From W7-X to a HELIAS fusion power plant: motivation and options for an intermediate-step burning-plasma stellarator

As a starting point for a more in-depth discussion of a research strategy leading from Wendelstein 7-X to a HELIAS power plant, the respective steps in physics and engineering are considered from different vantage points. The first approach discusses the direct extrapolation of selected physics and engineering parameters. This is followed by an examination of advancing the understanding of stellarator optimisation. Finally, combining a dimensionless parameter approach with an empirical energy confinement time scaling, the necessary development steps are highlighted. From this analysis it is concluded that an intermediate-step burning-plasma stellarator is the most prudent approach to bridge the gap between W7-X and a HELIAS power plant. Using a systems code approach in combination with transport simulations, a range of possible conceptual designs is analysed. This range is exemplified by two bounding cases, a fast-track, cost-efficient device with low magnetic field and without a blanket and a device similar to a demonstration power plant with blanket and net electricity power production.


Introduction
One of the high-level missions of the European Roadmap [2] to the realisation of fusion energy is to bring the HELIAS stellarator line to maturity. The near-term focus is the scientific exploitation of the Wendelstein 7-X experiment in order to assess stellarator optimisation in view of economic operation of a stellarator fusion power plant [3]. The highlevel scientific goals of W7-X are consequently the demonstration of improved neoclassical confinement as well as improved confinement of fast ions, further, plasma stability up to a volume-averaged β of 5%, and a stiff magnetic equilibrium to facilitate the island divertor concept while achieving steady-state operation. W7-X will play a decisive role for these studies but will be too small to investigate stellarator burning-plasma issues. Therefore, an intermediate burning plasma stellarator appears prudent to mitigate the risks which would otherwise arise from the incomplete physics basis [4]. The focus of such an intermediate device would be the investigation of effects associated with a 3D burning plasma and the corresponding confinement and control of fast alpha particles. A decision on the necessity of a burning plasma experiment, however, should wait for the results of the high-performance steady-state operation of W7-X and the burning plasma phase of ITER.
To be more specific, the optimisation of fast-particle confinement needs to be proven, especially involving collective effects in burning plasmas within a sufficiently large Plasma Physics and Controlled Fusion From W7-X to a HELIAS fusion power plant: motivation and options for an intermediatestep burning-plasma stellarator plasma volume [5]. 3D-specific, Alfvénic instabilities may give rise to physics which cannot be explored in tokamaks (like ITER) [6]. In particular, Alfvénic instabilities driven by fast alpha particles may result in increased losses of the latter. The threshold in terms of the fast alpha particle pressure, above which such effects occur, cannot yet be precisely predicted, but is likely above what can be achieved in W7-X. In addition, looking at the extrapolation of relevant physics and engineering para meters, the step from W7-X directly to a power plant is significant for some of the relevant quantities (e.g. energy of the magnet system, stored energy in the plasma, heating power, ratio of heating power to major radius P/R, fusion power gain, triple product, normalised gyroradius).
These arguments lead to the concern that a direct step from W7-X to a HELIAS reactor bears large scientific and technological risks. Plasma conditions anticipated in a burning plasma experiment of smaller size than a reactor are therefore investigated to assess the potential for risk mitigation with an intermediate-step, burning-plasma HELIAS device. Such a device will require far fewer resources than a reactor due to its smaller size, much relaxed requirements for structure materials (dpa limits) and space. At the same time, this intermediate-step device offers accessibility for scientific exploration and could also serve as a facility for fusion engineering tests. Such an approach would offer synergy effects in line with the parallel development of technology for tokamaks.
This work discusses the latest developments towards a stellarator power plant using three methods: the extrapolation of selected physics and engineering parameters, the consideration of progress in stellarator optimisation, and the application of dimensional analysis techniques. The gaps revealed in physics and engineering understanding are presented in section 2 from today's point of view. A risk-reducing strategy foresees an intermediate-step stellarator to bridge those gaps and the resulting high-level requirements for such a device are outlined in section 3. On this basis, systems studies have been carried out for two possible devices with different technological sophistication and the results are presented in section 4. The economic aspects of these different concepts are compared in section 5 and the implications and conclusions of this work are summarised in section 6.

