Economically optimized design point of high-field stellarator power-plant

High temperature superconductors (HTSs) expand the design space of stellarator power-plants (PPs) toward high magnetic fields B, enabling compact major radii R. The present paper scans the space of B, R and other design parameters, finding solutions that are promising from a physics and engineering standpoint, while minimizing the capital cost of the PP and the levelized cost of fusion electricity. Similarly, it identifies minimum-cost design points for next-step burning plasma stellarator experiments of fusion gain 1<Q<10 . The study assumes advanced stellarator configurations of reduced aspect ratio, heated by neutral beam injection. Plasma-facing, flowing liquid metal (LM) walls protect it from high heat and neutron fluxes. The study relies on analytical first-principle calculations, and established zero-dimensional (0D) empirical scaling laws. Power flows are illustrated by Sankey diagrams. Plasma operating contours are used to determine the reactor’s start-up path. Sensitivity analyses are conducted to identify the most critical reactor parameters within physics, engineering and costing, quantifying their influence on the economics of the PPs. Such 0D study suggests that the assumed next generation HTS, flowing LM walls, and advances in compact plasma configurations could lead to an ignited stellarator PP of aspect ratio A∼4 , R⩽4  m, B > 9 T, and normalized plasma pressure β∼5% which would minimize both the cost of electricity and capital cost while achieving a net electric power of about 1 GW.


Introduction
Stellarators exhibit plasma confinement as good as tokamaks of comparable plasma size and magnetic field [1] and offer additional benefits such as steady state operation, no disruption and low recirculating power.They also present disadvantages, most notably their hard-to-build, non-planar coils [2].
At fields of about 5 T in the plasma, obtainable with low temperature superconductors, stellarator and Heliotron powerplants (PPs) are expected to have large major radii R, between 7 and 29 m [3,4].However, high temperature superconductors (HTSs) such as rare earth barium copper oxides (REBCOs) recently enabled the construction of large-bore planar, toroidal field coils generating 20 T at the coil and about 10 T at the plasma center, in steady state [5].If reproduced in stellarators, these field-strengths could significantly reduce the size and cost of stellarator PPs.Furthermore, developments are currently being made to create wide HTS tape which would enable novel coil architectures for stellarators [6,7].Moving from non-planar modular coils with intense toroidal excursions [8] toward complex current patterns engraved on wide HTS wound on simplified coil winding surfaces, enabling increased coverage and strong shaping of the plasma column with simplified magnet structures [6,7].These developments could allow for compact, high-field stellarators which echoes ongoing research on the optimization and development of novel compact advanced stellarator plasma configurations (low aspect ratio and major radius) [9][10][11].
Flowing liquid metal (LM) walls are another fusionenabling technology [12], synergistic with HTS: thick LMs shield HTS from neutrons and prevent crystal damage or loss of superconductivity; at the same time, strong fields stabilize LM flows and favor the adhesion of current-carrying LMs to tilted or even inverted solid substrates, thus enabling full coating and neutron-shielding of the vessel, and heat removal.LM walls enable increased wall loading constraints, which have been traditionally ∼10 MW m −2 for solid wall concepts [4,13] but could reach 25 MW m −2 or higher as described in recent first wall developments [14][15][16][17].Furthermore, flowing liquid walls intercept α particle losses, which can be significant in some stellarators.
Stellarator reactor sizing and costing studies were issued in the past [3,[18][19][20].The one presented in this paper explore the possible new opportunities offered by developments of wide patterned HTS tapes, thick LM flows and reduced aspect ratio plasma configurations.The study integrates plasma physics, engineering and PP economics calculations.This zero dimensional (0D) system analysis identifies economically viable high-field stellarator PPs and experiments,highlighting the need for continuing the technological developments on HTS, LMs, and compact plasma configurations for stellarators as well as offering a starting point for future 3D studies in a smaller parameter-space.
It also isolates trends, regions of interest in the design space and principal design parameters affecting the cost of the reactor and cost of electricity (COE).This will serve as a basis for further, 3D studies and refinements in a smaller parameter-space by system-design codes such as PROCESS [4,21], TREND [22], BLUEPRINT [23] or ASC [19].Due to the limits of 0D analyses and the technological assumptions, absolute estimates are therefore only indicative, but relative arguments are reliable, e.g. in cost-savings with field increase, reduced aspect ratio, improved confinement, etc.
The paper is organized as follows.Section 2 describes the 0D system analysis calculations as well as the major underlying assumptions.Section 3 illustrates how physical, engineering and economic parameters depend on the fieldstrength B and major radius R. In section 4, the design point is optimized for minimal reactor cost or electricity cost.In section 5, said costs are found to highly depend on the confinement re-normalization factor and on the aspect ratio, among others.Two specific PP case studies are examined in greater detail in section 6, under different assumptions on HTS unit costs.Details include a Sankey diagram of power flow, Plasma OPerating CONtours (POPCON), a discussion on helium ashes and cost breakdown.Section 7 is dedicated to experiments not producing net electricity but producing net heat, i.e. fusion gain Q > 1, investigating burning stellarator plasmas.

0D reactor system analysis
Figures 1 and 2 schematically illustrate the stellarator model and the optimization procedure to minimize the COE and capital cost of a stellarator PP.Here a stellarator design point is defined by the following reactor parameters (top of figure 2): the magnetic field on axis B, the plasma major radius R, the plasma aspect ratio A = R/a, with a the plasma minor radius, the volume-averaged plasma temperature T, the blanket thickness b, the normalized pressure β, and the re-normalization factor f ren assigned to a specific plasma configuration in the International Stellarator Scaling ISS04 [24].
From them other physics parameters, highlighted in pink in figure 2: the density (section 2.1), fusion power P fus , radiated power, diffused power (section 2.2) and energy confinement time section 2.3) are calculated.We then solve the steady-state power balance (equation ( 6) in section 2.4) with the externally injected heating power P aux required to sustain the fusion reaction.This yields the fusion gain Q = P fus /P aux .The information is combined with the power spent to operate various plant systems, ultimately yielding the thermal power and net electric power from the PP (sections 2.4 and 2.5), associated with the PP engineering block in figure 2.
Sections 2.6-2.9 feature well-established costing models for the PP and its subsystems, adapting them to the present study: the result is the total capital cost (TCC) of the PP, and section 2.10 leads to the COE estimate.These two quantities are then optimized (equation ( 23)), subject to constraints.This 0D model and the corresponding results, do not consider specific density, temperature profiles, nor 3D geometries of coil architectures and plasma configurations.It allows for high level promising design space identification under specific technological assumptions which will require refined 3D analyses.

Plasma density
We assumed a helium concentration f He = n He /n e = 5% similar to Alonso et al [25] and equal amounts of D and T: n D = n T = 0.45n e .The effects and implications of helium accumulation are discussed in section 6.3.The line-averaged electron density n e is computed from the normalized plasma pressure β = 2n e T B 2 /2µ 0 (1) and is compared to the line-averaged radiative density limit found in W7-AS [26] as: with C c a numerical constant set to 1.46 for a radiative density limit in units of 10 20 m −3 if power, volume and magnetic field are expressed in MW, m 3 and T, respectively.The stellarator design points were chosen such that the plasma density remains under the empirical radiative density limit as a conservative estimate for 0D calculations which do not take into account density profiles and edge impurities which seems to have a major effect on the density limit in stellarators.However, the proposed system codes allow for varying a prefactor for the radiative limit constraint λ n as the above empirical relation has been exceeded up to a factor of 3.5 in W7-X and LHD experiments [19,27,28].λ n could then be varied to correspond to specific plasma configurations and edge density profiles identified in future 3D analyses [27].

Power balance in the plasma
The steady state, simplified 0D plasma power balance can be described as: In this analysis, the deuterium-tritium (D-T) fusion reaction was considered and all the species in the plasma were assumed to have the same temperature T. The alpha heating and fusion power can be calculated as follows: with E n = 14.08 MeV and E α = 3.52 MeV being the neutron and alpha particle energies from the D-T reaction, n D and n T the line-averaged deuterium and tritium densities, ⟨σv⟩ D-T (T) the D-T fusion reaction reactivity, and V a the plasma volume.
The D-T fusion reaction reactivity was calculated using the parametric fit from Bosch et Hale [29], valid for temperatures between 0.2 and 100 keV.The plasma volume was estimated as V a = 2π 2 Ra 2 (figure 1).
The externally injected heating power P aux necessary to sustain the D-T fusion reaction was calculated from the steadystate power balance (equation (3)) written as: (6) with P h the net diffused power, P rad the Bremsstrahlung radiation power, P α the alpha particle heating power, and k α the alpha particle heating efficiency.The alpha particle heating efficiency was set to 90% as a conservative estimate, although recent work [11] suggest alpha particle heating efficiencies up to 99%.Synchrotron radiation losses were assumed negligible for the considered reactor design points in comparison with Bremsstrahlung radiation losses and diffused power as shown in other stellarator studies [19,25] for similar compact highfield considerations.Verification of the synchrotron losses for our selected design space using Trunikov's formulation [30] is conducted in sections 6 and 7.The Bremsstrahlung radiated power is: TV a (7) with Z eff the effective ion charge set to 1.1 for our analysis (consistently with the assumed 5% of He ashes), and C B a numerical constant set to 5.35 10 −3 for a Bremsstrahlung radiation power in units of MW if temperature and density are expressed in keV and 10 20 m −3 respectively.The net diffused power P h fulfills the following steady state power balance equation: where the total 0D internal plasma energy W, under our plasma composition assumption, is given by

