Measurements of fusion reaction history in inertially confined burning plasmas

A high-gain inertial confinement fusion (ICF) implosion is designed to confine fusion products, specifically ⁴He or alpha particles produced in the deuterium–tritium (DT) fusion reaction, within the compressed fuel assembly, which produces self-heating of the cryogenic fuel plasma leading to enhanced thermonuclear fusion ignition.^1–4 The National Ignition Facility (NIF) has recently made a significant step in this direction by achieving fusion ignition in the laboratory for the first time.^5–9 This achievement represents a substantial advance over previous NIF shots by an increase in the gain by several orders of magnitude. This increase in the yield paves a new experimental way to unlock the physics of self-heating and thermonuclear burn propagation. Since the self-heating and burn propagation phenomena are highly sensitive to the design of ICF capsules, a direct measure of the self-heating and burn propagation is crucial to provide insight into the underlying physics of igniting plasmas and to optimize the capsule design.

Direct evidence of the passage into the ignition regime is an abrupt temperature increase caused by alpha particle deposition with a consequent increase in the burn rate as seen in the reaction history.^10–13 Frenje and Cerjan et al. used the two-dimensional HYDRA simulation code and calculated the effect of alpha-heating on the reaction history, in which the degree of alpha-particle energy deposition is artificially adjusted.¹⁰ Using the NIF shot N130927 as a baseline, Cerjan et al. examined the effects of no alpha heating [Fig. 1(a), black bottom curve]. Without alpha-heating, the imploding capsule's energy losses, either by radiation or thermal conduction, are greater than the capsule's compressional work (or PdV work, where P is the pressure, and dV is the volume change), and therefore, the fuel temperature decreases at stagnation. As alpha heating is increased (e.g., 4× for the green curve, 25× for the blue curve, and 83× for the red top curve), the fuel temperature is maintained or increased during the capsule's stagnation phase; therefore, reaction rates continuously increase. Figure 1(b) shows four normalized reaction rates divided by each peak values, highlighting the peak times of the reaction rates (i.e., bang time) shift to later in time, compared to no alpha-heating case, as yields increase. In Fig. 1(c), peak times of Fig. 1(b) were aligned to time zero and it shows decreasing reaction rate's full width at half maximum (FWHM) (i.e., burn width) as yields increase.

Another independent example of the effect of alpha-heating on the reaction history was studied by Wilson et al.¹⁴ An independent numerical simulation was performed by varying deuterium fractions with a hydro-equivalent fashion in a tritium-hydrogen-deuterium (THD) fuel mixture.¹⁴ As deuterium fractions increase from 2%, 25%, 35%, and up to 50%, plasma heating by alpha particles raises the yield rate or reaction rate, eventually resulting in ignition in the 50% deuterium capsule. The same as Cerjan et al.'s simulation, the bang time occurs later in time and the burn width gets narrow as deuterium fractions increase. For the igniting reaction rate (shown in the 50% deuterium concentration calculation), the burn width can be significantly narrower than 100 ps owing to alpha energy deposition. To resolve this narrow burn width and a fast increasing slope in the igniting burn rate, the detector's temporal resolution is required to be on the order of 10 ps.^11,12

A primary goal of reaction history diagnostics on NIF is, thus, to measure igniting reaction rates with a 10 ps temporal resolution. The most accurate way to achieve this goal is through the measurement of the γ rays produced in a rare branch of the D + T reaction: D + T → ⁵He + γ (16.75 MeV) or D + T → ⁵He^* + γ (13.25 MeV).^15–21 While fusion neutrons produced by the reaction: D + T → n + ⁴He experience a time-of-flight temporal broadening and also scattering from the compressed DT fuel, γ rays preserve the birth rates of the reaction history²² without temporal broadening. The Gas Cherenkov detector (GCD) and Gamma Reaction History (GRH) instruments were developed to isolate the DT fusion γ rays from other non-fusion γ rays by adjusting the energy threshold with different gases and pressure in the Cherenkov pressure cell.^23–29 Both GCD and GRH on NIF observed the decreased burn width and temporal shift in the peak burn time during high-yield shots (yields greater than 10¹⁷ neutrons).

