Demonstration of improved laser preheat with a cryogenically cooled magnetized liner inertial fusion platform

Magnetized Liner Inertial Fusion (MagLIF)^1–3 is an inertial confinement fusion (ICF) scheme that combines fuel magnetization, fuel preheat, and compression by the Z pulsed-power generator to produce fusion-relevant conditions. The purpose of fuel preheat is to set the fuel adiabat at the start of the implosion to enable sufficiently high temperatures at a point near peak compression (stagnation). Fuel magnetization is required to thermally insulate the preheated fuel by suppressing radial electron thermal conduction to the cold beryllium tube (liner) walls during the ∼60 ns long implosion time. Two-dimensional (2D) magnetohydrodynamic (MHD) simulations^1,4 and experimental observations^4–7 suggest that the optimum preheat energy is set by the requirement for the fuel to reach a high temperature without advecting significant applied axial magnetic field out of the fuel by the Nernst effect. As such, the preheat energy required to optimize neutron yields is a function of the fuel density and applied axial magnetic field with higher densities and magnetic fields generally requiring higher preheat energies.

Recent advances in the MagLIF platform have resulted in record neutron yields from the (to-date deuterium) fuel by increasing the preheat energy to ∼1.3 kJ in a 1.05 mg/cc fuel, peak current drive to 20 MA, and applied magnetic field to 15 T simultaneously.⁵ Simulations suggest that at these conditions, the preheat energy required to optimize yields should be greater than 2 kJ;⁸ however, such energies have not been demonstrated previously at the Z facility. The two primary limitations to energy coupling on Z are the maximum energy delivered to the target by the Z-Beamlet (ZBL) laser⁹ and the efficiency with which energy incident onto the target is coupled to the gas.

To effectively preheat a MagLIF experiment, the laser needs to first penetrate through a polyimide laser entrance hole (LEH) foil before coupling energy to the fuel through inverse Bremsstrahlung absorption. The most important metric is the energy deposited within the 10 mm tall imploding region of the target—energy deposited below this region will not participate in the experiment and, worse, may liberate mix material into the fuel that degrades performance. Several factors play a role in the efficiency of this process, including energy losses to heating the LEH foil, losses to stimulated Brillouin and Raman backscatter (SBS and SRS, respectively), and the stopping length of the beam in the fuel, which primarily depends on the laser energy, spot size, and fuel density.

Several preheat configurations have been developed for MagLIF that were found to couple various amounts of laser energy to the fuel and introduce varying amounts of LEH foil mix.^10,11 These configurations are first tested offline in the “Pecos” chamber¹² where the energy deposition is assessed with a multi-frame shadowgraphy diagnostic.¹³ All the previous preheat configurations were developed at room temperature, which, along with the fuel density, determines the pressure of the gaseous fuel. The pressure, in turn, determines the thickness of the LEH foil material required for a given LEH aperture size. The LEH thickness affects how much laser energy is coupled into the gas and how readily the foil material is pushed into the imploding region of the target creating mix. To date, the peak demonstrated coupling efficiency in these experiments has been ∼67%, which is insufficient to couple >2 kJ preheat energy to the fuel, given limitations in the energy delivered by ZBL.

In this paper, we describe experiments utilizing cryogenically cooled MagLIF target designs that demonstrate improved preheat coupling. Cryogenically cooling the targets allows equivalent fuel densities to be achieved at lower pressures, enabling thinner and larger diameter LEH foils. The preheat design was motivated in part by 2D and 3D HYDRA¹⁴ simulations that suggested laser energies >2 kJ can be achieved with ZBL using a 1.5-mm laser spot, 500-nm thick LEH foil, and 1 mg/cc fuel density,¹⁵ which can only be achieved at cryogenic conditions. To assess the coupled preheat energy, a cryogenically cooled laser-only platform was developed that enabled blast-wave measurements similar to those used to assess energy deposition in warm experiments.^12,13 A Bayesian analysis of data from cryogenically cooled laser-only experiments spanning incident energies from 1800 to 2900 J suggests that the deposited energy goes as E_dep = (0.834 ± 0.086) × E_incident + (125 ± 30) J, which approximates to 89% ± 10% of energy coupled. This preheat configuration was applied to Z using a novel cryogenically cooled target design that employed two cryostats to enable minimal temperature gradients across the target length without the need for insulating breaks in the transmission line. The cryogenically cooled integrated MagLIF experiment, z3576, coupled 2.3 kJ preheat energy based on offline tests, demonstrated nominal current delivery to the load, and produced a neutron yield of Y_DD = 7.6 × 10¹² and a high pressure stagnation column (P = 2.19 ± 0.17 Gbar),¹⁶ in line with similar warm experiments. The increased preheat energy demonstrated in this study has implications for future MagLIF scaling experiments and target designs with lower convergence ratio stagnation columns.