Energy confinement
The energy confinement time τ e is taken from the ISS04 scaling (equation ( 5) in [24]): τ ISS04 E = f ren 0.134 a 2.28 R 0.64 P −0.61 h n 0.54 e B 0.84 ι 0.41 2/3 (10) with f ren the re-normalization factor and ι 2/3 the rotational transform at the r = 2a/3 magnetic surface.τ ISS04 E is provided in unit of s for n e expressed in 10 19 m −3 .The energy confinement time scaling can also be expressed in terms of A and β instead of n e and a: The optimal temperature T is dictated by the D-T fusion reactivity, and the maximum, yet safe β by equilibrium and stability limits, with a safety margin.Therefore, with good approximation, for fixed ι 2/3 , From equations ( 8) and ( 9) it is concluded that the triple product scales like the 4th power of B: In this study, advanced compact plasma configuration parameters with optimized neoclassical transport and alpha particle confinement were fixed and assumed to match ongoing developments [9] and past reactor studies [19,20,31,32].The re-normalization factor was set to f ren = 1.4 to match other stellarator reactor studies, recent developments and expectations for W7-X [19,20,31,32].The ι 2/3 was set to 0.9 to match HELIAS [18,33] and novel compact stellarator configurations [9].The normalized plasma pressure β was chosen to be 5%, as a conservative estimate similar to those obtained in LHD and HELIAS studies [3,18,19] although higher values were shown to be possible for NCSX-type plasmas [3,10,11].These optimistic plasma configuration parameters for low-aspect ratio will need to be further validated through 3D studies and plasma simulation codes [9].

Thermal power and net electric power
The net electric power produced by the PP is with η th the thermal plant efficiency and P th the gross thermal power generated by the fusion reactions and energy multiplication occurring in the blanket.P pump is the pumping power required to sustain the LM flow in the stellarator blanket and P cryo the required cryogenic system operating power.η aux and η pump denote the electric conversion efficiencies for the plasma heating and LM pumping systems.The thermal power can be calculated as the sum of the power from the neutrons, from lost α particles, from radiation and from diffusion, as all these contributions are captured by the LM plasma-facing wall.
The fraction of neutron-to-alpha fusion power is given by 8 and the neutron energy multiplication factor set to f m = 1.24 (consistently with our choice of fusion blanket described below [34] and with typical ranges of f m = 0.9-1.4,depending on the blanket configurations [25,[35][36][37].
The wall loading on the reactor blanket can then be calculated from the thermal power as: with S a the plasma facing surface, estimated using the equivalent toroidal surface S a = 4π 2 Ra, as shown in figure 1.This 0D model considers uniform wall loading and heat extraction through the LM wall as it does not include any 3D considerations such as separatrix, divertor locations, peak heat loads, or transient effects due to specific 3D plasma configurations.

Power consumption
The LM pumping power P pump was calculated from the total pressure drop in the LM loop ∆P loss and the volumetric flow rate Q LM .The volumetric flow rate was computed through the LM transit time in the plasma facing region required to heat the LM from a temperature T LM in to T LM out .These inlet and outlet temperatures were set to match the heat conversion system operating temperatures.As a 0D analysis simplified model, the LM mass flow rate through the plasma facing region can be calculated as: with c LM P the LM heat capacity, and ṁLM the LM mass flow rate.The volumetric flow rate can then be simply computed using the LM mass density ρ LM , as The total pressure drop from the LM loop was estimated as: ∆P loss = ∆P head + ∆P pipe + ∆P MHD (18) with ∆P head the gravitational head losses, ∆P pipe the pressure drop from viscous pipe flow, and ∆P MHD the pressure drop from the magneto-hydrodynamic (MHD) drag within the reactor [38].
The gravitational head losses were estimated as ∆P head = ρ LM gh, with h = 2(a + b) assuming LM flowing from the top to bottom of the plasma vessel (a the plasma minor radius, and b the LM blanket thickness).
The pressure drop from viscous pipe flow was estimated as pipe D pipe , with f D the Reynolds dependent Darcy friction factor, L pipe the total pipe length, D pipe the average pipe diameter and v pipe the mean LM velocity through the pipes.The mean LM velocity through the pipes was calculated so as to match the required LM mass flow rate (equation ( 17)) when accounting for the number of inlet pipes and pipe diameter.
The pressure drop from MHD effects was estimated as ∆P MHD = kσ LM B 2 v LM L MHD , with σ LM the LM electrical conductivity, v LM the LM velocity and k the MHD drag coefficient [38].
The total electric power required to run the cryogenic plant P cryo can be estimated from P th , following the EU-DEMO studies [39][40][41] and the TREND systems code [22], as: with f cryo the cryogenic power fraction, previously estimated in the range of 0.8%-1.3%for fusion reactors with P th = 2.3-2.4GW.The value of f cryo = 1.3% was chosen conservatively for this study, and could be further refined with a cryoplant design model.The balance of plant system efficiencies described in equation ( 14), LM composition, and operating temperatures were held fixed in the design exploration study.The thermal plant efficiency was set to η th = 0.49 assuming a combined Brayton cycle with LM temperatures set to T LM in = 700 • C to T LM out = 900 • C [42][43][44].The LM pump efficiency was set to η pump = 0.20 to reflect current electromagnetic pump technologies [45][46][47].The conceptual blanket is composed of a 33 cm LM layer flowing on the LM vessel (5 cm), followed by a 50 cm neutronic shielding layer (vanadium hydride VH 2 ) before the stellarator coils [34].The LM layer is composed of a 15 cm thick moderator/multiplier layer of Lead, and a 18 cm tritium breeding layer of non-enriched lithiumlithium hydride chosen to be f Li = 5% lithium and f LiH = 95% lithium hydride [34].The flowing LM blanket was selected for radiation protection, tritium breeding, and heat extraction considerations [15,34].Heat extraction was assumed to be carried out by the flowing LM layer (Li-LiH) and the LM characteristics (mass density, heat capacity, conductivity and kinematic viscosity) were calculated from published temperature dependent properties [48][49][50][51].This assumed highly compact radial build proposed by Renaissance Fusion [6,34] follows ongoing development toward compact radial build blankets [52,53].
Using equations ( 14)-( 19) and the plasma power characteristics from section 2.2, the PP steady state net electric power, P e , can thus be calculated from the reactor parameters B, R, T, β, b, A, f ren as shown in figure 2.

Reactor cost model
The cost model developed in this study is based on the ARIES Cost Structure (ACS) [54,55] similar to other stellarator studies [19,56].The ACS cost model was updated for specific reactor characteristics and components, such as the HTS magnets and flowing LM blanket.All costs are presented in 2021 dollars translated from the 2009, 2004 and 1992 dollars cost values included in the ACS cost model.The developed cost model is used to calculate both the capital costs of the major PP components as well as the COE.It should be emphasized that the focus of such cost models is the variation in the COE, rather than its absolute value.
The cost accounts used to calculate the PP total capital cost (TCC) are listed in table 1.The PP TCC can then be computed as the sum of the direct and indirect capital costs (items 90-98), with the total direct capital cost (TDC) calculated as the sum of cost accounts 20-27.The indirect costs are calculated as fractions of the TDCs for construction services and equipment, home office engineering and services, field office engineering and services, the owner's cost, process contingency, project contingency, and interest and escalation in cost during construction.A detailed description of these costs is provided in [54], including cost scalings with reactor's parameters, components power, mass or volume.In general, the cost accounts have a multi-level structure that includes subaccounts for which the costs are evaluated as c i • (X i ) ei , where c i is the unit cost for the sub-level account i (given in $ kg −1 , $ W −1 , $ m −3 , etc), X i is the quantity to which the cost is proportional to (mass, power, volume etc) and e i is an exponent [54,57].
The cost account 22.1 in table 1, which includes the reactor's blanket, was updated to reflect the flowing LM wall

HTS cost model
The magnets' cost sub-account 22.2.1 for plasma confinement was also updated to reflect the use of ReBCO HTS material.As a simplified 0D model, considering the engraved current pattern HTS coil architecture [6,7], the peak magnetic field B peak in the coils was calculated from the on-axis magnetic field and the reactors parameters following the 1/R dependence of toroidal fields [36,58] The study considered k peak = 1 instead of conventional peaking factors k peak ⩾ 1 linked to modular non planar stellarator coils with large toroidal excursions [8,19,20], due to the assumed patterned wide HTS coil architecture combined with current developments of coil winding surface optimization which have been shown to allow for reduced magnetic field peaking factors [7,59].Appendix A investigates increased peaking factors k peak = 1, 1.2, and 1.5 as seen in modular nonplanar stellarator coils.
From the B peak at the coils, the HTS tape critical current density J c was evaluated from the parametric relationships that describe the dependency of ReBCO HTS tape critical current density based on the magnetic field, temperature and field angle [60][61][62][63][64].In this study we assumed a field angle of 0 • .Note that this is a pessimistic assumption, corresponding to having the magnetic field perpendicular to the tape.In reality, accurate stellarator fields in the plasma volume require the field to be tangential to the plasma boundary and, by extension, to a close-fitting Coil Winding Surface.Therefore, the field will typically be parallel to properly wound tapes.
We also assumed an operating temperature of 20 K, and a ReBCO 2G HTS tape from SuperPower Inc. (Glenville, USA) which provided the following critical current dependency on the peak magnetic field: (21) with J c in A m −2 .This parametric relation is valid for B peak between 1 and 20 T, and was derived from a 4 mm tape with a 1.6 µm thick ReBCO layer.
We used 12 mm ReBCO tapes for the cost calculations, with a total thickness of 0.1 mm, and a 1.6 µm thick ReBCO layer.The number of layers of HTS tapes was then derived from the required current to generate the peak magnetic field B peak and the critical current density, assuming HTS tapes operating at 75% of the critical current density value (critical current safety factor SF Jc ≃ 1.33) for quench protection.The total length of HTS tape L HTS was then computed from the reactor geometry and required number of HTS layers.Two HTS tape unit costs were considered in the study; an optimistic bulk cost of 12 $ m −1 (or 30 $ kAm −1 ) that assumes further cost reductions due to the increasing development of HTS manufacturing technologies and a conservative unit cost of 78 $ m −1 (or 200 $ kAm −1 ) reflecting the current cost of HTS tapes [64,65].The tape cost was finally calculated from L HTS and the unit cost.