Two reaction history diagnostics are operational on NIF: the single-channel GCD [shown in Fig. 2(a)] and the four-channel GRH instrument [one of the channels is shown in Fig. 2(b)]. The GCD uses a linear configuration, which allows the instrument to be placed in a diagnostic well, thus allowing operation closer to the target.^30–34 The GRH, however, uses a folded design, requiring it to be operated outside the target chamber, but allowing the photomultiplier tube (PMT) to be better shielded from x rays or other sources of background radiation, such as neutron-induced secondary γ rays.^35–39 

Table I shows the operational summary of GCD and GRH including temporal resolution, sensitivity, and energy threshold used. Two GRH channels (i.e., cell A and cell D) are dedicated to measure the burn history by setting an energy threshold at 10 or 12 MeV. The remaining two GRH channels (i.e., cell B and cell C) have been used to isolate the 4.4 MeV γ rays generated from (n, n'γ) reactions on the ¹²C ablator by setting one γ-ray detector threshold just below 4.4 MeV and another just above it, and then subtracting the signals. The 4.4 MeV γ rays provide the areal density of the carbon in a plastic or diamond capsule shell, which monitors the compression of the shell at the burn time.^40–44 

Since the inception of National Ignition Campaign in 2010, the folded-design GRH diagnostic on NIF has measured time-resolved measurements of fusion γ rays from implosions.^45–48 While Cherenkov conversion process and its optical collection together provide a 10 ps temporal response, GRH is limited in the temporal resolution by ∼100 ps due to temporal response of the PMT.⁴⁹ The linear-design GCD has been developed to improve the temporal resolution down to 10 ps by incorporating a pulse dilation (PD) PMT technology.^50–53 High bandwidth γ reaction histories measured by the GCD/PD-PMT confirmed that the fusion burn widths measured by the slower instrument, GRH/PMT, are still in good agreement with the faster GCD/PD-PMT data. However, the 10 ps GCD/PD-PMT measurements (using CO₂) have been limited by the presence of a long-duration (∼500 ps) tail on the fusion signal (see Fig. 2 in Ref. 54), which is not observed on the better-shielded folded-design GRH (also using CO₂). It has been confirmed that the long-duration tail is produced in the gas cell and is not an artifact of the PD-PMT or recording system.⁵⁴ The current hypothesis is that the tail is caused by sub-threshold γ rays (i.e., γ rays with energy lower than GCD's energy threshold at the given gas pressure), which induce scintillation in the gas. These sub-threshold γ rays are likely caused by neutron-induced secondary reactions on the Hohlraum wall and the thermomechanical package (TMP) used in indirect-drive cryogenic NIF implosions. The folded-design GRH does not see the tail due to the convoluted optical path used in the GRH, which efficiently transports the forward-directed Cherenkov radiation, but may not be efficiently collecting the scintillation, which is isotropic. As a near-term resolution, neon (Ne) gas is being used in the GCD/PD-PMT because Ne produces enough late-time tail signal so it can be measured at high thresholds without the Cherenkov signal (i.e., >17 MeV), and its longer decay time makes the temporal signature distinguishable from the DT gamma signal.⁵⁴ 

