Papers

on Power Plant Engineering & System Analysis,
on Stellarator Optimization,
on Materials (Neutronics, Plasma-Wall Interaction)

Papers on Power Plant Engineering & System Analysis

F.R. Famà, V. Prost, G. Calabrò, F.A. Volpe, S. Ubertini, A.L. Facci, Thermodynamic and economic analyses of the retrofit of existing electric power plants with fusion reactors, Energy Conversion and Management: X (2024): 100668

https://doi.org/10.1016/j.ecmx.2024.100668 (open access)

  • “Retrofit” is the installation of new or modified parts in something previously manufactured, for example to re-purpose it. This paper examines the retrofit and re-purposing of two existing power-plants (one fission-based, the other coal-fired) into fusion power-plants of the stellarator type. Four different retrofit scenarios are considered and compared with the “greenfield” option of building a fusion plant from scratch, finding significant capital savings of up to 50%. The best strategy is to (i) select a site that already implements cutting-edge thermodynamic parameters and (ii) reuse or adapt the existing systems (buildings, steam cycle, electricity generation, heat rejection) as much as possible. For the the coal-fired plant in Italy considered here, we predict Levelized Costs of Electricity (LCOE) as low as 39 - 51 $/MWh, depending on the interest rate. Such costs are competitive in the current European energy market and yield significant Net Present Values at the plant end of life.

  • "thermal” power-plants convert heat (for instance from fission, or from burning coal) in electricity. However, the whole world agrees on the urgency of phasing out coal, and some countries decided to move away from fission. At the same time, building a first-of-a-kind fusion pilot-plant might require significant time and capital. Retrofitting a coal plant (or, in selected countries, a fission plant) by replacing the heat-source with fusion would solve both problems. Contact us if you are curious about the retrofittability of a power-plant in your country 😉

V. Prost, F.A. Volpe, Economically optimized design point of high-field stellarator power-plant, Nuclear Fusion 64 (2024), 026007. 

DOI 10.1088/1741-4326/ad142e (open access)

  • In scanning the magnetic fields B, major radius R and other parameters, including unexplored ranges recently made accessible by HTS, we find combinations of values (stellarator “design points”) that are simultaneously promising from a physics, engineering and economics perspective. We do so for both a next-step burning stellarator plasma of net fusion heat, Q > 1, and for a power-plant. The “knob” with the highest effect on economics is plasma confinement, followed by reducing the blanket thickness, developing compact configurations looking more like cored apples than bicycle tires, with R = 3-5 m and B = 7-10 T, and lastly minimizing the HTS unit cost and auxiliary heating system’s cost. A comparison with other energy sources is also provided. The study relies on first principles and established empirical scalings; it assumes neutral beam injection heating and plasma-facing, flowing liquid metal walls protecting from neutrons and extracting the heat. It also finds how to evolve density, temperature and heating power to reach “ignition” (when fusion heat sustains further fusion reactions, and external heating can be turned off) and computes the power consumption to operate the power-plant (“power recirculation”) and net power put on the grid.

  • To our knowledge this is the most comprehensive study of its kind, navigating dozens of dimensions under a unique combination of physical, engineering and economical constraints. Low aspect ratios A are found to be essential to simultaneously satisfy all constraints. This is why Renaissance Fusion pursues the lowest aspect ratios of all stellarator startups and institutes. In that respect we are to other stellarators what Tokamak Energy is to other tokamaks (but we know how to shield the equivalent of the central column 😉). We show that GW-class stellarator plants will out-compete nearly all energy sources in unit cost per W installed and per kWh put on the grid. In fact, stellarators will compete with solar in terms of LCOE, with the added benefit of 24/7 availability 😉. Stellarators are not competitive with solar in unit cost of the power-plant, yet, but our first-of-a-kind cost estimates are expected to decrease for the Nth-of-a-kind.