Heating
The externally injected fusion heating system, part of cost account 22.3 (plasma formation and sustainment), was assumed to be a negative neutral beam injection (NNBI) from its high neutralization efficiency (above 60%) compared to positive ion beams for beam energies above 100 keV [66].NNBI is a relatively mature technology capable of efficiently (30%-60%) heating the high-density, high-field plasmas required for compact fusion devices [67][68][69].A single heating system was considered in this analysis for simplification although electron cyclotron heating (ECH) could also be used in conjunction with NNBI, provided that gyrotrons of sufficiently high power and frequency can be developed to operate in high magnetic field environments (10 T and above) [70].Other heating systems such as ion cyclotron heating (ICH), heating by lower hybrid (LH) waves, or helicon heating were not considered due to the complex plasma boundary shape of stellarators, the reduced need for current drive, or their lower technology readiness level [8,19,71,72].
For each reactor design point, the required beam energy level was estimated primarily based on the average plasma density and reactor geometry.The requirement was set for the beam to deposit 95% of its energy by charge exchange, proton collisions, and electron collisions after traveling a distance of 3a/2 in the plasma core.For this calculation, the plasma was assumed to have an elongation of 4, leading to a reduced beam penetration distance for an adequately positioned NNBI system injection port.The NNBI system's beam energy requirement is further described in the high-field stellarator case study (section 6).The auxiliary heating system's unit cost was assumed at 6.23 $ W −1 , based on other reactor studies [19,54,56].
Note that most PPs in this study are ignited and, as it will be shown in section 6.2, the heating can be turned off within a minute of initiating the plasma discharge.A shortpulse heating system will certainly be less expensive than a steady-state one, but these cost-savings are not estimated here.Considerations on how often the heating system needs to be turned on again during a plasma pulse, e.g. for control purposes, are also left as future work.

Structure and support
The primary structure and supports, cost account 22.5, was also updated for the use of 316LN-IG stainless steel for the plasma confinement magnet's support structure and Hastelloy C-276 for the vacuum vessel.The materials choices were motivated by their mechanical, neutronics and corrosion resistant characteristics as well as their use in other fusion experimental reactors [73,74] and reactor studies [19,42,54,56].A maximum allowable stress of 750 MPa was used for 316LN-IG stainless steel under 20 K and a maximum allowable stress of 790 MPa was used for Hastelloy C-276 [73,75,76].The structural materials mass densities and unit costs are summarized in table 2.
The magnet support structure was sized using a thickwalled cylindrical pressure vessel model [77] using the peak magnetic field to compute the resulting Lorentz force.The structure thickness was determined with a safety factor of 2.0 on the maximum allowed stress, as a conservative limit.The sizing calculation was verified against the virial theorem limit [78] and the empirical scaling from Warmer [79], which is based on superconducting devices such as W7-X, LHD and ITER: M struc = 1.3483W 0.7821 mag , with M struc the total structure mass expressed in t, and W mag the magnetic energy in MJ.
From the magnet support structure sizing, the reactor radial build inboard clearance r inboard is then calculated to ensure a minimum space on the reactor inboard side for structures and shielding.The 0D system code enforces an inboard clearance positive constraint meaning that the radial buildup from the magnet and structure thicknesses, blanket size, vacuum vessel size, plasma minor radius is smaller than the plasma major radius.Additional constraints could also be applied when considering specific coil architecture, for instance discrete nonplanar modular coils which would require a large minimum inboard clearance [19,20].

COE
The COE is calculated as: where C AC is the annual capital cost charge (TCC multiplied by the fixed charge tate (FCR)), C OM the annual operations and maintenance cost, C SCR the annual scheduled component replacement cost, and C F the annual fuel cost.In this equation, the annual costs are given in $ for a COE given in $ MWh −1 .FCR is a charge to the TCC annualized over the operating life of the plant: here it is set to 0.043, assuming a reactor lifetime of 40 years, a discount rate of 3% that reflects the 2021 low interest rates [80][81][82][83][84][85][86], and the Gen-IV guidance on simplified FCR values [54].A broader range of discount rates, up to 7%, will be considered in Sec 4.2. to understand their effect on the COE [83].y is the assumed escalation rate, chosen as 5% to reflect the current inflation rates [82,87,88] and Y the construction time, set to 6 years.The C AC is given as 101 • (P e /1.2) 0.5 in [M$ 2021] with P e in units of GW [54].
The fuel cost was calculated based on P fus assuming a unit cost of deuterium of 13.4 k$ kg −1 [89,90].The cost of tritium is not included in the annual fuel cost as it will be bred from the blanket and conditioned through a dedicated tritium plant (cost account 22.8).
The C SCR considers the expenses of replacing plasmafacing components or equipment subject to radiation damage.The lifetime of these components are estimated when radiation damage reaches 200 dpa (displacement per atom) in the materials for a given neutron wall loading power [15,34,42].Our chosen LM blanket would not exceed 3-5 dpa yr −1 on the blanket backing solid wall for the considered fusion PP solutions.These components would thus not require replacements over the plant's lifetime, leading to negligible C SCR relative to over cost accounts [15,34].
The C DD represents the decontamination and decommissioning allowance estimated at 3.49 M$ yr −1 following the ACS model [54].The plant capacity factor f avail was set to 85% similar to other reactor studies [54].For reference, the TCC of the PP generally accounts for more than 75% of the COE [19,42,56,89]

Exploration of (B, R) design space
In this section we apply the 0D stellarator system analysis of section 2 across the (B, R) stellarator design space for fixed T = 10 keV, β = 5%, f ren = 1.4,blanket thickness b = 83 cm (consisting of 15 cm of Pb, 18 cm of Li-LiH and 50 cm of VH 2 ) and for two values of A (3 and 9).Other combinations of T, β, b, A, f ren were considered and not shown for brevity but highlighted in the remainder of the paper.
For each B, R pair we calculated the density n e needed to achieve the target T and β.We then computed the resulting energy confinement time, triple product and peak magnetic field at the coils.The results of this physics analysis are plotted in figures 3 and 4. Likewise, powers relevant to the engineering analysis are contoured in figures 5 and 6 and costs from the economic analysis are plotted in figures 7 and 8.
In all contours, different color-scales are adopted for quantities to be maximized or minimized: respectively shades of blue and red, with lighter shades indicating preferred values.'Boxes' around the color-scales highlight the targeted ranges.Solid lines mark essential limits (for instance the triple product for break-even).In other cases there was some degree of arbitrariness, so those values were marked as desirable and boxed with a dashed line.
These hard, essential limits and the somewhat softer, desirable limits, as well as the radiative density limit from equation (2) (orange curve in figures 3(a) and (e)) define regions of interest in (B, R) where operation is possible, or at least preferable, from a physical, engineering and economic point of view.Such regions are highlighted respectively in green in figure 4, in brown in figure 6 and in blue in figure 8. Two shades of green are used because the desirable value τ E = 2 s can only be obtained for A = 3, hence a relaxed τ E = 1 s is also considered.

Physics parameters exploration
Per figure 4, physics operation is bound by τ E and by the radiative density limit.For A = 3, it is also bound by the limits on the maximum B peak and minimum n e (figure 4(a)).The essential limit is on n e Tτ E , but T is fixed and soft limits are imposed on n e and τ E to 'share the weight' in how they contribute to high triple products.The radiative limit density having been exceeded in some specific cases [27], the threshold of twice the radiative limit is also shown highlighting a larger design space (figure 3(a)).For A = 9, instead, physics operation can also be limited by impractically large R, as expected, and large B (figure 4(b)).

