived from this signal is relatively inaccurate because of its slow rise time (≈150-ps rms jitter), and its use is limited to the confirmation that the sensor was triggered. The jitter on the sensor integration start time is 35 ps rms, well below the 2 ns recording width of one frame of the sensor. Table I gives a summary of the jitter and uncertainty values associated with all of the aforementioned signals.

TABLE I.

Jitter and uncertainties.

Signal or componentJitter (ps rms)
Laser trigger out 22 
Timing system 25 
HV pulse electronics 10 
Laser timing fiducial 
Photocathode monitor 3–4 
Laser to HV pulse relative timing 
hCMOS sensor triggering 35 
hCMOS sensor monitor ≈150 
Signal or componentJitter (ps rms)
Laser trigger out 22 
Timing system 25 
HV pulse electronics 10 
Laser timing fiducial 
Photocathode monitor 3–4 
Laser to HV pulse relative timing 
hCMOS sensor triggering 35 
hCMOS sensor monitor ≈150 

The broadening of the electron packet created by the interaction of the input laser pulse with a 20–nm-thick gold photocathode is measured by increasing the trigger time of the hCMOS sensor with respect to the laser arrival time. For each shot, we record fractions of the packet that have drifted for increasing amounts of time. Effectively, we measure the convolution of the hCMOS sensor gate with the temporal profile of the electron packet, for each point inside the mask aperture placed in front of the photocathode. The sensor readout time is ∼15 s per frame, and to save time, only the first out of the four frames obtainable with the sensor is read. In addition to changing the aperture mask in front of the photocathode, two operating modes of SLOS are used: in the first one, the HV pulse sent across the photocathode is designed to provide a constant temporal magnification of 60× (Ref. 2). This is the mode the camera is operated in when running on a NIF experiment. In the second mode, only the “pre-pulse” is used, biasing the photocathode to −2.2 kV for several nanoseconds (Fig. 1), but without the fast voltage ramp used to achieve the pulse dilation. In other terms, this mode of operation is equivalent to using the camera with a temporal magnification of 1×. Since the width of the laser beam temporal profile is only a few tens of picosecond, the width of the electron packet when it reaches the hCMOS sensor is expected to be small compared to the gate time of the sensor for all but the highest laser intensities, where SC broadening will be significant enough. However, the benefit of using the camera in this mode lies in the fact that the measurement is then much less sensitive to jitter: in the 60× magnification mode, care must be taken that the laser arrival time (Fig. 1) falls precisely at the same position on the photocathode voltage ramp, which is made difficult by the jitter in the timing system and HV pulse electronics (as discussed in Sec. I); any variation in the laser arrival time with respect to this ramp is amplified 60 times when it reaches the hCMOS sensor. In the 1× magnification mode, these variations remain small compared to the 2-ns sensor integration period, and the electron profile measurement is less affected by timing uncertainties.

In practice, in the 60× magnification mode, we use the laser fiducial and PC monitor signals to reject data points that fall outside of a ±7 ps interval around the target time on the PC ramp. The time difference Δ between the obtained time and the target time is accounted for by equating it to a delay of −60Δ in the trigger time of the hCMOS sensor, and the 6.4 ps rms uncertainty in the determination of Δ (Sec. II A) translates to 380 ps rms uncertainty on the electron packet arrival time at the hCMOS sensor location, assuming the temporal magnification is constant. In the 1× magnification mode, the timing uncertainty is dominated by the hCMOS sensor jitter trigger of 35 ps rms (Sec. I). For both modes of operation, temporal electron cloud profiles are estimated by averaging the image intensity in different regions of interest (ROIs) at the center and at the edge. Since there can be a small timing skew of several hundred picoseconds between the two halves of the hCMOS sensor, the ROIs only extend on one of the halves. While the recorded images are subject to shot noise as well as dark current and readout noise of the hCMOS sensor, the uncertainty on the averaged intensity is dominated by the 2% rms shot to shot variations of the laser output.