The structure of this paper is as follows: Sec. II will describe the cryogenically cooled platform used to assess laser preheat energy coupling in offline experiments, show experimental results, and make comparisons to simulations. Section III will describe the experimental results from the cryogenically cooled integrated MagLIF platform and detail modifications that overcame limitations of previous target designs. Finally, Sec. IV will present conclusions.

As discussed in Sec. I, the desired experimental parameters for MagLIF targets to enable >2 kJ preheat coupling are a 1 mg/cc fuel density contained with a 500-nm thick LEH foil with a 3 mm diameter aperture. Testing indicated that the maximum safe operating pressure for this LEH foil design is below 25 psi requiring temperatures below 83 K for a 1 mg/cc gas fill, which sets the maximum temperature requirements for the platform. Previous preheat configurations have been tested in laser-only experiments in the Pecos chamber¹² (so-called “Pecos” experiments) before being applied to integrated MagLIF experiments on Z. The primary diagnostic in laser-only experiments is multi-frame shadowgraphy, which allows for the expansion of the cylindrical blast wave produced in the fuel after the laser deposits energy to be tracked in time, typically around 5, 30, 55, and 80 ns after the start of the laser pulse. The radius at the latest time can then be related to the deposited energy using the method described by Harvey-Thompson et al.¹³ A cryogenically cooled version of the preheat platform was developed in Pecos to enable the same shadowgraphy measurements. This platform needed to meet the desired experimental parameters discussed above while producing minimal temperature gradients and allowing for optical access for shadowgraphy measurements. Other aspects of the Pecos chamber layout and diagnostics were kept as described by Geissel et al.¹² 

The cryogenically cooled target design is shown in Figs. 1(a) and 1(b). The target consists of a cubic copper body with four 25.4 mm diameter circular apertures cut out for diagnostic access and a further aperture at the front where a copper washer holding the LEH foil is glued. The design is intended to be relatively easy and cost-efficient to fabricate since the body itself is disposed of after each shot. The LEH fits into a conical recess that allows for side-on diagnostic access to the gas immediately behind the LEH foil. Two of the diagnostic windows are acrylic, transparent to the 532 nm probe beam that passes through the target to provide shadowgraphy data. The other two diagnostic windows are copper disks with a 20 × 3 mm² slit that have a 12.7 µm polyimide foil glued to the fuel-facing side that allows x-ray pinhole cameras to view the plasma. The copper disks are mounted to the target body by compression rings that push the diagnostic windows onto an indium gasket that provides the pressure seal.

The target body is cooled by a separate reusable cryostat bolted onto the back. An indium plate is sandwiched between the cryostat and the target body to provide better thermal coupling. The cryostat is cooled by cryogen lines wrapped around the diameter. The target temperature is monitored by using two sensors placed at the front and back of the target. Typical on-shot temperature readings from the two sensors are shown in Fig. 2. Typically, the front and back temperature sensors agree to within 0.5 K corresponding to a <1% temperature (and therefore density) uncertainty in the gas. The He cryogen is supplied by a 30 L Dewar situated ∼3 m away from the chamber. Rather than transport liquid He cryogen to the target, He is heated to the gaseous state close to the Dewar by a heater that provides the primary method of temperature control at the target. This prevents the need for further active heating at the target itself. The desired target temperature is usually achieved through manual control of the heater although the Proportional Integral Derivative (PID) temperature controller can use active feedback from the temperature sensors placed on the target to automatically achieve a temperature setpoint.

