- 1HB11 Energy Holdings Ltd Pty, Sydney, NSW, Australia
- 2School of Electrical Engineering and Telecommunications, Faculty of Engineering, UNSW Sydney, Kensington, NSW, Australia
We have revisited recent results on the ideal ignition of H11B fuel, in the light of the latest available reactivity, an alternative self-consistent calculation of the electron temperature, an increased extent of the suprathermal effects and the impact of plasma density. At high density, we find that the ideal ignition temperature is appreciably relaxed (e.g.,
1 Introduction
The 11B(p,3α) fusion reaction, with a Q-value of 8.6 MeV, is experiencing a renewed interest for energy production purposes, in the light of recent experimental and theoretical findings [1–11]. The reaction is aneutronic and involves only abundant and stable isotopes. Moreover, the α particles in its final state may release all their energy to the fusion plasma. The reaction is also of interest for studies in stellar evolution, where relative abundances of 11B, Li and Be provide insight into stellar processes [12]. Proposed approaches for energy production span magnetic [13], magneto-inertial [14, 15] and laser-driven [5, 16, 17] fusion. The exploitation of H11B fuel, however, remains extremely challenging because of its low reactivity and high radiative losses at temperatures attainable in present-day fusion devices.
The existence of ideal ignition conditions has been demonstrated only lately by Putvinski et al. [6], who have used a recent fusion cross section dataset [4] for the calculation of the thermal reactivity and added to this latter a contribution coming from kinetic (particularly, suprathermal) effects, calculated self-consistently. Suprathermal effects are due to elastic collisions between the fusion-born α′s and background thermal protons [6, 18], which develop a bolder tail in the proton energy spectrum compared to the Maxwell-Boltzmann distribution [19–21]. Putvinski et al. [6] have found fusion power to overcome bremsstrahlung losses only marginally, for
In this Brief Research Report, we first revisit those findings in the light of the latest available reactivity, an alternative self-consistent calculation of
We recall that hot-spot fuel configurations are relevant to laser-driven inertial confinement, which is a promising method to achieve fusion energy [22]. Ignition of DT fuel has recently been achieved at the US National Ignition Facility [23], by exploiting an indirect-drive scheme based on a nearly isobaric fuel configuration [24]. Fast ignition is a technique alternative to hot-spot ignition and is based on the ignition of precompressed fuel by means of an external trigger. Laser-driven fast ignition was proposed by Tabak et al. [25] 30 years ago and it is today the subject of significant theoretical and experimental investigation [26, 27].
2 Ideal ignition
The ideal ignition conditions of Putvinski et al. [6] have been recalculated and plotted in Figure 1A (blue curve) in terms of the ratio
is the fusion power (per unit volume),
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Figure 1. (A) Revisit of Putvinski et al’s ideal ignition and burn conditions [6], at low plasma density. (B)
From Figure 1A, we note that ignition is not possible if the suprathermal contribution is not accounted for (
As for the self-consistent calculation of
where
which yields slightly higher values of
While ignition and self-burn appear less marginal than previously found, low-density plasmas remain of a primary interest for magnetic confinement approaches, which can operate at sub-ignition. More meaningful conclusions can be drawn for ignition-based schemes, at high density. While the explicit square-density dependence of the P-terms cancels out in Eqs 2, 3, a residual dependence on density remains in Eq. 3 through the Coulomb logarithms of
As
The high
3 Hot-spot ignition
The power balance condition for a hot spot of radius R and density ρ at the ignition threshold reads
where
where
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Figure 2. Left-hand ordinate: Confinement parameter vs.
