Continuing progress toward fusion energy breakeven and gain as measured against the Lawson criteria

TL;DR

This paper reassesses progress toward fusion breakeven and gain by compiling peer‑reviewed experimental results published since 2022 and updating plots of Lawson parameters, triple products, and the new scientific energy gain metric $Q_{\mathrm{sci}}$. It refines ignition criteria by incorporating experimentally measured stagnation times, discusses the limitations of the triple product as a universal metric, and presents a correction to a key equation. New data from NIF, OMEGA, Z Facility, JET, ST40, FuZE, C‑2W, PCS, and PI3 illustrate ongoing progress across both ICF and MCF concepts, including record fusion energy outputs and updated confinement estimates. The updated data tables and plotting code enhance transparency for cross‑comparison and guide interpretation of breakeven prospects for future devices like SPARC and ITER.

Abstract

This paper is an update to our earlier paper ''Progress toward fusion energy breakeven and gain as measured against the Lawson criterion'' [Phys. Plasmas 29, 062103 (2022)]. Plots of Lawson parameter and triple product vs. ion temperature and triple product vs. date achieved are updated with recently published experimental results. A new plot of scientific energy gain vs. date achieved is included. Additionally, notes on new experimental results, clarifications, and a correction are included.

Figures (8)

• Figure 1: Experimentally inferred Lawson parameters ($n_{i0}\tau^*_E$ for MCF and $n\tau_{\rm stag}$ for ICF) of fusion experiments vs. $T_{i0}$ for MCF and $\langle T_i \rangle_{\rm n}$ for ICF (see Sec. III of the original paper for definitions of these quantities), extracted from the published literature (see Tables \ref{['tab:mainstream_mcf_data_table']}--\ref{['tab:icf_mif_data_table']}). The red contours correspond to the Lawson parameters and ion temperatures required to achieve the indicated values of scientific gain for an advanced-tokamak (AT) model, which may be considered generally representative of MCF and are labeled as $Q^{\rm MCF}_{\rm sci}$. The contour colors in the original paper have been replaced by varying shades of red here to emphasize that they originate from a tokamak model. The finite widths of the $Q_{\rm sci}^{\rm MCF}$ contours represent a range of assumed impurity levels. The black curve corresponds to the Lawson parameters and ion temperatures required to achieve hot-spot ignition and the onset of propagating burn for direct- and indirect-drive laser ICF and is labeled $(n\tau_{\rm stag})^{\rm ICF}_{\rm ig, hs}$. See caption of Fig. \ref{['fig:scatterplot_nTtauE_vs_year']} regarding the gold box on one of the NIF data points. For all contours, we assume representative density and temperature profiles, external-heating absorption efficiencies, and D-T fuel. For experiments that do not use D-T, the contours represent a D-T-equivalent value. See Sec. IV of the original paper and Sec. \ref{['sec:icf_hot_spot_ignition_condition']} of this paper for details on how the $Q_{\rm sci}^{\rm MCF}$ and $(n\tau_{\rm stag})^{\rm ICF}_{\rm ig, hs}$ contours are calculated and how individual data points are extracted.
• Figure 2: Experimentally inferred triple products of fusion experiments vs. ion temperature, extracted from published literature. See the caption of Fig. \ref{['fig:scatterplot_ntauE_vs_T']} for more details, and the caption of Fig. \ref{['fig:scatterplot_nTtauE_vs_year']} regarding the gold box around one of the NIF data points.
• Figure 3: Triple products ($n_{i0}T_{i0}\tau^*_E$ for MCF and $n \langle T_i \rangle_{\rm n} \tau_{\rm stag}$ for ICF, as defined in Sec. III of the original paper and updated in Sec. \ref{['sec:icf_hot_spot_ignition_condition']} of this paper) that set a record for a given concept vs. year achieved. Record values for different concepts are shown to illustrate the progress towards energy gain of different concepts over time. The horizontal lines labeled $Q_{\rm sci}^{\rm MCF}$ represent the minimum required triple product to achieve the indicated values of $Q_{\rm sci}^{\rm MCF}$. The thickness of these lines are equal to the thickness of the equivalent contours in Fig. \ref{['fig:scatterplot_nTtauE_vs_T']} at their minimum values. The central ion temperatures required to achieve the minimum triple products (corresponding to the indicated values of scientific gain on Fig. 16 of the original paper) are in the range $20~\mathrm{keV}$ to $27~\mathrm{keV}$, which is now indicated on the plot. The black horizontal line labeled "$(nT\tau_{\rm stag})_{\rm ig, hs}^{\rm ICF} @ T_i = 4~\mathrm{keV}$" represents the required triple product to achieve ignition and the onset of propagating burn in an ICF hot spot, assuming $T_i=4~\mathrm{keV}$. The dashed gold-and-black horizontal line labeled "$@ T_i = 10~\mathrm{keV}$" represents the required triple product to achieve ignition and the onset of propagating burn in an ICF hot spot, assuming $T_i=10~\mathrm{keV}$. Although the NIF shot from August 8, 2021 did not set a triple-product record, we include it in this updated plot because it achieved hot-spot ignition and the onset of propagating burn and is an appropriate terminal data point for NIF on this plot and have added a gold box to highlight this fact. This final data point for NIF lies below the black line (and was not a record triple product because stagnation time $\tau_{\rm stag}$ for an ignited fuel assembly is depressed due to the more rapid disassembly that results from the dynamics of an ignited hot spot), but it did achieve $T_i > 10~\mathrm{keV}$ and is above the dashed gold-and-black horizontal line, which denotes the requirement for hot-spot ignition and onset of propagating burn at 10 keV. See Sec. \ref{['sec:triple_product_limitations']} of this paper and Sec. IV B 4 of the original paper for a discussion of the limitations of using the triple product as a figure of merit for experimental results near and beyond ignition for ICF. More recent and even higher-performing NIF shots are not shown on this plot but are shown on Fig. \ref{['fig:Qsci_vs_year']}. The projected triple-product ranges for SPARC and ITER are bounded above by their projected peak triple products and below by the original stated missions of each experiment (i.e., $Q_{\rm fuel}^{\rm MCF}=2$ for SPARC and $Q_{\rm fuel}^{\rm MCF}=10$ for ITER). The timelines for both SPARC and ITER have been delayed since the publication of the original paper, and the most recently announced timelines2024_CFS2024_ITER are reflected here.
• Figure 4: Plot of actual $Q_{\rm sci}$ vs. date achieved for D-T fusion experiments. Inset plot shows the same data on log-linear axes. Values of $Q_{\rm sci}$ for NIF and OMEGA results are reported on an energy basis ($Q_{\rm sci}=Y/E_{\rm in}$, where $Y$ is the fusion energy yield and $E_{\rm in}$ is the laser energy). Values of $Q_{\rm sci}$ for JET and TFTR are reported on a power basis ($Q_{\rm sci}=P_{\rm F}/P_{\rm in}$, where $P_{\rm F}$ is fusion power and $P_{\rm in}$ is heating power crossing the vacuum-vessel boundary). JET shots 99971 and 99972 (taken on the same day in 2021) use power levels averaged over 5 and 2 s, respectively. JET shots 104522 and 104600 (taken in 2023) use power levels averaged over 3 and 5 s, respectively. Earlier shots from JET and TFTR (from the 1990s) are instantaneous values taken at the time of peak fusion power.
• Figure 5: Data for tokamaks and spherical tokamaks.