Cryogenically cooling deuterium gas in the Pecos chamber presents hazards that must be controlled. Since deuterium is flammable, there is a risk that if excessive amounts remain in the chamber and are mixed with air during venting or due to a chamber leak, the deuterium could ignite and over-pressurize the chamber or create a fire hazard. This is a particular concern with cryogenic cooling since controls that monitor the chamber pressure are not effective (excessive cold D₂ may be present even at low pressures). To prevent this occurrence, the target is filled from a 150 cm³, 160 psi sample cylinder that limits the maximum D₂ inventory to a safe level for the target chamber. The pressure provided to the target is controlled by a dome-loaded regulator that maintains a consistent pressure in the target during cooldown, allowing the target to be filled early in the shot sequence. This setup will also replace any gas lost from the target due to small leaks that can develop in the diagnostic windows during cooldown, allowing for the target pressure to be maintained.

A particular concern with cryogenically cooled MagLIF targets is ice growth on the surface of the LEH foil that can increase the effective thickness of the material. To address this concern, the target is housed within a debris enclosure, shown in Fig. 1(c), which includes ice mitigation features. First, there is an actively cooled copper cone at the entrance to the enclosure that acts as a cryopumping shroud similar to the one used in integrated MagLIF targets.¹⁷ The laser entrance cone is cooled with cryogen that exits the target cryostat and follows the temperature of the target closely, typically within 20 K during cooldown. The cone effectively limits the probability that water molecules present in the chamber will interact with the LEH material and form ice. Given the entrance area of the cone of 8.25 cm² and the distance from the entrance to the LEH of 18.5 cm, only ∼1/3000 particles entering the cone will reach the LEH foil without first interacting with the cone wall. Ice growth is further mitigated by ensuring that the chamber vacuum is below 1 × 10⁻⁷ psi prior to cooldown. Assuming similar numbers to those of Awe et al.,¹⁷ for the target geometry with a 1 × 10⁻⁷ psi chamber pressure dominated by water vapor (a conservative assumption for Pecos) and a target temperature of 75 K, the ice accumulation rate will be ∼1 nm/minute and the total ice thickness during a typical shot will be < 20 nm, a small value compared to the 500 nm thick foil.

The cryogenically cooled laser platform described in Sec. II A enables laser preheat configurations to be developed and tested using ZBL for use in integrated MagLIF experiments on Z. Guided by simulations,¹⁵ the laser spot size at best focus on the LEH foil was set by a distributed phase plate (DPP) optic to be 1.5 mm diameter, increased from the 1.1 mm diameter spot used in warm experiments. The pulse shape consisted of a 1-ns, ∼0.2-TW foot pulse followed by a 5.5-ns-long, ∼0.5-TW main pulse delivering up to ∼2.8 kJ of energy to the target, as shown in Fig. 3. At lower energies, both the foot and main pulse powers were reduced proportionately. The preheat configuration was guided by simulations¹⁵ that showed a 1.5-mm spot size is necessary to prevent the laser from propagating past the imploding region. In simulations, the foot pulse allows the laser to rarify and penetrate the LEH foil while remaining at a low intensity, reducing the amount of foil material pushed into the fuel. The 1.5 mm spot size also kept the peak intensity ≤3 × 10¹³ W/cm², below the ∼5 × 10¹³ W/cm² that was found to produce significant (>100 J) SBS backscatter, and equals the lowest intensities previously tested in preheat experiments.¹² We also expect losses from SRS backscatter to be relatively small at these low intensities although this is not well constrained in experiments.

The energy deposited into the fuel using the cryogenically cooled preheat configuration was determined in Pecos experiments for laser energies at the target ranging from 1830 to 2770 J, as shown in Fig. 4. The energy deposited in each shot was determined by relating the radius of the cylindrical blast wave observed by the shadowgraphy diagnostic ∼80 ns after the start of the laser pulse to the energy deposited as described by Harvey-Thompson et al.¹³ One-dimensional Gorgon simulations were used to find the relationship between the late-time blast-wave radius and deposited energy per unit length at each axial position in the gas. The total energy was calculated simply by integrating the energy/unit length along the axis. The total uncertainty for each measurement using this technique ranged from ±9.5% to 12.5%. Using a Bayesian analysis of the data, we fit a linear relation to the energy deposited vs energy delivered, assuming an unknown fractional error between the experimental data and model. The Bayesian analysis gives a value for the deposited energy of E_dep = (0.834 ± 0.086) × E_incident + (125 ± 30) J. Across the data range from 1800 to 2900 J, this can be more simply approximated to a deposited energy of 89% ± 10%, the value quoted elsewhere in the paper, with only a small variation over that energy range (90.3% ± 10.2% at 1800 J and 87.7% ± 9.6% at 2900 J). When properly accounted for, these model uncertainties give rise to the 1-sigma model prediction interval shown in Fig. 4. The analysis enables an assessment of the preheat energy coupled to the gas on a given integrated MagLIF shot, as will be discussed in Sec. III C.