Development steps towards a stellarator power plant
The understanding of the physics and technology of stellarators has made significant progress in recent years. Essential contributions came from the design process of W7-X (stellarator optimisation [7]), from the construction experience itself [8], and from the ongoing theoretical work during the construction phase [9,10]. Nevertheless, stellarators are still less mature than tokamaks. The underlying reason is the threedimensionality of the magnetic configuration which produces a rotational transform by magnetic field coils without needing a toroidal plasma current, but also introduces an additional level of complexity. As a consequence, stellarators need an elaborate optimisation procedure [11] to fulfil basic confinement properties. Before the advent of high-performance computers, this problem could not be solved. In addition, the 3-dimensional configuration offers more degrees of freedom to find the optimum magnetic field configuration. This, however, also means that finding and empirically testing the optimum configuration can be a very costly procedure. The optimisation, which forms the basis of the W7-X design, already includes an extensive set of criteria. However, it is not immediately obvious how to extrapolate to a HELIAS power plant, even assuming that the optimisation can be verified in the coming years of W7-X operation.

Extrapolation of physics and engineering parameters
To improve the understanding of the necessary steps between W7-X and a power plant one can look at several aspects. First, one can compare important physics and engineering parameters. An overview, comparing such parameters for W7-X, ITER and a HELIAS power plant, is given in table 1. The ITER values are taken from [14]. ITER is included in this discussion because it represents a confinement experiment aiming at a burning fusion plasma which can be characterised by an alpha-power exceeding the auxiliary heating power, i.e. > α P P aux or Q > 5. Extrapolating from the W7-X design, the HELIAS 5-B has the typical parameters of a stellarator fusion power plant [13]. The increase of the size of the devices, e.g. reflected by the plasma volume, and the increase of the magnetic field strength is required to achieve the necessary energy confinement times which for a burning fusion plasma or even an ignited plasma have to be in the range of a few seconds. The magnetic field strength, however, is limited by the mechanical forces, which have to be accommodated by the support structure, and by the available superconductor technology. Interestingly, the magnetic field strength of ITER is similar to the HELIAS 5-B values. In fact, the case has been made that a HELIAS 5-B could use the ITER toroidal magnetic field technology [15]. As a consequence, the triple product rises by about two orders of magnitude in the step from W7-X to HELIAS 5-B. While also plasma densities and temperatures increase, the dominating part of the increase of τ nT , when going from W7-X to ITER or a HELIAS reactor, is the increase of the energy confinement time by about a factor of ten. In contrast, the expected MHD stability limit for W7-X already has the value of a power plant. This is in contrast to tokamaks which require a further increase to achieve the desired pulse lengths when extrapolating from ITER to a demonstration power plant [16]. The steady-state heating power of W7-X, given in the table is the initial value (the numbers in paranthesis represent a possible power upgrade).
W7-X will not be operated with tritium. Therefore, the heating power comes entirely from external sources. Nevertheless, the heating technology using electron-cyclotron resonance heating (ECRH) is, at least for a stellarator power plant, a promising candidate [17] as stellarators do not need any significant amount of current drive. In ITER the heating power is composed of alpha-heating and auxiliary heating.
The HELIAS 5-B is assumed to operate ignited. Thus, the auxiliary heating during steady-state operation is zero. This does not mean that auxiliary heating systems are not required. Depending on the actual confinement time and impurity content during plasma build-up heating power on the order of 100 MW may become necessary [18]. The heating power divided by the plasma surface area gives an approximate value for the average heat flux reaching the in-vessel components assuming a completely homogenous heat deposition. Plasma radiation supports such a homogenous distribution, but full homogeneity will never be achieved.
With respect to these values the different devices do not lie so far apart. In contrast, the P/R-scaling considers the heatflux arriving in the divertor assuming that the power decay length does not change with size [19]. This means, the wetted area on the divertor scales only with R, but as the power must be exhausted by the divertor, a consequent figure-of-merit for the power exhaust results in P/R [20], which has in particular been used in ASDEX Upgrade to mimic conditions to be expected in ITER and beyond [21].