Figure 2 shows an example of the recorded electron signal intensity when the photocathode is uniformly illuminated through an 8-mm-diameter mask, under severe SC broadening, with the camera operated in the 60× magnification mode. The generated electron cloud is axisymmetric along the drift direction, with an initial spatial extent in that direction determined by the input laser temporal profile and the drift velocity of the electrons. Frames shown in Fig. 2(a), where a slice corresponding to the center of the electron cloud was recorded, and in Fig. 2(b), triggered 4.8 ns earlier when most of the electrons have yet to reach the sensor, show how SC can affect an image: while electrons sitting in the center of the cloud see a superposition of forces that even out, electrons on the leading (or trailing) edge of the cloud are pushed away from the center by the combination of forces whose components in the drift direction have the same sign. The magnitude of this collective repelling force decreases for electrons further away from the axis as their distances to other electrons increase. The intensity profiles taken along the diameter of these images clearly illustrate this effect, displaying an excess electron density in the center of the early electron slice that fades away closer to the edge, and in contrast, showing a slight depletion in charge density near the axis in the frame recorded at the center of the cloud.

FIG. 2.

Space charge broadening affects the electron signal intensity recorded by the sensor differently at (a) peak intensity and (b) 4.8 ns earlier. Lineouts have been blurred by a 200-μm Gaussian kernel. The upper/lower intensity variation in (b) corresponds to skew in integration time between the two halves of the sensor. (c) Space charge broadening is also visible when comparing the average electron density vs time at the center and edge of the mask as delimited by the dashed circles on the images and restricted to one-half of the sensor. 1-σ error bars are given at x ≈ 80 ns data points only (see the body of text for discussion).

FIG. 2.

Space charge broadening affects the electron signal intensity recorded by the sensor differently at (a) peak intensity and (b) 4.8 ns earlier. Lineouts have been blurred by a 200-μm Gaussian kernel. The upper/lower intensity variation in (b) corresponds to skew in integration time between the two halves of the sensor. (c) Space charge broadening is also visible when comparing the average electron density vs time at the center and edge of the mask as delimited by the dashed circles on the images and restricted to one-half of the sensor. 1-σ error bars are given at x ≈ 80 ns data points only (see the body of text for discussion).

Close modal

This effect is also visible in Fig. 2(c) where the variation of the electron density vs time is plotted for both the center and the edge of the mask, showing how differently the temporal shape of the electron packet is affected in these regions. For both ROIs, the FWHM of the electron profile, in the order of 5–6 ns, is significantly wider than the 2–3 ns that would be expected in the absence of SC broadening. Figure 2(c) is also a good illustration of how jitter affects the quality of the measurement for the 60× magnification mode of operation, with each point having a combined time uncertainty of 380 ps rms.

Before using PIC simulations, it is interesting to see what a model of electron packet propagation can predict of its broadening. To that end, we modify the “mean-field” model proposed by Ref. 11 for femtosecond electron packets to take into account the initial stretching forces imposed on the electrons in the acceleration region. While developed for shorter electron packets than the ones we are dealing with in this work, Ref. 11 model can be applied to clouds that have an initial geometry that can be approximated to a uniform disk of charges. This applies relatively well to the cloud created by the 8-mm-diameter aperture mask, which has a longitudinal extent of ∼1 mm when it leaves the photocathode. Starting from Eq. (3) of Ref. 11, one can write the acceleration of an on-axis electron, in the drift region, at the leading edge of the packet,

d2ldt2=Ne2mε0πr21ll2+4r2,
(1)

where N is the number of electrons in the cloud, e and m are the electron charge and mass, respectively, ɛ0 is the permittivity of free space, and r and l are the cloud radius and length, respectively. Integrating with r fixed and imposing the initial condition,

dldtt=0=(M1)liT,
(2)

with M being the magnification, T being the total drift time, and li being the initial cloud length, we get

dldt=2Ne2mε0πr2ll2+4r2li+li2+4r2+(M1)liT.
(3)

Using numerical integration, we can use Eq. (3) to predict the amount of SC broadening one can expect for a given SLOS operating mode as well as when Coulomb repulsion will have the most impact. To get to the FWHM of the electron packet, we use the same empirical modification the authors of Ref. 11 used for a Gaussian temporal profile and apply a 0.5 multiplication factor to the total number of electrons, which represents cancellation effects in the field seen by electrons sitting at the FWHM. Figure 3 shows how the electron cloud broadens under space charge as it travels in the drift tube (60× magnification mode) for three electron densities, relative to how it would stretch if no space charge effect occurred [i.e., keeping only the second term in the right-hand side of Eq. (3)]. While increasing levels of broadening are predicted at higher electron densities, it is also apparent that in all cases considered, most of the broadening takes place in the first half of the drift space, with more than 90% of the total broadening occurring in the first 14 ns.