Since 2020, NIF experiments began to create burning plasma conditions in which energy produced by the alpha-particle self-heating (i.e., E_α) is greater than that of PdV compressional work.⁵ While the inferred PdV work on the DT fuel was on the order of 10–15 kJ, two experiments performed in 2020 (N201101 and N201122) achieved approximately 20 kJ of E_α. Two other experiments in 2021 achieved even higher E_α about 33 kJ for N210207 and about 31 kJ for N210220. Furthermore, the N210808 produced ∼260 kJ of E_α, which gained by about an order of magnitude over previous comparable shots. Figure 3(a) shows the measured burn width for the above five burning plasma experiments. For comparison purposes, four prior experiments performed during 2017–2019 are also included in Fig. 3(a). The previous four experiments (N170601, N170827, N180128, and N191110) produced only a few kJ of E_α with an associated burn width of 160 ± 30 ps measured by the folded-design GRH/PMT. Starting from N201101, as the alpha-heating increases, the GRH burn width began to decrease to 130 ± 30 ps. On N210808, the GRH burn width further decreased to 90 ± 30 ps, marking the first time a measured burn width reached the GRH temporal response (∼100 ps). GCD/PD-PMT's neon operation successfully extracted the burn width from the N210808 experiment (88 ± 15 ps) and confirmed the GRH's burn width (90 ± 15 ps). As predicted in Fig. 1(c), both GRH and GCD demonstrated that burn width decreases as alpha-heating increases. While the slow GRH detector can still provide the igniting regime's burn with accurately, it cannot resolve the asymmetry of the temporal profile because the igniting regime's burn duration becomes narrower than the GRH's instrument response function. In Fig. 3(b), N210808's reaction history is compared: GCD/PD-PMT measurement (red curve, a background tail was removed) to two-dimensional HYDRA code simulation (blue curve). The 10 ps resolution GCD data agree well with the simulated reaction history, showing an asymmetric temporal profile with a slower rising time than a fall time.

After the success of the N210808 experiment, the NIF team performed a series of repeat shots, which maintained capsule and laser conditions as those of N210808. While the hydrodynamic compression conditions remained identical, the yield output varied from ∼5 × 10¹⁶ to ∼2 × 10¹⁷ attributed mainly to capsule variations. Figure 4 shows such yield variations as a function of bang time [Fig. 4(a)] and burn width [Fig. 4(b)], respectively, measured by a 100 ps resolution GRH. As yield increases due to increasing alpha-heating, bang times get pushed later in time and burn widths decrease, which are consistent with the effect of alpha-heating predicted by the numerical simulation shown in Fig. 1. Additionally, an unique shot N220220 with 24:74:2 T:H:D fuel instead of 50:50 D:T fill shows a significantly lower yield (4.4 × 10¹⁴), an earlier bang time [9.17 ns, marked with a red closed circle on Fig. 4(a)], and wider burn width [149 ps, marked with a red closed circle on Fig. 4(b)]. Since the THD shot is not expected to have significant alpha-heating, the earlier bang time and the wider burn width than those from the DT shots producing yields higher than 10¹⁷ neutrons are also consistent with the simulation prediction by Wilson et al.¹⁴ 

Taking the hot spot pressure for the weak-alpha regime as approximately 200 Gbar,⁵ the observed burn width change from the weak-alpha regime (∼160 ps) to the burning plasma regime (∼130 ps) implies a stagnation pressure change to 260 Gbar, consistent with other independent estimations. Similarly, the burn width change to ∼90 ps implies a pressure increase to 400 Gbar—also consistent with other estimates of hot spot pressures for N218080. Scaling with the thermodynamic expectation of the burn width further supports that the observed nuclear burn width is indicating a sharp and rapid increase in the internal hot spot pressure.

The long-duration scintillation tail of linear-design GCD may become more prominent for alternative ICF capsules, such as a high atomic number (or high-Z) pushered single-shell⁵⁶ and double-shell targets.⁵⁷ The areal density of the high-Z shell could result in a much larger population of sub-threshold γ rays, which would produce a much larger scintillation tail. Thus, to obtain fusion burn histories on the high-Z based capsules, the scintillation tail must be eliminated. This tail could also pose a problem for burn history measurements on pulsed-power ICF facilities, such as Sandia Z-accelerator, due to the large amount of material in the vicinity of the burn in pulsed-power liner implosions. Additionally, as capsule implosions become more and more compressed, the standard neutron-based yield measurement could be problematic due to neutron scattering from the fuel. As shown in Ref. 48, fusion γ ray can be an alternative yield measurement, if the Cherenkov-to-scintillation ratio is acceptable.