Here, the step from W7-X to a HELIAS results in a factor for P/R of about ten. ITER lies in-between. The much larger aspect ratio of the stellarator devices leads to generally lower values of P/R which helps to reduce the peak heat-fluxes. However, one should also keep in mind that the magnetic island divertor as tested in W7-AS and realised in W7-X [22] is different in many other aspects to the poloidal divertor used in ITER. The long connection lengths of the open magnetic field lines in the scrape-off layer of an island divertor configuration (about 300 m in W7-X, 110 m in ITER and about 1200 m in a HELIAS [23]) support the broadening of the power deposition zones. On the other hand, while the strike zones are toroidally continuous in a poloidal divertor, they are discontinuous along the helical coordinate of the island divertor leading to a focusing of the power. The peak heat-fluxes which form the basis of the W7-X and ITER divertor designs are the same. The lower value for the HELIAS 5-B takes into account that, in order to achieve a reasonable full power life time in the presence of the neutron fluxes expected in a power plant, the heat flux reaching the divertor has to be reduced [16].
Finally, table 1 also shows the average neutron fluxes expected for the ITER Q = 10 operation and for the HELIAS power plant. Although the fusion power is much larger in the HELIAS 5-B device the average neutron flux increases only by a factor of two since its aspect ratio is larger. However, the main difference between ITER and any power-plant-like device are the integrated neutron fluxes which over time determine the life-time of the in-vessel components and the blanket. While ITER is designed for neutron load range corresponding to values below 10 dpa [24], the highly loaded components of a power plant will have to achieve 100-150 dpa to accomplish sufficiently long intervals between the replacement of divertor and blanket [25]. Here, the larger aspect ratio of the HELIAS compared to a tokamak DEMO helps as the neutron fluxes normalised to the fusion power decrease by about a factor of two thereby increasing the lifetime of the exposed components. Comparing the spatial neutron flux distribution in the plasma vessel and normalising the values to the fusion power the values range between 0.32-⋅ − − 0.86 10 m 3 2 for a 1.57 GW tokamak DEMO [26] and 0.07-⋅ − − 0.50 10 m 3 2 for a 3 GW HELIAS [18].

Advances in stellarator optimisation
Another viewpoint concerning how to extrapolate from W7-X to a power plant is obtained by looking at the original physics optimisation of W7-X and comparing it to the scientific progress during the construction period of W7-X. The original optimisation forming the basis of the W7-X design comprised several criteria: improved neoclassical confinement, a drift optimisation for improved fast ion confinement, plasma stability up to a volume averaged β of 5%, and low Shafranov-shift and low bootstrap currents for a stiff equilibrium facilitating a magnetic island divertor in combination with low magnetic shear and a rotational transform of ι −= 1 at the plasma edge [11,27]. Aspects which have not been part of the optimisation are density and impurity control. To avoid hollow density profiles caused by neoclassically driven thermo-diffusion central particle sources are required [28]. Thus, pellet injection is now a part of the future W7-X programme. Concerning the prevention of impurity accumulation a suitable confinement regime has to be established. A promising candidate is the so-called high-density H-mode found in W7-AS [29], although it is not clear how this regime will extrapolate to W7-X with its lower collisionality.
Concerning the drift-optimisation based on an quasiisodynamic configuration, it has been realised that the region of improved fast ion confinement is rather narrow in W7-X making it difficult to verify this effect by neutral beam injection [5]. Studies about the possibility to use ion cyclotron resonance heating for this purpose are ongoing [30,31]. However, at this stage it already can be said that achieving a large fast ion population will be difficult as the slowing down times at the high plasma densities, at which the improvement of the neoclassical confinement is most effective, are rather short. While minimising the fast ion population is desirable in a burning fusion plasma, the short slowing-down times constrain fast ion studies considerably. As the isodynamic driftoptimisation requires a minimum β (of about 4%) to become effective, reducing the density and at the same time increasing the temperature might be an option for increasing the fastparticle population in W7-X. However, the strong temperature dependence of the neoclassical heat diffusivity ( ) in combination with the limited heating power restricts this option. All in all, to provide a configuration in which alphaparticle production and the region of improved fast-ion confinement are consistent, further optimisation of the magnetic field configuration is required [32]. Finally, turbulent transport was not considered at all during the W7-X optimisation. It turns out that the magnetic field configuration of W7-X has a profound effect on turbulent modes, e.g. stabilising trappedelectron-modes [33] or leading to poloidal localisation of the ion-temperature-gradient modes [34]. With the growing understanding of the behaviour of turbulence in 3D magnetic field configurations, tailoring of turbulent transport may become a future criterion of stellarator optimisation [35].