FIG. 3.

The mean-field model applied to a 4-mm-radius electron cloud predicts that space charge broadening predominantly happens in the first half of the drift for a wide range of photocurrent levels.

FIG. 3.

The mean-field model applied to a 4-mm-radius electron cloud predicts that space charge broadening predominantly happens in the first half of the drift for a wide range of photocurrent levels.

Close modal

A number of assumptions were made for the input parameters in the PIC simulations. First, the initial velocities of the electrons extracted from the gold photocathode need to be chosen. The electron energies are drawn from a symmetric triangle-shaped distribution peaked at 1.08 eV and with a FWHM of 0.97 eV, in an attempt to imitate the experimentally measured photoemission energy distribution by Ref. 12. The emission direction is assumed to follow a cosine distribution.13 However, we found that running the simulations with different energy distribution widths (0 and 2 eV) did not affect the predicted space-charge broadening. At NIF, cesium iodide is typically used as a photocathode material in experiments, because of its higher sensitivity to x rays in the 1–10 keV range, compared to gold. According to Ref. 14, the photoemission energy distribution of CsI is mostly independent of x-ray energy in the 100 eV to 10 keV range, with a FWHM of 1.7 eV, comparable to the ones of the distributions used in the simulations.

The frequency-quintupled laser temporal profile was characterized with the spare NIF SPIDER15 streak camera equipped with an aluminum photocathode. It was measured as a close to Gaussian profile of 32 ps FWHM, with a 25% after-pulse seen 35 ps after the main pulse, which we attribute to a reflection of an inner optics interface in the beam path. Taking into account the temporal resolution of the streak camera (21 ps FWHM), the corrected laser pulse width becomes 24 ps, assuming both widths add in quadrature. In consequence, in our simulations, the laser temporal profile is modeled as a 24-ps FWHM Gaussian followed by this after-pulse.

The electron drift velocity in the 1× mode of operation was measured by comparing their time of flight (in the drift space) to the time of flight of 213 nm photons going straight through the photocathode and detected by the hCMOS sensor. For the 60× magnification mode of operation, the average time of flight delay compared to the 1× mode was used to infer the average electron drift velocity. Based on these measurements, electrons are set to exit the acceleration region with an average energy of 2.2 and 1.35 keV for the 1× and 60× magnification modes, respectively.

The relationship between the recorded laser intensity on the photocathode and the electron density inside the drift tube was established by first measuring the peak number of counts in the hCMOS sensor in the 1× mode of operation at low laser intensity and then converting that number into photoelectrons, using previously measured sensitivity of this family of sensors to electrons.16 

The PIC simulations are run with cell dimensions of 25 × 10 μm2 in the axial and radial direction, respectively. The simulated drift length is limited to 200 mm in order to reduce computation time. The arrival time of the electrons is then calculated based on their velocities and the remaining distance to the detector (300 mm), i.e., assuming the space charge effect is negligible after 200 mm of propagation. Select cases with the highest input photon fluences were run with the full 500 mm of the drift length and showed only a 3% increase in space charge broadening, which falls in line with the mean-field theory results discussed in Sec. III A, suggesting that most of the space charge broadening is taking place during the first half of the electron drift length.