The data show that over the range of delivered energies tested, the cryogenically cooled preheat configuration couples energy to the imploding region very efficiently with ∼89% ± 10% of the incident energy being accounted for in the blast wave. This is a significantly higher fraction than was coupled with previous warm configurations, which demonstrated a maximum coupling efficiency of ∼67%. Also plotted in Fig. 4 (bottom) is the “missing energy” or the incident energy minus the energy observed in the blast wave. The data suggest that this increases slightly with higher incident energies, although with significant uncertainty, given the low levels of energy unaccounted for overall. As discussed in Sec. I, some amount of energy will be lost to heating the LEH foil material, and this is expected to be approximately constant across the range of delivered energies. Losses to backscatter would be expected to increase with beam intensity (energy). If this is a factor in these experiments, then the losses are sufficiently small as to be within the ∼10% uncertainty of the blast wave inferences.

A 2D Hydra simulation was performed as one of the cryogenically cooled Pecos experiments, B21020503. The simulation used the measured fuel density, LEH foil thickness, and laser power pulse. Comparisons between the simulation and laser shadowgraphy data are shown in Fig. 5 where the electron density map is used as a proxy for the shadowgraphy image (the shadowgraphy diagnostic being sensitive to the electron density jump formed at the edge of the plasma channel). As shown in Figs. 5(a) and 5(c), the simulation approximately reproduces the observed plasma channel 3.5 ns into the main pulse with some minor differences. The simulation tends to form a long narrow filament on axis that propagates beyond that observed in the experiments. This is a product of the simulations’ 2D axisymmetry forcing reflected and refracted rays toward the axis. Another difference is the presence of “bump” features in the experimental shadowgraphy data ∼2–3 mm beyond the LEH location. These have been observed previously and do not appear in simulations. They may be related to how the laser light interacts with the shock ahead of the LEH foil material or side-scatter, but their origin remains unclear.

As shown in Figs. 5(b) and 5(d), the simulations match the observed shape of the blast wave at 53.2 ns very closely. We note that the 53 ns rather than 80 ns frame time was chosen for this comparison because the blast wave still retains more information about energy distribution and is faster to simulate. Figure 5(e) shows the energy per unit length inferred from the experimental blast wave and from the simulated blast wave, which is processed using the same techniques as the experimental data. Both the total amount of energy deposited inferred from the experimental and simulated blast waves, stated in Fig. 5(e) and plotted in Fig. 4, and their axial distribution are similar. The data show that almost all energy is deposited within an 11.5 mm length, which is the distance from the LEH foil to the bottom of the target in integrated MagLIF experiments.

The green plot in Fig. 5(e) shows the simulated energy per unit length deposited by the laser into the gas and into LEH foil material as a function of distance calculated directly from the simulations. The profile of the simulated energy in the gas at the end of the laser pulse is somewhat different from that inferred from the experimental blast wave. This is expected since the blast wave motion has an axial component not accounted for in the analysis that will tend to smear the deposited energy profile along the axis.