As for a scintillation mitigation technique, an optical relay is being proposed for the linear-design GCD that will efficiently transport the Cherenkov light to a location shielded from the direct radiation from the target, while suppressing scintillation transport. Currently, the optical relay idea is being tested by adding a PD-PMT to a cell of the folded-design GRH. This would confirm that the tail is not present in the GRH system, which already has the optical relay. In addition, a magnetic filter can be considered to deflect sub-threshold Compton electrons converted by the sub-threshold γ rays away from the gas cell. The essential concept is to form a magnetic field between a γ-to-electron converter and a Cherenkov gas cell. While the high-energy Compton electrons specifically converted by the 16.75 or 13.25 MeV DT fusion γ rays are deflected by the magnetic field less, the low-energy Compton electrons converted by the sub-threshold γ rays will be more strongly deflected away from the gas cell.

While the linear-design GCD coupled with PD-PMT has achieved successfully 10 ps temporal resolution, its signal-to-background is significantly limited to ∼2 due to the gas scintillation background issue and the direct interaction of x rays or non-fusion γ rays with a PD-PMT. The folded-design GRH is better shielded, and one of the GRH channels will be coupled with PD-PMT, but its signal-to-background is still limited to ∼10 due to the high radiation environment in the NIF target bay. Due to their limited signal-to-background and the fact that both GCD and GRH's radiation background are yield-dependent, the existing GCD and GRH diagnostics cannot detect the onset of alpha heating, where the slope of reaction history changes the most abruptly. (For example, in Fig. 1, the onset of alpha heating is seen at 16.15 ns.) To record the onset of alpha heating, a yield-rate coverage of at least 1000 will be needed as shown in Fig. 1(a).^11,58

The GRH-15m (i.e., GRH located at the 15 meter from the target chamber center) originally proposed in 2009 will provide reaction history data at higher signal-to-background ratio than is possible with the existing GRH (i.e., GRH-6m currently located at 6 meter from the target chamber center) or GCD. To accomplish this improvement, the optical detectors (i.e., PMT or PD-PMT) must be removed from the high radiation environment in the target bay because the direct interaction of x rays and neutron-induced γ rays is dominant background sources. As shown in Fig. 5, we propose transporting the Cherenkov light from gas cells located inside the target bay at 15 meter to optical detectors located on the other side of the six-foot-thick cement shield wall. This will reduce the radiation background on PMT or PD-PMT significantly, therefore increasing the signal-to-background ratio, while maintaining temporal resolution on the order of 10 ps. The proposed GRH-15m is sensitive enough to diagnose reaction history at yields approaching near 1 MJ and beyond (i.e., 10¹⁷–10²⁰, where 3.5 × 10¹⁷ DT neutrons are equivalent with 1 MJ of fusion energy).