By analogy with the DT and DD cases, we expect that 1D simulations of pre-assembled fuel would actually show a lower branch of the ignition curves in the proximity of and after their knee, due to a cooling/re-heating mechanism of the hot spot for initial points located just below the analytic curves [32–35]. In the case of isochoric DT, for instance,
Although the confinement parameter is high at the minimum of ignition curves, we have checked that the plasma is still optically thin, i.e., the Planck mean free path,
is the free-free Planck mean opacity [35], with
For instance,
The ignition energy,
where V is the volume of the plasma sphere and p is its pressure, as given by
The quantity
4 Discussion and conclusion
Despite the fact that self-heating is possible in a pre-formed hot spot, we have verified that implosion-driven formation of the hot spot is hydrodynamically impossible, on the basis of the same argument preventing it in pure D fuel [34], i.e., a cooling timescale shorter than the hot-spot confinement time
Proton fast ignition [36] is particularly suited to H11B fuel, not only because of its superior ballistic properties in the energy deposition and the potential capability of inducing the hot-ion mode, but also because of the additional heating provided by the in-flight fusion reactions of the proton beam [21, 37]. It has been put forward [21] that in a fully degenerate 11B plasma, under certain conditions, this contribution could become as large as the initial kinetic energy of the proton beam. Such an effect could then appreciably reduce the ignitor energy required in a H11B mixture. Taking also into account the reduction of
The ignitor pulse will have to be delivered to the compressed target within a timescale shorter than
With a 300 kJ ignitor and the highest reported laser-to-proton energy conversion efficiency, 15% [41, 42], an overall laser energy of 2 MJ will be needed to drive the ignitor. This energy will have to be delivered to the foil target over a timescale of 1 ps. Suitable laser amplifiers and laser architectures will have to be developed to this extent as well as for the ns-scale implosion of the fuel, where driver energies above 10 MJ are expected. Both Diode-Pumped Solid-State Laser (DPSSL) and excimer laser systems show the potential to be scaled up to the large energy outputs required for compression and fast ignition of H11B fuel, on both the ns and ps timescales [43, 44].
We finally recall that within the frame of a very specific fast ignition scheme, based on a laser-driven relativistic shock wave, Eliezer et al. [45] have found that a laser pulse with intensity of 1.6 × 1025 W/cm2, duration of 1 ps and energy of 21 MJ impinging on fuel pre-compressed at 4,800 g/cm3 can generate a side, cylindrical hot spot with a depth of 8.3 g/cm2,
On the contrary, our preliminary analysis shows that proton fast ignition of isochoric H11B fuel requires compression and ignitor performances which, though challenging, are in line with near-future laser capabilities. We plan to devote further work to demonstrate burn propagation, better quantify ignition parameters and calculate gain in such scheme, considering actual target configurations.
Data availability statement
The original contributions presented in the study are included in the article/Supplementary Material, further inquiries can be directed to the corresponding author.
Author contributions
EG: Formal Analysis, Writing–original draft, Writing–review and editing, Data curation, Investigation, Software, Visualization. FB: Formal Analysis, Writing–original draft, Writing–review and editing, Conceptualization, Methodology, Supervision, Validation.
Funding
The author(s) declare that financial support was received for the research, authorship, and/or publication of this article. HB11 Energy Ltd. Pty. has supported this work through the consultancy contract of the first author and the payment of the publishing fee. This work has been carried out under the Collaborative Science Program of HB11 Energy.
Acknowledgments
The authors wish to thank D Batani, S Pikuz, E Turcu and D Margarone for useful discussions. The authors are indebted with I Morozov for an independent verification of their results. FB is grateful to F Ladouceur for hosting his fellowship at UNSW Sydney.
Conflict of interest
Author EG was affiliated to HB11 Energy Holdings Ltd Pty.
The remaining author declares that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
The authors declare that this study received funding from HB11 Energy Pty. Ltd. The funder was involved in the discussion of the results and in the decision to submit the manuscript for publication.
Publisher’s note
All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.
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Appendix A: Formalism
Power density terms
Explicit expressions for the power density terms in Eqs 1–6 are given hereafter (electrostatic cgs units are used):
where
where
is the classical heat exchange rate [29],
is its relativistic correction [6], and
according to Spitzer [47];
where
is the Spitzer thermal conductivity, with
where
Fusion energy partition and stopping power
The fusion power fraction to ions,
has been used for the fusion-born α particles, with
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FIGURE A1. Fusion power fraction to ions (electrons) as a function of
Useful relations
The densities
with
Keywords: proton-boron fusion, inertial confinement fusion, hot-spot ignition, proton fast ignition, laser boron fusion, aneutronic fusion
Citation: Ghorbanpour E and Belloni F (2024) On the ignition of H11B fusion fuel. Front. Phys. 12:1405435. doi: 10.3389/fphy.2024.1405435
Received: 22 March 2024; Accepted: 24 June 2024;
Published: 05 August 2024.
Edited by:
Eliezer Shalom, Soreq Nuclear Research Center, IsraelReviewed by:
Zohar Henis, Soreq Nuclear Research Center, IsraelDimitri Batani, Université de Bordeaux, France
Fuyuan Wu, Shanghai Jiao Tong University, China
Copyright © 2024 Ghorbanpour and Belloni. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
*Correspondence: Fabio Belloni, f.belloni@unsw.edu.au
†Present address: Fabio Belloni, European Commission, Directorate-General for Research and Innovation, Euratom Research, Brussels, Belgium