The simulated blast wave analysis also infers more energy in the target than is deposited directly by the laser (2.35 vs 2.01 kJ). This can be explained by the motion of material, particularly from the LEH, into the target and the fact that laser energy initially deposited at x < 0 mm is not counted in the green curve since it was not initially deposited “inside” the target. This can also be seen by comparing the green and blue curve in Fig. 5(e) that shows the sum of kinetic and internal energy of material inside the target (past x = 0 mm) at the end of the laser pulse. Past x = 3 mm into the target, this agrees with the simulated deposited laser energy, as expected, but shows more energy between x = 0 and 3 mm. This is because the initial location of the LEH foil material is at x < 0 mm since it deflects outward from the target, forming a bubble with height ∼0.4 mm that is included in the simulations. The laser initially deposits energy into the material at this location; hence, the energy is not accounted for by the green curve in Fig. 5(e). A significant amount of the foil material however is pushed inward into the target by end of the laser pulse and so is accounted for when summing the kinetic and internal energy, shown in the blue plot in Fig. 5(e). The summed kinetic and total energy is closer to that inferred from the simulated blast wave (2.21 vs 2.35 kJ), suggesting that the blast wave analysis is accounting for some of the energy associated with the LEH foil material that has moved into the target. While the motion of the LEH material into the target can degrade performance,^8,10 simulations suggest that the LEH foil material should not migrate into the imploding region of the MagLIF targets for these cryo-cooled preheat configurations.¹⁵ The analysis shows the complexity of defining and measuring a true “preheat energy” in the target.

Overall, the simulation is in very good agreement with experimental data without requiring any additional loss factors to account for the energy deposition or propagation length as was necessary in comparisons to warm datasets.¹² This further suggests that effects not accounted for in the simulations, such as laser plasma instability (LPI) backscatter, are likely not significant in the cryo-cooled preheat configuration.

As discussed in Sec. II, the cryogenically cooled preheat configuration developed using laser experiments in the Pecos chamber has demonstrated excellent coupling efficiency into the fuel. Realizing this preheat configuration in integrated experiments on Z requires cooling the targets to similar cryogenic temperatures, so the same pressures and LEH foil parameters can be used. Applying cryogenic cooling to Z experiments requires additional experimental considerations since the MagLIF target is connected to a metallic transmission line and must be magnetized by external field coils that generate 10–20 T over a 2–4 ms timescale. The overall objective of the cryogenic MagLIF target design development is to produce a cooled target design that can demonstrate similar performance to warm targets, given similar input conditions (current, fuel density, preheat, and applied magnetic field), while enabling the cryogenically cooled preheat configurations described in Sec. II that are expected to improve MagLIF performance beyond what is achievable with warm targets. Realizing an effective cryogenic configuration required several iterations of hardware that balanced cryogenic and current coupling concerns described in this section. A summary of important hardware differences between the cryogenic and warm shots described is given in Table I.

The progression of MagLIF cryostat designs is illustrated in Fig. 6. Early cryogenically cooled MagLIF experiments performed used a single stainless steel and brass cryostat connected to the top of the liner as shown in Fig. 6(a) and is described in depth by Awe et al.¹⁷ This cryostat was compatible with the early magnetic field coil designs and the high inductance “extended” inner Magnetically Insulated Transmission Line (MITL) that was most commonly used in experiments at the time. The design included nylon insulating breaks close to the liner in both the anode and cathode, which limited thermal conduction to the anode and cathode hardware. The top of the cryostat formed a cooled cylindrical entrance region above the LEH foil to reduce ice growth similar to that present on the debris case in laser-only experiments. Temperature control was provided by heating a nichrome wire wrapped around the cryostat and the temperature monitored with sensors placed on the top cryostat and on the bottom gas line.

Two shots, z3137 and z3157, were performed with the cryostat configuration shown in Fig. 6(a) that aimed to repeat the results from warm experiments. The cooled experiments used the same input parameters as shot z3040, described in Refs. 4 and 7, that is, a 10 T magnetic field, a 0.7 mg/cc D₂ gas fill, a 1.77 µm thick LEH foil, and the “with-DPP” preheat configuration. Shots z3137 and z3157 produced neutron yields of Y_DD = 0.27 × 10¹² and 0.65 × 10¹², respectively, within the range, albeit toward the low-end, of warm experiments with similar input conditions (Y_DD = 0.3–4 × 10¹²). Another experiment that used the same cryostat design but different preheat configuration, z3170, returned current velocimetry data that allowed for a comparison of the current delivery to equivalent warm target designs, as shown in Fig. 7. The data suggest that current delivery to the liner in z3170 deviated early in time from the equivalent warm target, z2851, although reached a higher peak current before stagnation. It is not known whether the apparent change in the current delivery profile affected the performance in z3170 or in other experiments that used the same cryostat design.