Power parameters exploration
Figure 6 shows that power engineering is upper-limited by manageable values of wall load P WL and radiated power P rad .The high P WL = 25 MW m −2 is not achievable with solid plasma-facing components [94,95], but can be easily removed by fast-flowing LM walls [12,15].At the lower boundary, the region of interest is limited by the minimal Q [25,[96][97][98], P fus and P e , and maximum P max aux .The latter quantity will be discussed below but, in brief, it denotes the maximum auxiliary heating power to be administered to the plasma at any time ('saddle point' in the POPCON analysis described in section 6) in its start-up and ramp-up toward steady state operation.While most PPs in the present paper are ignited and P aux can eventually be turned off, the heating system must be capable of P max aux , and excessive values of P max aux are deemed impractical.The Q, P fus , P e and P max aux limits are all close to each other in the A = 3 case.For A = 9, the most stringent limit comes from P max aux .The effect of A on P fus and P rad in figure 5 is easily understood from their increase with the plasma volume V a ∝ R 3 /A 2 , assuming the same n e and T. Most of the power characteristics are linearly related to V a meaning that, for fixed T and B, the same value of V a , thus P fus for example, could be achieved in a device with a major radius ∼2.1 times smaller when considering A = 3 instead of A = 9.Similarly, design points of which can be derived from equations ( 1) and ( 5) assuming constant values of P fus , T, A, and β.This relationship emphasizes that high-field magnet technologies can enable more compact stellarator devices.

Economics exploration
Figure 8 highlights that PP's economics are mostly bound by the COE and the PP's capital cost TCC.There is a trade-off between low COE and low TCC (figure 7).The region of economic interest is defined to include design points with COE ⩽ 50 $ MWh −1 , and TCC ⩽ of 7.0 $B.The COE threshold was chosen to be competitive with renewable [83][84][85][86]99] and the TCC threshold was chosen to represent the lower end of clean baseload electric plant technologies (such as nuclear fission plants) [83][84][85][86]100] in order to allow some margin and account for our cost model uncertainties.This cost exploration highlights that lower aspect ratio (A = 3) devices enable reduced TCC for similar COE values, and a wider range of reactors within the region of interest compared to higher aspect ratio devices (A = 9).In addition, the design space exploration for A = 3 (figure 8(a)) highlights that there is a region of B ≃ 8 T and R ≃ 4 T that would minimize both the COE and TCC for fixed value of A = 3 and T = 10 keV.Within the regions of potential reactor design points, the design space exploration scan also shows that decreasing R for a constant B results in design points with increased COE but decreased TCC and C OM .There is a trade-off between low COE and high TCC fusion PP designs.This initial design space exploration for fixed A and T suggests that there is a specific set of reactor parameters (B, R, T, A) that could minimize both the COE and the TCC.

Reactor design point optimization
Using the 0D stellarator system analysis described in sections 2.2-2.6, the reactor parameters (B, R, T, A) were optimized to minimize the COE and TCC, for chosen plasma parameters (fixed f ren , ι 2/3 , and β values) under a set of physics and engineering constraints (figure 2).The reactor parameters were varied from 5 to 15 T for the onaxis magnetic field, B; from 1 to 9 m for the major radius, R; from 5 to 15 keV for the plasma temperature, T; and 3 to 10 for the reactor aspect ratio, A. Peak magnetic fields at the coils, B peak , was constrained to remain under 20 T to reflect current HTS conductors performance [91][92][93].The B peak limit is not a hard limit but mostly indicative as even higher magnetic fields have been achieved with HTS (higher than 40 T in small devices [101,102]) and it is not excluded that it could be reproduced within a stellarator.The density limit is not an absolute limit neither but linked to experimental results and λ n = 1 was chosen to be conservative although higher density limit have been achieved in specific configurations [27].In addition, an inboard clearance constraint on r inboard was defined in order to allow for increased margin, plausible physical model and engineering basics.The stellarator parameters multi-objective constrained optimization was conducted in Python using a non-dominated sorting genetic algorithm [103].The resulting solution was a set of Pareto optimal design points with respect to the COE and TCC.

Minimizing COE and TCC
Optimal designs in terms of both COE, and TCC, obtained for varying reactor parameters (B, R, T, A) are presented below (figure 10).
The COE, TCC, and output grid power P e of the Pareto optimal PP design points are shown in figure 10.There is a trade-off between large PPs that minimize the COE and compact PPs that minimize the TCC (figure 10).Large fusion plants benefit from economies of scales, with increased net electricity output which reduces the COE (see equation (22)).On the contrary PPs of smaller size require reduced volume of materials (such as HTS, structural and blanket material) and operate at lower powers which reduces the TCC (section 2.6).
A design point lying in the region of low capital cost (C 22 ) and high COE is an attractive first of a kind (FOAK) PP (figure 10 B, R, T, A) along with several PP characteristics are shown here.Each marker represents an optimal reactor resulting from the fusion PP cost optimization (section 4.1).Red markers represent the design points that achieve ignition (Q = ∞) and blue markers the ones with finite fusion gains.For the the electron density plot, markers with light red and light blue colors represent the corresponding radiative density limit for each reactor design point.at 47.5 $ MWh −1 for a TCC around 5 B$.A more in depth analysis and description of such a reactor is carried out in section 6.
To further understand the family of Pareto cost optimal reactors, the reactor parameters and reactor characteristics are shown in figure 10.Each marker represents a Pareto optimal reactor (shown in figure 10).The markers colored in red describe ignited plasmas (P aux = 0) and in blue non-ignited plasmas (P aux > 0).Minimizing the TCC of the PP corresponds to reducing both A and R, resulting in a more compact device of lower B and T.These highly compact reactors (R < 4 m, with A = 3) would minimize the TCC needed to provide net electric power.However, they operate close to the radiative plasma density limit, and require increased steady state P aux as they do not reach ignition.B peak within all the reactors in the Pareto front seems to be insensitive to the size of the device with values between 16 and 20 T, below the optimization constraint of 20 T. Compact reactors operate at lower T, with reduced on-axis magnetic field.The reduced T compared to the optimal 14 keV for fusion power production can be linked to maintaining high plasma density n and energy confinement time τ E , under an assumed constant β (equation ( 1)), resulting in reduced auxiliary heating power P aux and increased electric output.
Although our analysis only provides a high-level 0D outlook on the potential of compact high-field stellarators within the limits of the technological assumptions, the result of the cost minimization (figure 10) was overlaid with current electric plant technologies in figure 11 from published annual world energy outlook data [83-86, 99, 100].To account for the uncertainty of the financial landscape and varying economics per country, the cost minimization results for the stellarator PP are also provided assuming a discount rate of r = 7% [83,84].
Showing the TCC per watt of the stellarator reactor designs with the corresponding COE (figure 11), we can further notice that there is diminishing returns with plants producing more than 2-3 GWe as the TCC per watt and COE reach asymptotic values around 3 $ W −1 and 25 $ MWh −1 .In addition, targeting plants around 1 GWe would allow for a competitive COE with standard renewable energies (solar, hydro, wind, . ..) while providing a TCC per watt below existing nuclear fission electric plants.
A discount rate of r = 7%, would increase the COE and TCC per watt of a stellarator based electric PP, however reactor designs around 1 GWe would still remaining competitive with the upper range of standard renewable electric plants.This is even more so as stellarator based plants would provide firm, base-load electric power unlike traditional renewables without energy storage.Taking into account the reduced capacity factor of standard renewable energy [85] and the current high cost of energy storage, a net-zero carbon electric grid without firm base-load clean power, such as stellarator fusion plants, would require up to five times the installed capacity and 50% increased electricity cost [104,105].

Reactor economics sensitivities
The sensitivity analysis described here identifies the reactors parameters with the highest effect on PPs economics, and highlights target values for future research developments that would allow for the realization of cost-effective stellarator PPs.
To investigate the effects of the reactor configuration, and model assumptions on the PP economics; f ren , β, k α , f He , f m , b, η th , η aux , auxiliary heating system unit cost and HTS unit costs were systematically varied before conducting the costoptimization calculation described in section 4.1.Similarly, the effects of the reactor's geometry on the system's economics were explored by conducting the cost-optimization with varying fixed/constant values of R, A, T, B, and the B peak constraint.For each of these sensitivity analyses, the effects on the reactor economics (figures 12-14) were recorded through the minimum achievable COE or minimum achievable TCC from the Pareto front curve (figure 10).

