A correction to the analysis by Frank et al. (2025 J. Plasma Phys. 91, E110) is provided. We correct an error in the root-finding method used to generate the plasma operation and performance contours (POPCONs) that resulted in invalid operating points being generated at which power balance was not satisfied. Our updated analysis corrects this error while retaining otherwise identical methodology and finds new self-consistent operating points. Some parameters of the optimised device change, but the key conclusions by Frank et al. (2025 J. Plasma Phys. 91, E110) remain the same: an end plug using high-temperature superconducting magnets and modern neutral beams enables a classical tandem mirror pilot plant producing a fusion gain Q >5. The tandem mirror pilot plant operating points identified here remain more conservative than others found in the literature with lower temperatures, neutral beam energies and end plug performance requirements.

3. An updated tandem mirror operating point

The corrected POPCON analysis indicated that an end plug with $n_p\sim (2.0 \pm 0.5)\times 10^{20}\,\textrm {m}^{-3}$ and $a_m \sim 0.25\pm 0.05\,\textrm {m}$ would be required to consistently achieve $Q\gt 5$ for $\ell _c =50\,\mathrm{m}$ and central cell linear power densities comparable to those of Frank et al. (Reference Frank2025): ${\gt} 5\,\mathrm{MW}\,\mathrm{m}^{-1}$ . The corrected analysis also predicted lower values of $T_{ec} \sim T_{ic}$ (at fusion-relevant temperatures) and thus lower $\phi _e \approx 4{-}5T_e$ . The large $T_e\sim 100\,\mathrm{keV}$ values found by Frank et al. (Reference Frank2025) were a result of the root-finding error. However, in the operating points identified here, $T_e$ is still somewhat greater than $T_i$ at $T_i \leqslant 50\,\mathrm{keV}$ in spite of the roughly four times larger electron channel energy losses due to strong alpha heating.

Table 1.

Parameters for the revised optimised end plug and central cell.

Figure 1.

(a) POPCONs for the tandem mirror. Red contours denote supplemental RF heating power in the central cell in MW. Black contours denote the fusion power in the central cell in MW. Green contours denote the plasma $\beta$ . The hatched regions in red and grey are disallowed operating regions where the central cell is ignited (red) or has a value of $\beta \gt 1$ (grey). The operating point shown in table 1 is denoted with a star. (b) Profiles in the tandem mirror end plug calculated by RealTwin simulations and assumed when generating the POPCONs. Density $n$ (blue) and ion energy $\langle E_i\rangle$ (red) are plotted versus the square root of the normalised poloidal flux $\sqrt {\psi _n}$ .

Repeating the Bayesian optimisation technique and RealTwin simulations as done by Frank et al. (Reference Frank2025) in § 4^* once again yielded an operating point with self-consistent high-fidelity end plug simulation and central cell POPCON parameters. RealTwin simulations optimised end plug conditions over parameter ranges: $a_m = 0.2{-}0.3\,\textrm {m}$ , $B_m = 25\,\mathrm{T}$ , $B_0 = 6.0{-}8.0\,\mathrm{T}$ , $\ell _p = 4.5\,\mathrm{m}$ , $E_{\mathrm{NBI}} = 300{-}500\,\mathrm{keV}$ and $P_{\text{NBI}} = 20{-}40\,\mathrm{MW}$ . This optimisation process combined with standalone self-consistent runs identified the parameters shown in table 1, the POPCONs in figure 1(a) and the simulated end plug profiles shown in figure 1(b). The set-up of these simulations was identical to that of Frank et al. (Reference Frank2025) in § 4^* with the exception of the previously noted change in parameter ranges and a change in the ML library used for the backend (we used BoTorch (Balandat et al. Reference Balandat, Karrer, Jiang, Daulton, Letham, Wilson and Bakshy2020) rather than Scikit-learn (Pedregosa et al. Reference Pedregosa2011) here as it provided better computational performance). The optimisation identified an optimum at $a_m=0.3\,\mathrm{m}$ , $B_0 = 6.5\,\mathrm{T}$ , $P_{\mathrm{NBI}}=35\,\mathrm{MW}$ . This operating point is slightly larger and has a higher central cell mirror ratio than the original operating point identified by Frank et al. (Reference Frank2025), but otherwise is similar to it. The slightly higher central cell mirror ratio does increase the risk of trapped particle modes and this must be addressed in future design studies. POPCON analysis indicated that the performance benefit of moving to $P_{\mathrm{NBI}} =40\,\mathrm{MW}$ from $35\,\mathrm{MW}$ was marginal and the lower recirculating power solution was favoured. Furthermore, at higher $P_{\mathrm{NBI}}$ , the plasma was more susceptible to a radial profile instability described in § 4^* in which $\beta$ rapidly grows on axis due to the NBI power deposition profile. If this instability can be mitigated in future self-consistent simulations with more careful NBI aiming and power/energy modulation, greater plug performance may be obtainable. The POPCON analysis here indicates that $Q$ is insensitive to applied heating power if density is varied commensurately. This implies that as long as the stabilisation actuators necessary for axisymmetrisation have acceptable wall plug efficiency, they will not substantially impact the viability of the operating point. If higher NBI energies are obtainable, it may be possible to operate at slightly higher $T_e$ and $Q$ , but $E_{\mathrm{NBI}} \gt 600\,\mathrm{keV}$ provided little performance benefit in exploratory simulations as the shine-through fraction became large.