A possible reason for the change in current profile delivered to the liner in z3170 is the inclusion of nylon insulating breaks in the anode and cathode. While the width of these breaks is small (250–550 µm), it is possible that their initially high electrical resistivity before plasma is formed could result in an excessive voltage being produced between the anode and cathode surfaces early in time. This could affect convolute and transmission line plasmas and losses and may produce additional plasmas in the load region that affects current delivery. To test this hypothesis in shot z3331, a similar cryostat design was used but with the nylon insulating break in the cathode replaced with a stainless-steel break and the break in the anode replaced with a slip-fit contact between the liner and anode [see Fig. 6(b)]. During testing, the changes were found to increase the discrepancy between temperature measurements at the top and bottom of the liner. During the setup of the downline shot, the bottom temperature sensors failed and it was decided to execute the experiment warm. The current delivery to the target, shown in Fig. 7, is similar to the reference shot without cryogenic hardware, z2851, but with a higher apparent peak current. The data provide some evidence that nylon insulating breaks affect current delivery although there are limited current velocimetry data with the high inductance transmission line used in these experiments, so a degree of shot-to-shot variability may be present that could account for this difference. Second, an alternative hypothesis for current delivery on z3170 is that ice growth on the liner and cryostat surfaces may have introduced additional plasmas in the load region that affected current delivery. This was not tested in z3331 because the target was not cooled. While the data are not sufficient to conclude that nylon insulating breaks affect current delivery, it was decided to continue developing designs that can eliminate nylon insulating breaks while maintaining axial temperature uniformity in the liner.

The next cryogenic MagLIF design iteration, shown in Fig. 6(c) and used in shots z3500 and z3501, made only small alterations to the overall cryostat design to accommodate a lower inductance transmission line and more advanced magnetic field coils capable of providing 15 T to the target. The overall design is similar to that used in shots z3209, z3289, and z3292 and described by Gomez et al.,⁵ which demonstrated a consistent, higher current delivery to the load. The current delivery in z3501 was very similar to z3209 (neither shots z3289 nor z3292 returned good current measurements), as shown in Fig. 7, coupling a peak current of 19.8 MA to the load. However, the absence of insulating breaks in the anode and cathode resulted in a large temperature differential between the top and bottom of the liner of 53 K, as shown in Fig. 8.

The intention of z3501 was to reproduce the results from warm experiments z3289 and z3292, which used the same transmission line design, 15 T applied magnetic field, and preheat configuration, including a fuel density of 1.05 mg/cc. Shot z3501 produced a neutron yield of 3.1 × 10¹², below the 11 × 10¹² and 5.5 × 10¹² neutrons in shots z3289 and z3292, respectively. This relatively low performance may be explained by the large uncertainty in the temperature and hence initial fuel density for z3501. Given the on-shot pressure of 42.4 psi and temperature of 134.5 ± 26.5 K, the fuel density was 1.09 ± 0.22 mg/cc. This large uncertainty in the density affects preheat most significantly. Low densities increase the risk that the laser will penetrate beyond the imploding region of the target and introduce mix, and high densities reduce the effective preheat specific energy. Since the fractional fuel density uncertainty in these experiments is dependent on $ΔTT$⁠, where T is the average temperature and ΔT is the temperature measurement differential, at lower temperatures, such as the ∼72 K required for 500 nm LEH foils, the density uncertainty will increase assuming the temperature differential remains constant. Reducing the temperature uncertainty is therefore required for MagLIF to operate effectively at the desired lower temperatures.

The final cryogenic MagLIF design iteration, shown in Fig. 6(d) and used in shot z3576, aimed to reduce the top/bottom temperature difference while omitting insulating breaks and maintaining important aspects of the low inductance transmission line design. This was achieved by placing cryostats at the top and bottom of the liner that could be controlled independently. The bottom cryostat acts as part of the power flow surface. The cryostat design was altered to bring the cryogen closer to the surface of the liner with the cryostat body being made from stainless steel rather than brass to aid axial magnetic field diffusion and provide a more standard power flow surface material at the anode and cathode. Some previous experiments, such as z3170, began leaking at cryogenic temperatures and required continual supplies of gas before shot time, as shown in Fig. 8. One possible location for the leaks is the glue joint between the cathode and liner that may be compromised during cooling. To remedy this, in z3576, the Be liner was brazed to the bottom cryostat to form the pressure seal.