F.R. Famà, G. Loreti, G. Calabrò, S. Ubertini, F.A. Volpe, A.L. Facci., An optimized power conversion system for a stellarator-based nuclear fusion power plant, Energy Conversion and Management 276 (2023), 116572

https://doi.org/10.1016/j.enconman.2022.116572 (restricted access)

  • “Power conversion” is the conversion of heat-to-electricity, mediated by water becoming steam and propelling turbines. Unlike all other fusion devices, which are pulsed, the stellarator is inherently steady-state, and thus requires a different downstream power conversion. In this paper we conceive and optimize such a system for a stellarator plant equipped with plasma-facing liquid metal walls in the 700–900 °C temperature range. For maximum efficiency and safety, we rely on a “supercritical CO2 Brayton–Rankine Combined Cycle”. Despite the lofty name, this means that heat is transferred twice: first from the liquid metal to carbon dioxide (yes, the one we are trying to remove from the atmosphere), but in a special state called supercritical, halfway between liquid and gas, and secondly to water/steam. Brayton and Rankine are two important folks, with two thermodynamic cycles named after them. We obtain heat-to-electricity efficiencies of 51% (significantly higher than ~34% in tokamak reactors) and a net electrical efficiency of the complete plant, including auxiliary systems, of 34%. Finally, we discuss the technical feasibility and optimization of the two most critical components: turbo-machinery and heat exchangers. We obtain compact machines of, respectively, 1.2 m diameter and 40 m³ volume.

  • Even 1% of power-plant efficiency increase is worth tens of millions, and here we are talking factors, not percents... Let’s say we want to put 1 GW of electricity on the grid,. We could build a tokamak producing 6 GW heat with 34% conversion efficiency and 50% duty cycle. Alternatively, we could build a stellarator capable of 2 GW heat production with 51% conversion efficiency and near-100% duty cycle. The latter is roughly a 3x smaller investment, for the same result ! Continuous operation reduces costs even further (no thermo-mechanical transients, no intermediate energy storage, etc.). This is partly made possible by the steady state nature of stellarators, and partly by two new contributions of this paper. First, we envision a combined Brayton-Rankine cycle, more efficient than the traditional Rankine cycle of nuclear power plants. The second benefit stems from the high temperature of our first working fluid -the liquid metal-, resulting in high thermodynamic efficiency, and made possible by clever materials subject to lower evaporation than pure lithium. Finally, combining two cycles led to adopting a third, intermediate working fluid. This prevents liquid metal from entering in contact with water, with major benefits for safety.

Papers on Stellarator Optimization

Y. Privat, R. Robin, M. Sigalotti, Optimal shape of stellarators for magnetic confinement fusion, Journal de Mathématiques Pures et Appliquées 163 (2022), 231

https://doi.org/10.1016/j.matpur.2022.05.005 (final paper, restricted access)

hal-03472623 , version 2 (preprint, open access)

  • Magnetic confinement of stellarator plasmas is entirely achieved by optimized coils lying on a toroidal “Coil Winding Surface” (CWS). The surface is typically fixed at the beginning on the basis of the plasma boundary, or is varied a few times “by hand”. In this paper, the surface is optimized as well, self-consistently with the coils. The figure-of-merit is a single number combining several metrics. Metrics from an earlier paper (see below) include field accuracy in the plasma, coil simplicity on the surface (“regularization”) and minimal forces between the coils. New, additional metrics include proxies for surface simplicity, such as surface curvature. The paper proves the “shape differentiability” of the criterion. [This is part of a branch of mathematics known as “shape optimization”. It means that you can differentiate a number with respect to… a shape, which turns useful here, much like, when you optimize a number as a function of another number, you may need to differentiate one w.r.t the other.] The paper proves that an optimal shape exists, and provides a workable expression that was coded in the new STELLACODE. The code is flexible with respect to the figure-of-merit definition and can carry out its optimization either in the general space of all toroidal CWSs surrounding the plasma, or in some subspace of parametrized surfaces, for instance axisymmetric or piecewise cylindrical.