Sensitivity to plasma confinement parameters
The parameter f ren was varied between 1.0 and 2.6 to reflect the wide range of current stellarator configurations such as W-7AS and W7-X [24,31,106] as well as potential future optimized configurations [3,19,32,56,107].Increasing f ren has a positive effect on the reactor's economics, mostly on the minimum TCC.Increasing f ren increases the τ ISS04 E in the reactor leading to a reduction of the required auxiliary heating power system which reduces the reactor cost.However there are diminishing effects on the reactor's economics after f ren exceeds 1.6-2.0.The minimum COE has less sensitivity towards f ren as reactors that achieve minimum COE tend to be large reactors with relatively lower peak auxiliary heating power system cost.
β was varied between 2% and 8% to represent the variety of stellarator configurations [3,33,107,108].β has a major impact on the minimum COE design points, with increasing β decreasing the minimum COE.We also notice limited reductions in the minimum COE with β values above 4%-6%.The effects on the minimum TCC from varying β values differ depending on the configuration's re-normalization factor f ren .For f ren < 1.8, increasing β increases the minimum TCC as it increases n e and the required auxiliary heating system power leading to increased capital cost.For f ren > 1.8, β has little effect on the minimum TCC as for increased f ren values the required auxiliary heating system power is reduced leading to minimal cost increase.
The reactor design point cost-optimization was carried out with fixed values of R chosen between 3 and 8 m.In this case, the cost-optimization algorithm only varied B, A, and T in order to minimize the reactor's TCC and COE.This sensitivity analysis confirmed that low R reactors were favorable for reducing the TCC of fusion devices as shown in previous studies [91,109].In addition, there appears to be diminishing effects on the minimum TCC R ⩽ 6 m.It also shows that thanks to the increased allowable B by HTS materials, low COE reactors would not need to exceed 5-6 m in major radius.The reactor design point cost-optimization was carried out with fixed values of A chosen between 2 and 10.Similarly to the R parameter sensitivity analysis results, reducing A (compact reactors) has a significant impact on lowering TCC.Interestingly, the minimum TCC was most sensitive to changes in A than R.This could be explained from the fact that reducing A increases a relative to R, increasing the plasma volume at fixed R, making the reactor more compact and cost effective.There also appears to be diminishing returns from reducing the compactness of the reactor with A ⩽ 4. A has a lower impact on the COE except for a A < 3 as it reduces the allowable B due to the B peak constraint (equation ( 20)), and thus the resulting P fus .
The reactor design point cost-optimization was carried out with fixed values of T chosen between 7 and 14 keV.Increasing T leads to increased minimum TCC but lower minimum COE.Increasing T results in increased n e and B. This increases P fus and P aux , both of which lead to higher TCC.On the contrary, for large reactors that have low COE, the increased P fus increases the power density of the reactor, thus reduces the COE.
The reactor design point cost-optimization was carried out with fixed values of B chosen between 5 to 15 T. Increasing B results in lower COE devices as it increases P fus for fixed reactor size, thus the power density of the reactor.For the minimum TCC, increased B values leads to decreased TCC as it allows for more compact reactors for similar P fus .However, for B > 10 T, due to the B peak constraint of 20 T, it leads to larger reactors or larger A values causing the minimum TCC to increase.This means that for a given blanket thickness size, there is a range of B values, between 7 and 10 T, that minimizes the reactor's TCC.The reactor design point cost-optimization was carried out with fixed values of peak coil magnetic field B peak chosen between 10 and 20 T. For both the COE and TCC, decreasing the allowable B peak leads to increased COE and TCC reactors.However, the sensitivities toward B peak of the reactor's economics are low due to competing economic effects; reducing B peak reduces P fus and power density of the reactor causing the cost to increase but it also reduces the required amount of HTS material and support structure, causing the overall cost to decrease.Allowing for increased B peak enables more compact reactors that are less capital intensive and faster to build.

Sensitivity to alpha particle parameters
alpha heating efficiency k α was investigated for values between 80% and 98% [11] (figure 13).Increasing k α has little effect on the reactor's economics (TCC and COE).For plasma configurations that achieve f ren ⩾ 1.2, k α values of 80%-90%, currently assumed by stellarator system studies and existing plasma configurations [11], seem to be high enough to enable both compact high-field reactors with low TCC and large scale PPs with low COE.The small increase in TCC for low value of k α stems from the reduced alpha particles self-heating and increased auxiliary heating.
The helium ash fraction f He was varied from 1% to 10% to reflect the possible ash accumulation in the reactor core depending on the alpha particle confinement times in stellarators [110].Additional analysis regarding helium ash accumulation and f He is presented in section 6.3.Increasing f He increases the minimum TCC, as it decreases the reaction fuel densities, reducing P fus , and increases P rad leading to increased auxiliary heating and reduced P e .

Sensitivity to PP parameters and efficiencies
The blanket thickness b was varied from 60 to 140 cm to reflect the different fusion blanket configurations [15,19,20,56,111,112] (figure 14).b has a significant impact on the minimum TCC and COE as increasing b reduces how compact the reactor can be.In addition, increasing b requires increased B peak , thus increased magnet costs as the coils are further away from the plasma they need to confine.There are reducing improvements when b ∼ 60 cm, as smaller b also increases the required volumetric flow rate and P pump for extracting P th .This is especially the case for COE as the increased P pump leads to reduced P e .In addition, further reducing b will increase the neutron damage to the reactor core components leading to increased maintenance and replacement cost.
The energy multiplication factor f m , stemming from the tritium breeding reactions in the blanket, was varied from 1.0 to 1.5 to represent the range of potential blanket configuration choice [15,111,113,114].f m has a low effect on both the TCC and COE, as there are competing effects from increasing f m .On the one hand, it increases P e as it increases P th extracted by the flowing blanket.On the other hand, it increases the heat load on the blanket requiring increased P pump and P cryo , as well as the size of the turbine and heat rejection plant.Nonetheless, increasing the f m from 1.24 to 1.5 for the stellarator design point described in section 6, would still decrease the TDC cost per watt from 2.8 $ W −1 to 2.5 $ W −1 (TCC cost per watt from 5.1 to 4.8 $ W −1 ), and the COE from 47.7 to 44.3 $ MWh −1 , while increasing the TCC from 5.0 to 5.4 B$.
The thermal plant efficiency η th was varied from 35% to 70% to represent the current and possible improvements in thermal plant such as multi-stage improved Brayton or Rankine cycles, as well as the different operating temperatures [20,42,43,115].Increasing η th has a major impact on reducing the COE, as it increases P e for the same P fus .However, increasing η th could come from increasing the flowing LM blanket operating temperatures which would have a significant impact on the piping and cooling system constraints based on material limitations but also on the risk of increasing the plasma impurities from metal vapors produced by the increased evaporation rates [14].
The auxiliary heating system efficiency η aux was varied from 25% to 70%, and the auxiliary system unit cost between 2 to 7 $ W −1 to reflect the wide range of heating system technologies (PNBI, NNBI, electron cyclotron resonant heating (ECRH) and ion cyclotron resonant heating (ICRH)) and possible future developments [67][68][69].η aux had little effect on the reactor's economics as the reactors considered here achieve high Q values leading to small required heating power during steady state operation and thus a low impact on P e .However, the auxiliary system unit cost has a major impact on the minimum TCC, as reactors achieving the minimum TCC are compact reactors that require increased auxiliary heating power and thus high auxiliary heating system cost (figure 10).
The HTS unit cost was varied from 4 $ m −1 to 78 $ m −1 (corresponding to 10 $ kAm −1 and 200 $ kAm −1 for typical critical currents at the field and temperature of interest here) to reflect the current cost of HTS tapes and possible future cost reductions [64,65,91].The HTS unit cost impacts both the minimum TCC and COE values.The minimum TCC and COE are linearly correlated to the HTS unit cost which is mostly due to the linear relation between the magnet capital cost and HTS unit cost.To achieve reactor design points that result in a TCC below 6 B$ and a COE below 50 $ MWh −1 , the HTS unit cost should be decreased under 20 $ m −1 (50 $ kAm −1 for a 12 mm wide tape).

PP operations and cost
Two cost optimal high-field stellarators, Chartreuse P1 and Chartreuse P2, were designed to minimize the COE and TCC (section 4.1), with respective HTS unit cost of 12 $ m −1 (30 $ kAm −1 ) and 78 $ m −1 (200 $ kAm −1 ).The reactor parameters for Chartreuse P1 and P2 are shown in table 3.These reactors were selected from the 'elbow' of the Pareto front curve shown in figures 10(a) and (b).Both reactors are compact high-field stellarators with an estimated net electric output of 1 GW.
A detailed analysis of Chartreuse P1 was then conducted using the 0D system analysis (section 2) to understand the power flow through the reactor (figure 15), the reactor start up path using the POPCON analysis (figure 16), the helium ash exhaust (figures 17 and 18), and a cost break down of the PP cost accounts (figure 19).

Power flow through the plant
From the plasma and plant power balance of the Chartreuse P1 stellarator reactor (table 3), a Sankey diagram (figure 15) was constructed to show how the generated fusion power is used for self-heating, extracted for thermal-to-electricity conversion and re-circulated to power the reactor auxiliary systems such as cryogenic and pumping.The power flow diagram shown in figure 15 refers to steady state, for which the plasma has reached ignition and the auxiliary system power has been turned off.
For both P1 and P2, the radiative density limit constraint was not active and the electron density for both cases remained at respectively 65% and 54% of the density limit.Increasing the density at constant β and B, would lead the T to decrease, causing the Bremsstrahlung radiation to increase, fusion power and net electric power to decrease.For this 0D analysis, the synchrotron radiation loss were not considered as a first order effect compared to other power losses.Using Trubnikov's synchrotron power loss estimates [30,116], approximately 6 MW would be loss through synchrotron radiation compared to 48 MW of Bremsstrahlung radiation, and 245 MW of diffused power.The synchrotron power loss is accounting for larger fraction of the total power loss compared to other stellarator studies [19] but remains below 2% of the Bremsstrahlung and diffused power losses.
The overall PP efficiency defined as η PP = P e /P fus is equal to η PP = 57% for Chartreuse P1.This overall optimistic PP efficiency results from the simplifications that were carried out in the 0D system analysis, which did not account for the electric power consumption of a series of auxiliary systems such as the tritium plant, power supplies for the magnet systems, additional coolant pumps, or vacuum pumps.These additional internal electric power requirements could amount up to 320 MW [19-21, 37, 42, 56, 115] reducing P e to 0.7 GW and the plant efficiency to η PP = 39%, similar to other reactors studies [19,56,115].The reduction in P e would increase the COE to 71 $ MWh −1 and the TDC cost per watt to 4.2 $ W −1 and TCC cost per watt to 7.6 $ W −1 .