Experimentally measured and simulated electron packet profiles are compared in Fig. 4(a) and show a good agreement over a range of photon fluences varying by a factor of 26, both when considering the center of the electron cloud and its edge, in the two modes of operation. Since the measured profiles are the result of the convolution of the hCMOS sensor gate with the electron cloud profile, the PIC simulations are also convolved with the sensor gate. In the absence of a previously measured sensor gate profile, we use the one obtained with the 8-mm-square mask, 1× magnification mode, at the lowest laser intensity available of 34 nJ cm−2, or about 11 electrons/pixel. Since the SC broadening is low at this intensity (which is supported by both the mean-field theory and PIC simulation results, as shown later), the ∼2 ns gate profile is then probed with an electron beam of negligible temporal width of a few tens of picoseconds—the one of the excitation laser pulse. This gate profile is fitted to a model function,17 

Gate(t)=a11+ett0τ011+ett1τ1,
(4)

where a, t0, t1, τ0, and τ1 are fitting parameters, and the result of this fit is used as the convolution kernel for every PIC simulation temporal profile obtained. For each fluence level compared in Fig. 4(a), we allow for a unique intensity multiplier to scale the simulations to match the experimental profiles. We attribute the need for this multiplier to two causes. First, measurements of the laser energy in front of the vacuum chamber before and after the cloud profile data collection show a drift in the energy of up to 7%. Second, profiles have been collected over the course of several days and at different times of the day, and temperature variations of up to 30 °C in the electronics driving the hCMOS sensor will change the frequency of the relaxation oscillator8 by ∼5%.16 This frequency change will affect the integration time of the sensor linearly and modify its sensitivity, as observed by Ref. 18. Scaling factors used were 0.99, 1.08, 0.93, and 1.10 for fluences of 0.13, 0.69, 1.5, and 3.4 μJ cm−2, respectively.

FIG. 4.

The comparison of experimental results to PIC simulations shows a good agreement when considering (a) the temporal profile of the electron cloud convolved with the hCMOS gate, at increasing input fluences in both modes of operation, at the center and edge of the 2 mm diameter mask, or when considering the temporal width of the electron cloud for the 1× and 60× modes of operation, respectively, (b) and (c).

FIG. 4.

The comparison of experimental results to PIC simulations shows a good agreement when considering (a) the temporal profile of the electron cloud convolved with the hCMOS gate, at increasing input fluences in both modes of operation, at the center and edge of the 2 mm diameter mask, or when considering the temporal width of the electron cloud for the 1× and 60× modes of operation, respectively, (b) and (c).

Close modal

Figures 4(b) and 4(c) present the comparisons for the temporal FWHM of the (hCMOS gate convolved) electron cloud, for the 1× and 60× modes of operation, respectively. Error bars (1 standard deviation) on the y axis are calculated from timing and intensity uncertainties mentioned in Secs. II A and II B. As discussed there, we find that the impact of jitter is much more important in the 60× mode of operation. Not included in the error bar calculations are other sources of uncertainties such as temperature-induced variation of the hCMOS sensor gate width and input laser intensity drift that cannot be properly accounted for with the available data: the former should affect the measured width by less than 5% peak-to-peak as discussed above, mostly at low input fluence, where the measured profile is limited by the hCMOS gate width, while the latter will affect the electron fluence (x axis). However, we expect that this effect will be small in comparison to the systematic error introduced in using a typical sensor sensitivity curve16 to establish the relationship between input photon fluence and electron fluence (±10%).

The measured evolution of the electron cloud width is well reproduced by the PIC simulations in both modes of operation. At similar electron fluences, the 8-mm-diameter mask shows more broadening than the 2 mm one. For both masks, the broadening is more severe at the center of the cloud than at the edge. The 8-mm-square mask exhibits slightly more broadening than the 8-mm-circular mask for comparable input fluences, as one would expect from an increase in the total number of electrons. Included in the comparisons are the predictions from the mean-field theory (Sec. III A). The mean-field theory describes the expected broadening for an electron on the axis of the cloud and assumes that the cloud radius is much lower than the cloud length. This assumption quickly becomes invalid as the electrons travel in the drift space. In addition, the mean-field theory does not account for the specific temporal profile of the laser used in the experiment. Considering this, the relatively good qualitative agreement between the mean-field theory and the experimental data, especially for the 60× mode of operation, is noteworthy.