The temperature and pressure results from z3576 are shown in Fig. 8. The temperature difference between the top and bottom of the liner was reduced significantly to within 0.25 K; the uncertainty of the temperature sensors, combined with a 1% uncertainty in the pressure, gives a final fuel density of 1.05 ± 0.09 mg/cc. The current delivery was also very similar to the equivalent warm shot, as shown in Fig. 7. The dual cryostat platform therefore achieves the objective of providing similar input parameters to warm experiments while enabling cryogenically cooled preheat configurations. We note, though, that ice growth will still occur on the liner and powerflow surfaces and it is not known whether this affects the plasma environment in the return can region.

Shot z3576 was the first experiment to use the cryogenically cooled preheat configuration developed on Pecos and described in Sec. II B. The laser energy delivered to the target was 2.62 kJ, from which we infer a deposited energy of 2.32 ± 0.25 kJ (shown as the black point in Fig. 4) based on the data from offline Pecos experiments. This is a significant increase in coupled energy compared to the previously highest reported preheat energy of 1.88 + 0.6/−0.49 kJ,⁶ which used a smaller diameter beam and was noted to have a significant possibility of energy reaching the bottom of the target. Aside from the different preheat configuration coupling more energy, z3576 had similar experimental parameters to other high-performance MagLIF experiments, specifically z3289 and z3292, with 15 T applied field, 20 MA current delivery, and 1.05 mg/cc fuel density in all cases. The stagnation parameters for the three similar shots were analyzed by Bayesian data assimilation technique described by Knapp et al.,¹⁶ and the results are given in Table II.

The data suggest that shot z3576 achieved slightly higher stagnation temperatures and pressures compared to z3289 and z3292, but with a similar value of the dimensionless Lawson criterion, χ,¹⁸ as z3289 and a moderate neutron yield. Based on published 2D LASNEX simulations,⁸ it is expected that increasing the preheat energy from 1.15 to 2.31 kJ would lead to a modest improvement in the neutron yield (predicted a 10% increase in yield for a 10 T field and a 50% increase for a 20 T field). However, an increase in the neutron yield was not observed. There may be several explanations for this. It is possible that preheat-induced mix from the inner surface of the liner increases with preheat energy. This may be explored in future experiments using mid-Z dopants or coatings on the beryllium¹⁰ or mitigated with anti-mix layers.^19,20 Another possibility is that the stagnation performance is being impacted by the stagnation morphology. Figure 9 shows stagnation images from the high-resolution crystal imager (HRCXI) diagnostic for z3576 and the comparison shots, z3289 and z3292. The data show that x-ray emission in shot z3292, and z3289 in particular, is dominated by hot-spots, while the emission from z3576 is more axially uniform. The two brightest peaks accounted for 31% and 25% of the overall emission, respectively, in z3289, whereas in z3576, the two brightest peaks accounted for ∼14% and 12%, respectively. Poor stagnation morphology as a result of high convergence ratios is identified as a possible degradation mechanism for shot z3289 by Gomez et al.⁵ It should also be noted that there is a factor 2 variation in the neutron yield between z3289 and z3292, two notionally similar shots, which is greater than the expected improvement from the higher preheat energy in z3576.

The axially non-uniform morphology compared to previously published data, as in the work of Gomez et al.,⁵ is likely a product of the rapid implosion and high stagnation convergence ratio (ratio of initial to final fuel diameter), predicted to be 40–41 in LASNEX simulations of z3289, produced by the high peak drive current of ∼20 MA. Two-dimensional LASNEX simulations of z3576 show similar high average convergence ratios of 38. In contrast, simulations modeling “optimized” MagLIF configurations limit the convergence ratio to ∼30.²¹ At 20 MA, this would require significantly higher fuel densities and preheat energies.

In this paper, we described the testing and application of highly efficient MagLIF preheat designs enabled by cryogenic cooling. A new cryogenically cooled laser platform was developed to enable blast-wave measurements that constrain the preheat energy deposited. The data show an increase in preheat coupling efficiency compared to warm targets, from ∼67% to 89% ± 10%, with a deposition profile that is closely matched by Hydra simulations. The reason for the improved coupling efficiency compared to warm experiments is likely a combination of reduced losses to heating the LEH foil material and lower levels of LPI, which will be addressed in a future publication. The cryogenically cooled preheat configuration was applied to an integrated MagLIF experiment in z3576. The target design employed a cryostat both above and below the liner to minimize the temperature differential between the top and bottom of the target without the need for insulating breaks, which previous tests suggest may affect current delivery to the load. Based on the laser-only experiments and the laser energy delivered to the target, 2.31 ± 0.25 kJ was coupled to the fuel, significantly higher than in previous experiments.