Operating point and start-up path
Figure 16 shows the POPCON plot that represents the auxiliary (non-α) heating power P aux to sustain a plasma of given density and temperature.The steady state operation point is located beyond the ignition contour (P aux = 0) and shown with a red marker.
The radiative density limit described in equation ( 2) is shown with a yellow line.The thermally unstable regions defined as ∂Paux ∂T | ne < 0 are regions of the (n e , T) plane in which feedback control of the heating source is required [25,117].The start up path was chosen to minimize the peak heating power and time to reach the steady state operation point while remaining below the stellarator radiative density limit.This path usually referred to as the Cordey path is shown in green in figure 16 and goes through the saddle point shown as a purple marker.The auxiliary heating power at the saddle point represents the peak auxiliary power P max aux required during the operation of the reactor.P max aux was used to size the NNBI auxiliary heating system P sys aux .P sys aux has to exceed P max aux in order to reach the operation point through the start up path.The larger P sys aux , the faster the plasma can be heated to the operation point.Using a auxiliary heating system of P sys aux = 1.05 • P max aux , or P sys aux = 27.1 MW, the startup time to reach the steady state operation point, calculated from the equilibrium contours [117] would be τ start = 40 s.Although time-dependent simulations of the reactor start-up have been shown to increase τ start or P aux , time-dependent simulations tend to converge to the equilibrium contours analysis in cases where P sys aux /P max aux ∼ 1 [117].The reactor start-up time τ start also provides insight on the reactor's physics time constant at which the reactor's power output can be modulated to match the grid power demand (barring the time constants of the remaining sub-systems such as the HTS magnet or heat conversion plant).

Helium ash accumulation f He
The accumulation of helium ashes in the plasma can deteriorate the reactor's P fus and increase P aux as it dilutes the D-T fuel and enhances Bremsstrahlung losses [19,110,118].f He was systematically varied from 2% to 10% for the selected reactor design point (P1, table 3), and the changes in P e , COE and required steady state P aux were recorded in figure 17.
Increasing f He , reduces P e , and increases P aux and COE.Similar to other studies, to maximize the economics and P e , f He should be minimized.With increasing f He for constant density operations, the reacting fuel density decreases which reduces the P fus and thus P e .In addition, the increase in f He leads to an increase in P rad which increases P aux leading to further reduction of P e .For Chartreuse P1, the auxiliary system was sized for a peak power during operation of 27.1 MW, meaning that f He should remain under 8.7% in order for the fusion reaction to be sustained, and under 6.6% for the P aux to be almost zero during steady state operations.
The helium ash accumulation in the plasma is modeled by carrying a particle evolution analysis assuming fusion reactions as the only source of helium particles.In addition, the alpha particle confinement time τ * He is assumed to be correlated to the energy confinement time τ E such that τ * He ≃ f τ • τ E [19,25,110,118,119].Under these assumptions, the helium density fraction evolution equation can be described as: df He dt = For P1, the helium ash accumulation analysis was conducted for ratios of f τ ≃ τ * He /τ E varied between 1 and 7 to represent experimental and theoretical predictions [25,110,119].For each case, the helium ash fraction time variations were recorded in figure 18.
To achieve f He ≃ 5% in the Chartreuse P1 reactor, the helium particles confinement time should be τ * He ≃ 4.0 τ E .Increased values of τ * He led to increased f He values which could be detrimental to the reactor's operation and output power.As shown in figure 17, for Chartreuse P1, f He should not reach values above 6.6% to maintain plasma ignited conditions leading to a maximum helium particles confinement time of τ * He ≃ 5.7 τ E , unless active helium ash removal systems are implemented [120].
The helium ash analysis presented here was conducted to understand the effects on the reactor's performance.More refined simulations should be carried out based on transport simulations, in order to accurately calculate τ * He and f He .

Chartreuse P cost breakdown
To further understand the economics and costing of Chartreuse P1, breakdowns of the reactor's TDC main cost accounts (table 1) and the reactor core equipment's (C 22 ) sub-accounts are shown in figure 19.The reactor core equipment is the largest contributor (50.7%) to the TDC of the PP, followed by the building's cost at 15.4% and the turbine plant cost at 13.9%.Re-purposing decommissioned fission reactors into fusion PPs could cut the cost of the fusion plant by half without considering the cost of re-purposing the fission reactor plant's systems.
Within the reactor core equipment, with the optimistic assumption of a HTS unit cost of 12 $ m −1 (30 $ kAm −1 ), the  heat transfer systems and equipment become the main cost contributor, accounting for 21.0% of the reactor core direct cost.The heat transfer systems and equipment include pumps for all the heat transfer fluids (such as the blanket's flowing LM or the cryogenic fluids), motor drives, insulated pipes, tanks, pressurized equipment, interfaces with tritium extraction, fluid clean-up systems, as well as dedicated instrumentation and metering.The magnets and their structures account for 11.7% and 17.0% of the reactor core direct cost, respectively.The auxiliary heating system's cost accounts for 11.1% of the reactor core cost but becomes a major cost driver (25% or more of the reactor core cost) for plasma configurations for which f ren < 1.2 or β < 3%.The use of a flowing LM blanket that provides increased protection against neutron radiation [34], without a solid first wall nor divertors, also contributes to the reduction of the blanket and shielding sub-account cost in the reactor core equipment compared to other stellarator reactor studies [19,56], for which the blanket and shielding cost amount to about 11.2% of the reactor core cost.The effects of operating the superconducting magnets at 20 K will also reduce the reactor core equipment cost, since heat transfer systems sub-cost as well as the maintenance systems cost will be reduced, resulting in a more cost-effective PP.For P2, the HTS unit cost assumption of 78 $ m −1 (200 $ kAm −1 ) was used resulting in a slight larger major radius, but lower aspect ratio, on-axis field and peak magnetic field.In that case, the PP economics are increased by 13%-21%.Even with this increased cost, the fusion plant could remain competitive in respect to the other baseload electric plants and renewable energy sources [83][84][85][86]100].In the P2 cost breakdown provided in appendix B (figure 26), the magnet cost would reach 33% of the reactor core direct cost, closer to previous stellarator reactors system studies [56,107], in which the magnets amounted to almost half of the reactor core direct cost.Reducing the HTS unit cost has an significant impact on both the PP design point and its economics.
More detailed and extensive 3D analyses of the Chartreuse P1 device and corresponding plasma configurations [9] are necessary to refine the reactor parameters (major radius R, aspect ratio A, on-axis magnetic field B. ..) but this initial 0D high-level system analysis provide preliminary insights on potential high-field compact stellarators.

Burning plasma experimental stellarator design points
The 0D reactor system analysis (section 2) was applied to explore the physics, engineering and economics landscape of burning plasma (fusion gain Q ⩾ 1) experimental fusion stellarator reactors based on HTS magnets and flowing LM blankets.

Minimizing reactor cost for varying fusion gain targets
In this section, high-field compact burning plasma experimental stellarator reactors that minimize the reactor core cost C 22 were investigated by varying target fusion gain values from Q = 1 to Q = 10.The reactor design point optimization process presented in section 4.1 was modified to minimize the reactor core cost C 22 (table 1), and maximize the target fusion gain value Q, with the added constraint of 1 ⩽ Q ⩽ 10.C 22 was considered here instead of TCC as the burning plasma experiment will aim at validating the high-field compact stellarator core technologies and will not aim at producing net electricity.Since there will be no electricity production, there will be fewer systems compared to a PP (no turbine nor electric plant), leading to reduced land footprint and facilities' costs (table 1).The HTS unit cost of 12 $ m −1 (30 $ kAm −1 ) was assumed here as well as three blanket thicknesses were considered: half-sized blanket compared to Chartreuse P (section 2.4), a quarter-sized blanket, and an eighth-size blanket to assess the potential cost savings of reducing the blanket thickness for burning plasma experiments as lower neutron flux, and shorter run times are expected in line with the neutronics simulations results [34,96].In addition, the analysis was also conducted assuming catalyzed deuterium-deuterium (D-D) as reaction fuel to investigate the cost-saving from conducting a D-D experiment for which the D-T equivalent fusion gain Q would be assessed.Lastly, β = 1% was chosen for the burning plasma experiment cost optimization and blanket thickness investigation, in order to minimize P max aux and further reduce the cost of the device as explained further in section 7.2.
For each assumed blanket thickness and for each target fusion gain Q, the reactors that minimized C 22 are represented in figure 20.The device parameters, as well as the reactor characteristics for the family of burning plasma experiment reactors with the blanket thickness of 41 cm width and varying fusion gain values, are explored in appendix C (figure 27).A burning plasma experiment of higher fusion gain has higher core cost C 22 , and thermal flux P fus /S plasma .In addition, a reduced blanket thickness increased thermal flux but reduced reactor core cost C 22 as higher B can be achieved with smaller R. Interestingly, there is a cost asymptote for high fusion gains, which means that increasing the fusion gain target from Q = 4 to Q = 10 has a minor impact on the reactor core cost C 22 .However, to achieve higher fusion gain values Q, the reactor major radius, on-axis magnetic field, and plasma temperature have to be increased (figure 27).
A reactor with R = 3.82 m, B = 10.9T, T = 6.9 keV, and A = 3.5 would achieve a fusion gain of Q = 10 while minimizing the reactor core cost C 22 with a thermal flux P fus /S plasma = 0.5 MW m −2 .The device parameters of optimal burning plasma experiments (figure 27) show that in order to minimize cost, it is necessary to aim for compact reactors with low magnetic fields, but also to minimize the peak auxiliary heating power P max aux as most of the devices on the Pareto front display similarly low values of heating power.Reducing the cost of the plasma heating system or the blanket thickness could lead to further cost reductions but might represent a major technical and engineering challenge.