In ICF experiments, mix of the capsule ablator into the deuterium–tritium fuel is believed to have a major role in the degradation of capsule performance, due to a 10%–25% lower than intended fuel compression.19 The goal of the CBI Mix campaign19 is to study the evolution of the fuel–ablator interface of imploding ICF capsules of different designs by taking advantage of the new capability brought by the combination of CBI and SLOS: a series of four monochromatic radiographs with high spatial and temporal resolutions, taken along the same line of sight and separated in time by 90 ps. The evolution of mix conditions is diagnosed by measuring the broadening of the capsule limb on successive radiographs. The 35 ps temporal resolution of SLOS combines nicely with the ∼300 km s−1 implosion velocity so that the 11 μm motion blur and the 12 μm SLOS-CBI spatial resolution both contribute evenly to the overall resolution of 15 μm. The backlighter is created by focusing two NIF quads inside a 1-mm-diameter cobalt cylinder, creating a strong 7.2 keV line emission. A spherically bent crystal collects these x rays and focuses a ten times magnified image of the capsule onto the photocathode of the SLOS camera.6 By passing only a narrow bandwidth centered on the backlighter line emission, the CBI crystal can reject the x rays emitted by the hotspot late into the implosion, allowing an extended probing of mix conditions compared to other experiments using pinhole imaging.20 

The backlighter emission profile can be idealized as a 1-ns FWHM Gaussian, much longer than the width of the UV laser pulse that was used in the characterization discussed in Sec. III B. When it reaches the SLOS camera, it provides a nearly uniform background, which is obscured by the spherical ICF capsule [Fig. 5(a)]. We designed an experiment dedicated to creating an image similar to the ones obtained during the CBI Mix campaign and that could also be easily simulated with our PIC code. This experiment was using the same backlighting and imaging system, but no object was radiographed. Instead, a mask was placed in front of the camera to create a uniformly illuminated 8-mm-diameter circular aperture with a centered 20-μm-thick cobalt annulus creating 62% x-ray attenuation [Fig. 5(b)]. The annulus had a 1 and 2 mm inner and outer radius, respectively, effectively reproducing the shadow of a 100-μm-wide limb of a capsule compressed down to 150 μm radius, taking into account the 10× magnification of CBI.

FIG. 5.

(a) A typical radiograph of an imploding ICF capsule obtained with the SLOS-CBI platform and (b) test shot image designed to resemble the ICF implosion image, obtained with a mask in front of the camera. The grid pattern visible on both images is due to meshes inside the SLOS camera and can be removed numerically.

FIG. 5.

(a) A typical radiograph of an imploding ICF capsule obtained with the SLOS-CBI platform and (b) test shot image designed to resemble the ICF implosion image, obtained with a mask in front of the camera. The grid pattern visible on both images is due to meshes inside the SLOS camera and can be removed numerically.

Close modal

PIC simulations were set up with the temporal and spatial characteristics of the input electron beam described above, and different signal intensities were used to study how space charge impacts the temporal characteristics of the SLOS camera frames, and if distortion in the recorded images can occur and with what severity. The intensity was increased by treating the electrons as macro-particles with an arbitrary charge, and simulations ranging from an intensity multiplier of 0 (no Coulomb interactions) to 8 were generated, with a value of 1 corresponding to a peak photocurrent density at the photocathode of 0.04 A cm−2 that was obtained on the 500 counts image of the first of the CBI Mix campaign series of experiments. One can note that with an electron transit time in the acceleration region of about 100 ps and an electron density profile of 1 ns FWHM, a steady-state current is approximately achieved, and its amplitude is far below the 1 A cm−2 limit predicted by the Child–Langmuir law,21,22 even for an intensity multiplier of 8 (0.34 A cm−2).

Figure 6 shows how both the integration time and the position in the time of each frame, spatially averaged, are affected by increasing levels of photocurrent inside the camera. Over the range of values studied, the integration time varies by up to about 30%, with the duration of the first and last frames increasing and decreasing, respectively, with increasing intensity, while the center frames see a more modest variation of less than 10%. In terms of evolution in the position of each frame compared to where it would fall in the absence of SC effect, we observe a progressive shift of up to 15 ps, except for the first frame that remains stable. The delays in frames 2–4 are not changing linearly though, and the shift of the last frame starts to roll back after it reaches a maximum at an intensity multiplier of 4.

FIG. 6.