  • Typical optimizers find optimal coils (simple, subject to low forces, etc.) on a fixed surface. Therefore, the optimum depends on the surface assumed, but “an even better optimum” could exist -and typically does exist- for a different assumption. This is why it is important to self-consistently optimize the surface and the currents thereon. At the same time, we refrain from unnecessarily broad searches, and we restrict to coil-surfaces making sense from a construction perspective. In our case, these are piecewise cylindrical surfaces, not necessarily of circular cross-section. The STELLACODE developed for this paper is of general interest; in our case, it helps us finding coil-surfaces suitable for our wide HTS, laser-engraving approach and yielding accurate stellarator fields.

R. Robin, F.A. Volpe, Minimization of magnetic forces on stellarator coils, Nuclear Fusion 62 (2022), 086041. 

DOI 10.1088/1741-4326/ac7658 (final paper, restricted access)

arXiv:2103.13195 (preprint, open access)

  • This is a partly mathematical, partly numerical paper. In the mathematical part we considered a coil surface and proved that there is a natural and rigorous way to define the electromagnetic force, despite the magnetic field discontinuity across the current-sheet, In the numerical part we included force reduction in the stellarator coil optimizer REGCOIL, which we rewrote in python. Specifically, we added to the figure-of-merit two metrics to penalize the electromagnetic forces acting on the stellarator coils (one local, the other surface-averaged). By doing so, we found current-patterns that generate accurate stellarator fields and yet suffer from peak-forces 40% lower than usual (everything else remaining equal). We also discussed future, easy generalizations to parallel and normal force-components, as these will be subject to different engineering constraints.

  • Plasma confinement in small volumes requires high magnetic fields, which call for high coil-currents and cause high forces on the coils. This has consequences for the support structures, usable materials and maximum field achievable, ultimately constraining the minimum size and cost of an HTS stellarator. However, fear not! In this paper we upgrade a famous code and find coil configurations that generate accurate stellarator fields and yet are subject to peak-forces 40% lower than usual (everything else remaining equal). This gives valuable headroom in the pursuit of high fields.

Papers on Materials

V. Prost, S. Ogier-Collin, F.A. Volpe, Compact fusion blanket using plasma facing liquid Li-LiH walls and Pb pebbles, Journal of Nuclear Materials 599 (2024), 155239

https://doi.org/10.1016/j.jnucmat.2024.155239 (open access)

  • Deuterium-Tritium fusion reactors will produce neutrons and, from them, they will produce their own Tritium fuel in a Lithium-based component called blanket. The blanket will also capture neutrons’ energy: this is how reactors will generate heat and ultimately electricity! Our blanket will be liquid and directly face the plasma. It will adopt innovative materials: a liquid solution of lithium and lithium hydride with solid pebbles suspended in it. Such pebbles will be filled with lead (Pb) and, for electromagnetic reasons, will accumulate on the plasma side, where they are most useful. The paper presents the neutronic analysis and optimization of materials and thicknesses in cylindrical geometry. It finds that a 32 cm thick blanket composed of Pb-filled pebbles and liquid Li-LiH, a 54 cm thick, solid neutron shield of some heavy metal hydride such as vanadium hydride, along with 1.3 m of concrete, will fulfill all the tritium breeding, shielding and heat extraction requirements. Most importantly, our pebble and liquid materials will be 2-3x more compact than traditional materials such as liquid alloys of Li-Pb, or the molten salt FLiBe. Also, at the location of our choice, natural lithium works as well as enriched lithium, but is 25x cheaper.

  • In the race to net heat (Q>1) and to more compact fusion reactors (thanks to HTS), we sometimes overlook pre-existing and new challenges. Pre-existing challenges include: (1) tritium breeding and heat extraction have not been demonstrated yet and (2) the heat flux and neutron flux are already extreme in planned fusion reactors, at the limit of what solid materials can withstand. New challenges include: (3) such conditions get even more extreme in compact reactors (where comparable heat and neutrons impinge on smaller surfaces); (4) HTS are very delicate and, under neutron bombardment, they lose superconductivity; (5) there are diminishing returns and eventually a trade-off in making the plasma very small, if the surrounding materials are not miniaturized accordingly. Addressing these 5 challenges and breaking such a trade-off requires innovative materials, and we found them.