The increase in preheat energy afforded by higher coupling efficiencies demonstrated in this paper expands the design space for future MagLIF experiments. For example, MagLIF experiments with higher fuel densities and preheat energies could significantly reduce the stagnation convergence ratio while maintaining a reasonable predicted neutron yield. Simulations suggest that an experiment with 15 MA, 15 T, aspect ratio 6 liner, 1.4 mg/cc fuel density, and 2.3 kJ preheat energy could achieve a neutron yield of Y_DD = 5 × 10¹² with a peak stagnation convergence ratio ∼30, significantly lower than the 40–50 convergence ratios typically predicted for previous MagLIF experiments^5,6 and closer to those for optimized configurations.²¹ Such an experiment would test how stagnation morphology depends on the convergence ratio and whether lower convergence ratio experiments achieve stagnation conditions closer to 2D “clean” simulations that do not model liner instability growth or include material mix. The implementation of an effective cryogenic MagLIF platform also represents an important step toward realizing mix mitigation strategies²⁰ and future ice burning target designs¹⁹ that utilize cryogenic layers.

The authors would like to thank the Z machine operations team, the ABZ operations team, the ZBL operations team, and the target fabrication team for their contributions to this work. Sandia National Laboratories is a multimission laboratory managed and operated by the National Technology and Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under Contract No. DE-NA0003525. This paper describes objective technical results and analysis. Any subjective views or opinions that might be expressed in the paper do not necessarily represent the views of the U.S. Department of Energy or the United States Government.

The authors have no conflicts to disclose.

A. J. Harvey-Thompson: Conceptualization (equal); Formal analysis (lead); Investigation (lead); Methodology (equal); Project administration (equal); Writing – original draft (lead). M. Geissel: Conceptualization (equal); Formal analysis (supporting); Investigation (supporting); Methodology (equal); Project administration (equal). J. A. Crabtree: Conceptualization (equal); Formal analysis (equal); Investigation (equal); Project administration (equal). M. R. Weis: Formal analysis (equal); Investigation (equal); Methodology (equal); Software (equal). M. R. Gomez: Investigation (supporting); Project administration (equal); Writing – review & editing (equal). J. R. Fein: Formal analysis (supporting); Investigation (supporting); Writing – review & editing (equal). W. E. Lewis: Formal analysis (supporting); Methodology (supporting); Writing – review & editing (equal). D. J. Ampleford: Project administration (equal); Supervision (equal); Writing – review & editing (equal). T. J. Awe: Investigation (equal); Methodology (equal); Project administration (equal); Writing – review & editing (equal). G. A. Chandler: Data curation (equal); Writing – review & editing (equal). B. R. Galloway: Investigation (supporting). S. B. Hansen: Investigation (supporting). J. Hanson: Methodology (equal); Writing – review & editing (equal). E. C. Harding: Investigation (supporting). C. A. Jennings: Investigation (equal); Methodology (equal). M. Kimmel: Investigation (supporting). P. F. Knapp: Formal analysis (equal); Investigation (equal). M. A. Mangan: Data curation (supporting); Formal analysis (supporting). A. Maurer: Methodology (equal). R. R. Paguio: Resources (equal). L. Perea: Methodology (equal); Resources (equal). K. J. Peterson: Project administration (supporting). J. L. Porter: Project administration (supporting). P. K. Rambo: Investigation (supporting). G. K. Robertson: Methodology (supporting). G. A. Rochau: Project administration (supporting); Supervision (supporting). D. E. Ruiz: Formal analysis (supporting). J. E. Shores: Methodology (supporting). S. A. Slutz: Formal analysis (supporting). G. E. Smith: Methodology (equal). I. C. Smith: Investigation (supporting); Methodology (supporting). C. S. Speas: Investigation (supporting). D. A. Yager-Elorriaga: Investigation (supporting); Methodology (supporting); Writing – review & editing (equal). A. York: Investigation (supporting).

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