Both individual frame duration (a) and position (b) are affected non-linearly by increased signal intensity. The additional work of the electrostatic force (4× intensity multiplier) generated by Coulomb interactions (c) happens with a higher magnitude in the early stages of the drift and has a different profile for each frame.

FIG. 6.

Both individual frame duration (a) and position (b) are affected non-linearly by increased signal intensity. The additional work of the electrostatic force (4× intensity multiplier) generated by Coulomb interactions (c) happens with a higher magnitude in the early stages of the drift and has a different profile for each frame.

Close modal

It is not a goal of this work to provide a comprehensive explanation for these evolutions, which would only apply to the specific conditions studied here. Rather, it is interesting to understand the different factors that come into play in obtaining these results. To that end, we give in Fig. 6(c), for one electron sitting at the center of each frame, the work of the electrostatic force coming only from space charge, i.e., we subtract the work that would originate from the electrostatic field generated by the imposed potential on electrodes, which corresponds to an intensity multiplier equal to zero. Each of these electrons sees a similar work profile. Between the photocathode and the anode mesh, the potential is depressed by space charge, as dictated by the Poisson equation.23 After the anode mesh, the electrons still face a repelling force imposed by the potential gradient caused by the leading part of the electron packet. This equilibrates and then reverses further into the propagation as the balance of leading and trailing charges evolves and as a longitudinal charge density gradient in the drift space is created by the initial velocity spread introduced by the time dilation scheme.

While temporal effects cannot easily be inferred from the experimental data, any large influence of space charge on spatial characteristics of SLOS images should be perceptible. In Fig. 7, we compare azimuthally averaged intensity profiles of SLOS images obtained on the dedicated shot described above to our simulations. On this shot, the peak photocurrent intensity at the SLOS photocathode corresponded to an intensity multiplier of 8 in our simulations, and as a result, the first frame of the hCMOS sensor was saturated. The three remaining frames compare relatively well to the simulations. The contrast between the shadow of the annulus and the background is constant across the frames (within tolerance for the thickness of the cobalt sheet), as predicted by the simulations. However, the slight convexity expected in the background, inverting between the second and the last frame, is not observable in the experimental data. Possible reasons for this discrepancy include gradients in the backlighter flux on the camera, off-centering of the annulus with respect to the outer aperture mask diameter, as well as uncertainty in the relative timing of the backlighter peak intensity compared to the start of the high-voltage ramp across the photocathode. In any case, both observed and predicted image distortion is low at this intensity level, especially when compared to other image fidelity degradation mechanisms such as artifacts from the numerical grid removal procedure (Fig. 5), oscillations in the hCMOS sensor background level due to early excitation,24 and backlighter non-uniformity mentioned above.

FIG. 7.

Azimuthally averaged intensity profiles of the SLOS data on test shot N200801 compare well with the prediction from PIC simulations.

FIG. 7.

Azimuthally averaged intensity profiles of the SLOS data on test shot N200801 compare well with the prediction from PIC simulations.

Close modal

In light of these results, recent CBI Mix radiographs were recorded with a backlighter intensity corresponding to the intensity multiplier of 4 in the simulations, which offers a good compromise between an increase in signal-to-noise ratio (around 8) of the images on one side and conservation of the temporal performance of the camera and image fidelity on the other side. In a future shot, we are planning to use the SLOS-CBI platform to obtain radiographs of an undriven capsule of known density and demonstrate that the entire image acquisition and processing toolchain are able to recover the correct density profile.

While time-resolved x-ray imaging for ICF experiments has relied solely on MCP-gated detectors for the past 30 years, the introduction of pulse-dilation-based cameras at the NIF and other laser facilities has brought a jump in performance as well as unique new capabilities. This new technology also comes with a new set of challenges that need to be understood, mitigated, or overcome. We have shown here how the careful calibration of the SLOS camera, associated with the development of particle-in-cell simulations of the system, can be used to determine the optimum operating conditions and obtain the best image quality on NIF shots. New radiation-hardened versions of the SLOS camera are currently being built and are taking advantage of the lessons learned both in fielding this diagnostic and in this work to mitigate the impact of space charge and further improve performance and reliability.

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.

The authors have no conflicts to disclose.

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

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