Figure 6 shows an optical design of the proposed GRH-15m consisting of five off-axis parabolic (OAP) mirrors and one flat mirror. The gas cell, from γ-to-electron convertor to pressure window, is essentially identical to the existing GRH-6m, and the remaining OAP mirrors are duplicates of ones used in the GRH, except for OAP2. OAP2 is an 8 in. diameter mirror needed to relay the Cherenkov light ∼7 feet through the 6-foot-thick cement shield wall. (OAP2 of GRH-6m is of 4 in. diameter.) The preliminary optics design has the same optical acceptance into a 1 cm diameter spot at the PMT photocathode plane as the GRH-6m design. Hence, the system has essentially the same sensitivity in collected Cherenkov photons per incident γ rays as the GRH-6m. The overall system sensitivity then will be determined by the solid angle fraction at the γ-to-electron convertor located 15 meters from a target chamber center—a factor of ∼6 less than the GRH-6m. In order to increase the dynamic range (or yield-rate coverage), the signal will be split with a pellicle (not shown in Fig. 6) located at the waist between OAP3 and OAP4. As shown in Table II, 10% of Cherenkov optical signal will be sent to a PD-PMT and 90% to a PMT via an additional pair of OAP mirrors (OAP4 and OAP5). Under this configuration, the sensitivity of the PD-PMT channel will be ∼60× less than that of GRH-6m and sensitivity of PMT channel will be ∼7× less than that of GRH-6m. (Alternative split ratios may be employed.) We aim to utilize the faster PD-PMT detector to resolve the reaction history near the peak amplitude, where the temporal profile changes most abruptly. The peak amplitude is higher than the rest of reaction history; therefore, the weaker optical signal (i.e., 10% of Cherenkov signal) will be still adequate for the PD-PMT. While 10/90 optical split approach can provide a way to increase the dynamic range by a factor of ∼10, but this benefit comes from sacrificing sensitivity of detectors. Therefore, background reduction is still important to increase the overall yield-rate coverage.

As thermonuclear burn conditions at NIF begin to sample the alpha-heating regime, high-bandwidth measurements of fusion reaction history are required beyond just nuclear bang time and burn width measurements. On NIF, γ-ray reaction history detectors' temporal resolution has been improved [i.e., 100 ps for Gamma Reaction History (GRH) and 10 ps for Gas Cherenkov Detector (GCD)] and has observed the decreased burn width and temporal shift in the peak burn time during recent high-yield shots (>10¹⁷ neutrons), which is a diagnostic signature of ignition. However, due to their limited signal-to-background ratio, the existing GCD and GRH diagnostics cannot detect the onset of alpha heating, where the slope of reaction history changes the most abruptly. The GRH-15m is proposed to provide high-quality reaction history by increasing signal-to-background by more than a thousand.

This work was performed by the Los Alamos National Laboratory, operated by Triad National Security, LLC for the National Nuclear Security Administration (NNSA) of U.S. Department of Energy (DOE) under Contract No. 89233218CNA000001.

The authors have no conflicts to disclose.

Yongho Kim: Formal analysis (equal); Supervision (lead); Writing – original draft (lead). D. C. Wilson: Conceptualization (equal); Software (lead). Eric Loomis: Funding acquisition (supporting); Project administration (supporting); Supervision (supporting). Charles Cerjan: Formal analysis (lead); Software (lead); Writing – review & editing (lead). Alex Zylstra: Investigation (lead). Justin Jeet: Investigation (equal). David J. Schlossberg: Investigation (equal); Resources (equal). Michael Rubery: Software (lead); Validation (lead). Alastair Moore: Funding acquisition (supporting); Project administration (supporting); Supervision (supporting). A. L. Kritcher: Software (lead); Validation (equal). Jorge Carrera: Investigation (equal); Methodology (equal). Kevin Meaney: Formal analysis (lead); Investigation (lead). Eddie Mariscal: Investigation (equal); Methodology (equal). Daniel T. Casey: Investigation (equal); Methodology (equal). Eduard Liviu Dewald: Investigation (equal); Methodology (equal). Alex Leatherland: Software (equal); Validation (equal). Robert Michael Malone: Investigation (equal); Methodology (equal). Morris Kaufman: Investigation (equal); Methodology (equal). Hermann Geppert-Kleinrath: Formal analysis (lead); Investigation (lead). Hans Herrmann: Conceptualization (lead); Project administration (lead); Writing – review & editing (supporting). Thomas J. Murphy: Project administration (equal); Writing – original draft (supporting). Carl Young: Conceptualization (equal); Software (lead). Nelson Hoffman: Formal analysis (equal); Methodology (equal); Writing – review & editing (supporting). Harold Justin Jorgenson: Methodology (supporting); Resources (supporting). Tana Morrow: Methodology (supporting); Resources (supporting); Visualization (supporting).

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