Burning plasma experiment economic sensitivity to β
We also investigated the effect of varying β on the reactor core cost C 22 , as for a β value of 5% similarly to Chartreuse P, the heating system cost contributed the almost half of the C 22 cost for burning plasma experiments.Reducing β should reduce the plasma density and the required P max aux to sustain the fusion reactions (equations ( 1) and ( 6)).Similarly to section 7.1, the burning plasma experiment's design parameters were varied for each value of β with a fixed blanket thickness (b = 41 cm) so as to minimize C 22 and Q.
Figure 21, represents the heating power P max aux of the design points that minimize the reactor core cost C 22 for varying target Q values and for β = 1%, 3%, and 5%.Reducing β results in a lower reactor cost while achieving the same Q values.For lower β values, the plasma density is reduced leading to lower P aux , thus P fus to achieve the same Q value.The burning plasma experiment optimal devices for β = 5% all require high P max aux between 45-65 MW.With the auxiliary system power unit cost of 6.23 $ W −1 , these required P aux values have a major impact on the reactor core cost, amounting to 280-405 M$.Reducing the required P aux has a significant impact on the device's cost.This impact of lower β values for the burning plasma experiment led us to consider β = 1% for section 7.1.
For β = 1%, 3%, and 5%, the burning plasma experiment parameters that minimize C 22 for Q = 10 are shown in table 4. While reducing β reduces the required auxiliary heating power and cost, it leads to increased R and A. In this particular case, a compact device with high normalized plasma pressure value would prove more expensive to build than a larger device with lower β.However, for the burning plasma experiment scenario, a more refined cost analysis that includes more specific assembly, manufacturing, procurement, and logistics considerations might increase the cost for larger devices.Similarly, the construction of the larger experimental devices would likely take longer and increase the indirect costs.A tradeoff between reactor size and required heating power could be made with a β = 3% device.

Chartreuse X2 power flow and operation point
The power flow analysis through the burning plasma experiment, start-up time analysis, and helium ash accumulation calculations were carried out for Chartreuse X2 (β = 3%) as a case study.
Figure 22 represents the power flow through the burning plasma experiment, X2.In this case, there would be no heat to electricity conversion plant and thus no electricity generation.The electric power required to power the experiment's auxiliary systems is depicted as an input power flow accounting for 95 MW.For this 0D analysis, the synchrotron radiation loss were not considered as a first order effect compared to other power losses.Approximately 1.2 MW would be loss for X2 through synchrotron radiation [30,116] compared to 18 MW of Bremsstrahlung radiation, and 57 MW of diffused power remaining below 2% of the Bremsstrahlung and diffused power losses.
From the POPCON analysis of X2, P max aux also corresponds to the required steady state auxiliary heating power P aux .Similarly to Chartreuse P, the X2 auxiliary heating system sized to be P sys aux = 1.05 • P max aux , or P sys aux = 28 MW, would lead to a start-up time for steady state operation of τ start = 15 s.
For the helium ash fraction to remain below f He < 5%, the helium particles confinement time should remain under τ * He < 9 τ E .In the case of a lower τ * He , the required P aux would be lower and the achieved Q higher.For τ * He ≃ 5 τ E similar to other advanced reactors [110], the helium ash fraction would to f He ≃ 3%, leading to a peak auxiliary power of P max aux = 22.1 MW, and fusion power of P fus = 297 MW, thus resulting in an increased fusion gain of Q = 13.4.

Discussion and conclusion
The 0D physics, engineering, and economical system study for high-field compact stellarators presented here provides a framework to investigate, at a high-level, a wide range of reactor design points and highlight possible directions for research developments.The costing model provided an understanding of the required trade-offs to achieve PPs that minimize TCC and COE.(section 4).The use of HTS magnets enabling higher magnetic fields B, and flowing liquid metal walls ensuring a protection against high heat and neutron fluxes within a thin blanket thickness expand the design space towards compact high field devices.A stellarator PP of aspect ratio A = 4.1, R = 3.8 m, B = 10.2T, T = 10.2 keV, and β = 5% minimizes both the COE and TCC, at values of 47.5 $ MWh −1 and 5.2 B$ while achieving 1 GWe.
Similarly, a next-step burning plasma stellarator experiment of aspect ratio A = 3.0, R = 3.1 m, B = 8.8 T, T = 6.9 keV, and β = 3% could achieve a fusion gain Q = 10 while minimizing the reactor core cost C 22 to 670 M$ (section 7).
The economic sensitivity analysis described in section 5, highlighted the parameters with the highest effects on the reactor economics.To reduce the reactor TCC, improving the confinement properties (f ren ) would have the most impact up to f ren ≃ 1.8, followed by reducing the blanket thickness, developing advanced compact A plasma configurations, between 3 and 4.0, with R between 3 and 5 m and B between 7 and 10 T, and lastly minimizing the HTS unit cost and auxiliary heating system's cost.
The 0D model developed in this work relies on an extensive number of technological assumptions (high NWL, HTS performance and coil architecture, etc.) and simplifications that limit the generalization of the results.The 0D simplifications neglect the effects of temperature, density, and pressure profiles in the plasma, coil geometries, as well as the stellarator plasma shape (such as elongation, triangularity or field periods).A 1D analysis would improve the accuracy of the results as it has been shown that the 0D simplifications can lead to an over-estimation of the Bremsstrahlung radiation over the fusion power, thus the required auxiliary heating power [4,25].This means that the 0D analysis also over-estimates the required on-axis magnetic field for a target fusion gain (15% overestimation of B according to Alonso et al [25]).In addition, the current study relies on scaling laws for both the energy confinement time which could be improved by the use of transport codes [31,[121][122][123].Similarly, the cost models used in the study relies on costing power laws developed in the late 1990s and early 2000s which might not reflect the current cost of both raw materials nor services [54,55,58].Many reactor component costs were based on the raw material unit costs with few considerations [21,42,54,56] on the manufacturing, procurement, maintenance scheme [124][125][126] and assembly costs.
Future work will focus on iterating the design points with physics plasma configuration analyses, and refined engineering models allowing for more accurate plasma parameters and engineering assumptions that would be then fed to the 0D system analysis (inboard clearance, magnetic field peaking factor, NWL limits, alpha confinement times, etc).In addition emphasis will be put on refining the stellarator system study by carrying a 1D analysis using temperature, density and pressure profiles; including neutronics and transport simulations; and refining the costing structure with more detailed component list within the PP along with their current procurement cost.the peak field at the coils below the 20 T threshold.The most stringent peaking factor k peak = 1.5 which corresponds to standard non-planar modular coils [8,19] would still lead to a relatively compact high-field design point with R = 5.0 m, A = 4.7, B = 8.9 T. The increased in overall PP cost highly motivates the development of novel coil architectures with reduced peaking factors.

Appendix B. Additional power plant and burning plasma design points of interests
A specific case study was conducted in section 6 on Chartreuse P1, an identified stellarator power plant design that would minimize both the COE and TCC.In this study, additional design of interests were highlighted throughout the analyses; a first of kind power plant design that would minimize the TCC (figure 10), a large power plant that would minimize the COE (figure 10), an alternative power plant design (Chartreuse P2) based on increased HTS unit cost (section 6), as well as varying burning plasma experiments based on varying normalized plasma pressure values β (section 7.2).The power flow Sankey diagram are illustrated here for the FOAK and COE minimizing power plants (figures 24 and 25).
The FOAK design point could be: B = 7.5 T, R = 3.8 m , T = 7.7 keV, and A = 3.1 and generate 0.7 GW of fusion power and 0.3 GW of electricity at 100 $ MWh −1 for a TCC of 3.5 B$.This device has characteristics similar to Chartreuse X1, meaning that a combined burning plasma experiment and first of kind device could be although with varying operation plans, β = 1% up to β = 5%.The large PP minimizing the COE (figure 10) appears an unlikely design points with un-plausible large dimensions: B = 13 T, R = 6.3 m , T = 13.1 keV, and A = 6.9 and generate 8.3 GW of fusion power and 4.4 GW of electricity at 22 $ MWh −1 for a TCC of 12 B$.
In addition, the cost breakdown for the various burning plasma experiments (X1-X3) and chosen power plant designs (Chartreuse P1 and P2) is also shown her in figure 26.

Appendix C. β = 1% burning plasma design points parameters
The device parameters, as well as the reactor characteristics for the family of Pareto optimal burning plasma experiment reactors for β = 1% with the blanket thickness of 41 cm width and varying fusion gain values, are shown in figure 27.The device parameters show relatively similar devices suggesting that to achieve Q values from 1 to 10, a single cost-effective reactor of major radius R ∼ 3.4 with aspect ratio of A = 3.4, heating power P max aux ∼ 10 MW and varying B from 8 to 11 T could be used.

Figure 1 .
Figure 1.Stellarator reactor model considered in the 0D system analysis, main materials, along with an example plasma boundary shown in transparent red.

Figure 2 .
Figure 2. Schematic diagram of the 0D system analysis framework, with the color coding representing the different modules of the framework.The symbols and acronyms used in the schematic are detailed section 1.

Figure 3 .
Figure 3. Results of a scan of B and R, illustrating how it affects several physics plasma parameters for two aspect ratios, A = 3 (a)-(d) and A = 9 (e)-(h).fren is set to 1.4, T to 10 keV, and β to 5%.The orange dashed line in (a) and (e) represents ne/nc = 1, the radiative density limit threshold with nc the stellarator radiative density limit (equation (2)).

Figure 4 .
Figure 4. Regions of interest shown in green of physics operations within the design space scan of B and R for two aspect aspect ratios A = 3 (a) and A = 9 (e).fren is set to 1.4, T to 10 keV, and β to 5%.Regions of interest are bound by solid and dashed lines representing the radiative limit, target τ E , maximum B peak , minimum ne and neTτ E values.

Figure 5 .
Figure 5. Results of a scan of B and R, illustrating how it affects several physics power parameters for two aspect ratios, A = 3 (a)-(g) and A = 9 (h)-(n).fren is set to 1.4, T to 10 keV, and β to 5%.In the fusion gain plots (e) and (k), the black dashed line marks the boundary of the Q = ∞ design points, and the red dashed line the Q = 40 design points.

Figure 6 .
Figure 6.Regions of interest shown in brown of relevant power considerations within the design space scan of B and R for two aspect aspect ratios A = 3 (a) and A = 9 (e).fren is set to 1.4, T to 10 keV, and β to 5%.Regions of interest are bound by solid and dashed lines representing targets or engineering limits on Q, P fus , Pe, P max aux , P WL and P rad values.

Figure 7 .
Figure 7. Results of a scan of B and R, illustrating how it affects several economic parameters for two aspect ratios, A = 3 (a)-(d) and A = 9 (e)-(h).fren is set to 1.4, T to 10 keV, and β to 5%.

Figure 8 .
Figure 8. Regions of interest shown in blue of relevant economics considerations within the design space scan of B and R for two aspect aspect ratios A = 3 (a) and A = 9 (e).fren is set to 1.4, T to 10 keV, and β to 5%.Regions of interest are bound by solid and dashed lines representing targets or limits on COE and TCC values.

Figure 9
Figure 9 is constructed by overlaying contour lines of relevant physics, engineering, and economics parameters.Overlaying multiple parameters enables the identification of a region of interest (yellow shaded area in figure 9) within which physics, engineering and economics trade-offs can be visualized.The

Figure 9 .
Figure 9. Results of a scan of B and R for aspect ratios A = 3 (a) and A = 9 (b), with overlaid contour regions of interest from the physics (green solid line), engineering (brown solid line), and economics (blue solid line) parameters highlighted in figures 3-8.The intersection of these contours defines a PP region of interest (yellow shaded area) for physics, engineering, and economics perspective.
(a)) as it would demonstrate net electricity production while minimizing the capital cost.A PP with the following parameters: B = 7.5 T, R = 3.8 m , T = 7.7 keV, and A = 3.1 would fit in the Pareto curve FOAK region of interest.Such a design, could be retrofitted in a dismissed nuclear fission PP to reduce its capital cost and make use of existing installations such as the thermal power conversion plant.This FOAK PP would have a neutron wall loading of 5.1 MW m −2 , result in 0.7 GW of fusion power and produce 0.3 GW of electricity at 100 $ MWh −1 for a reactor core cost C 22 of 1.1 B$.A design point lying at the 'elbow' of this Pareto front curve (figure 10(b)) is economically attractive both in terms of COE and TCC.A PP with the following parameters : B = 10.2T, R = 3.8 m , T = 10.2 keV, and A = 4.1 would fit in the Pareto curve 'elbow' region of interest.Such a design would result in 1.8 GW of fusion power and produce 1.0 GW of electricity

Figure 10 .
Figure 10.Pareto front of the optimal design points in terms of cost of electricity (COE) and capital cost ((a) reactor core cost C 22 , (b) TCC).Each marker represents an optimal plant and the color of the marker represents the plant's net electric power (Pe).The arrows indicate how the stellarator characteristics changes along the Pareto front.(c) The Pareto optimal design point's parameters (B, R, T, A) along with several PP characteristics are shown here.Each marker represents an optimal reactor resulting from the fusion PP cost optimization (section 4.1).Red markers represent the design points that achieve ignition (Q = ∞) and blue markers the ones with finite fusion gains.For the the electron density plot, markers with light red and light blue colors represent the corresponding radiative density limit for each reactor design point.

Figure 11 .
Figure 11.TCC per watt and COE by technology assuming a discount rate r between 3% and 7%.The cost optimal reactors are shown with colored circular markers representing their net electric power output.The commercial plant green circle from figures 10(a) and (b), is represented with the stellarator fusion magenta shaded area.

Figure 12 .
Figure 12.Sensitivity analysis of the reactor's minimum total capital cost TCC for varying reactor configurations (fren, β, R, A, T, B and B peak ).The green marker represents the parameter value used in the cost-optimal design point selection (section 4.1).The β sensitivity analysis was carried out for varying fren values shown in varying shades of blue.

Figure 13 .
Figure 13.Sensitivity analysis of the reactor's minimum total capital cost TCC with varying model assumptions (kα, f He and ι 2/3 ).The green marker represents the parameter value used in the cost-optimal design point selection (section 4.1).

Figure 14 .
Figure 14.Sensitivity analysis of the reactor's minimum total capital cost TCC with varying reactor parameters (b, fm, η th , ηaux, auxiliary heating cost and HTS unit cost).The green marker represents the parameter value used in the cost-optimal design point selection (section 4.1).

Figure 16 .
Figure 16.Plasma operating contour plot for the example stellarator reactor design point.

Figure 17 .
Figure 17.Effects of variations in helium ash fraction f He on Chartreuse P1 output grid power Pe, the required steady state auxiliary power Paux, and the corresponding cost of electricity COE.

Figure 18 .
Figure 18.Helium ash evolution (equation (24)) within the plasma of Chartreuse P1 for varying ratios of the helium particles confinement time and the energy confinement time, fτ ≃ τ * He /τ E .

Figure 19 .
Figure 19.Breakdown of the reactor core cost components (a) and the power-plant total direct cost components (b) for the example stellarator design point, Chartreuse P1.

Figure 20 .
Figure 20.Pareto fronts of the optimal reactors in terms of fusion gain and reactor core cost, for three assumed blanket thicknesses, b = 10, 20 and 41 cm.Each marker represents an optimal reactor and the color of the marker represents the thermal flux P fus /S plasma .The arrows indicate how the stellarator characteristics change along the Pareto front.

Figure 21 .
Figure21.Sensitivity analysis on the reactor core cost for varying normalized plasma pressure β parameters.Each marker represents the minimum cost reactor for a given fusion gain (similar to figure20) for varying β values of 1.0%, 3%, and 5.0%.Here the peak auxiliary heating power P max aux for each design point is shown along with the reactor core cost, and the color coding represents the reactor's fusion gain.

Figure 23 .
Figure 23.Pareto fronts of the optimal design points in terms of cost of electricity (COE) and capital cost (TCC) with varying magnetic field peaking factor k peak = 1, 1.2, and 1.5 as defined in equation (20).Increasing peak factors are shown with increasing transparency.Each marker represents an optimal plant and the color of the marker represents the plant's net electric power (Pe).

Table 5 .
Reactor parameters and cost details for three Pareto optimal conceptual reactor design points corresponding to peaking factor of k peak = 1, 1.2, and 1.5 respectively.

Figure 24 .
Figure 24.Sankey diagram of the power flow through the minimum TCC reactor in the Pareto front shown in figure 10.

Figure 25 .
Figure 25.Sankey diagram of the power flow through the minimum COE reactor in the Pareto front shown in figure 10.

Figure 26 .
Figure 26.Cost comparison of the reactor design points considered in this study Chartreuse X1-3 and Chartreuse P1-2.

Figure 27 .
Figure 27.Stellarator reactor's characteristics of each optimal reactor along the Pareto front shown in figure 20 for a blanket thickness of b = 41 cm, and β = 1.0.The reactors' parameters (B, R, T, A) along several reactors characteristics are shown here.Each marker represents an optimal reactor resulting from minimizing the reactor core cost C 22 for a target fusion gain value Q.For the the electron density plot, markers with light blue colors represent the corresponding radiative density limit for each reactor design point.

Table 2 .
Cost model specific materials mass densities and unit costs used in this study.

Table 3 .
Reactor parameters and cost details for two conceptual reactor design points, assuming an HTS manufacturing cost of 12 $ km −1 and 78 $ km −1 respectively.

Table 4 .
Reactor parameters, characteristics and cost details for three conceptual burning plasma experiment design points, assuming β values of 1.0%, 3.0%, and 5.0% respectively.
Figure 22.Sankey diagram of the burning plasma experimental reactor, Chartreuse X2, power flow.