Step-ladder approach
Another approach, in order to link the physical behaviour of existing experiments to power plant devices, is to consider dimensionless parameter scaling techniques [36]. For this purpose, dimensional analysis [37] or transformation invariance of basic plasma physics equations [38] can be employed. Following this approach, a set of dimensionless quantities can be obtained where the exponents are restricted in a way that makes the quantities dimensionless. Consequently, any linear combination of the selected set of dimensionless parameters is valid. For the concept of magnetic confinement the three commonly employed dimensionless plasma physics para meters are the normalised plasma pressure β, the normalised gyroradius ρ * and the collisionality ν * , defined as: where a is the minor radius, R 0 the major radius, p the plasma pressure, v th the thermal velocity, ν th the thermal collision frequency and ι − the rotational transform. Despite the great insight which can be obtained from dimensionless scaling techniques, the method has some limitations which should be kept in mind for the following analysis. In particular, the dimensionless quantities give no information about the depend ence of phenomena which do not scale according to the dimensionless principle, e.g. atomic physics are not reflected in such an ansatz.
Although it is possible to simply compare the specific values of the dimensionless parameters between today's experiments and future fusion devices, such an approach is not very conclusive. In order to measure the reactor relevance of existing and planned magnetic confinement devices, it is convenient to additionally rephrase the leading operation parameters of a device in so-called 'dimensionless' engineering parameters  [39]. Considering the Kadomtsev similarity constraints [37], * * B P , and n * must remain constant in differently sized devices, in order to obtain the same dimensionless plasma physics parameters (omitting dimensional constants). In this approach the principle of similarity requires that the magnetic geometry of the compared devices is identical, i.e. the aspect ratio A, elongation κ, as well as the rotational transform ι − (the inverse of the safety factor, q) must be identical.
The formulation of such dimensionless engineering parameters allows one to link both the governing dimensionless physics quantities and the device parameters. To this extent scaling laws (empirical or theoretical) can be employed to transform the engineering to the physics parameters. This approach has the advantage that anticipated physic regimes can simultaneously be displayed within expected operation windows. Such a representation is referred to as a 'stepladder' plot due to its characteristic appearance.
The combined engineering-physics parameter view can be seen in figure 1, where the left side shows the step-ladder plot for ASDEX Upgrade, JET and ITER assuming the normalized plasma density n * = const. which has been adapted from [39].
The right side of figure 1 reflects the same approach for the HELIAS line employing the scaling law ISS04 for the energy confinement time τ E [40] with the same configuration factor / τ τ = f ren E E ISS04 for all devices. The renormalization factor f ren can serve as a confinement enhancement or degradation factor similar to the H-factor used in tokamaks but, for stellarators, f ren also reflects the complex structure of stellarator magnetic fields and is therefore, dependent on the magnetic configuration [40,41].
For the HELIAS-line, the transformation of the dimensionless parameters are determined by the relations Since the density is assumed to be determined by the ECH cut-off, changes in n * need to be considered in the sequence from W7-X to HELIAS 5-B, which is in particular important for the collisionality which scales as ν ∼ * * n 1.9207 . In the tokamak picture, n * is similar to the Greenwald density limit [42] and if all devices operate at a fixed ratio of the Greenwald density limit, n * is constant for all devices meaning that all tokamak devices lie in the same plane of n * . In the stellarator picture, however, n is constant instead of n * such that the right side of figure 1 becomes actually a 3D-plot with n * as the 'Z-axis'. Therefore, one has to consider the projection of the n * plane from todays devices to the n * plane of the power plant device. This is, however, only important for ν * since ρ * and β * depend only weakly on n * . The visualisation of differences of the dimensionless parameter ν * is given by the dotted line on the right side of figure 1, which is a projection of the W7-X plane to the HELIAS 5-B plane. The difference in collisionality between W7-X and the power plant scenario is therefore not a factor ten, but rather a factor two to three.
Comparing the step-ladder plot of ITER-like tokamaks with the HELIAS-like devices, indicates that the physics basis of advanced stellarators is less well covered than that of tokamaks. In physics dimensionless parameters, the gap from existent devices to burning plasmas appears evident. Comparing the gap between W7-X and HELIAS 5-B with the gap between JET and ITER or the gap between ITER and DEMO, the change both in B * , P * and n * as well as in ρ * and ν * is more substantial for the discussed stellarators. In fact, the gap between W7-X and HELIAS 5-B is similar to the gap between JET and DEMO.
The analysis of required control parameters in the form of dimensionless variables shows that the step from W7-X to a HELIAS reactor would be very large in the dimensionless engineering and physics quantities. Especially reactor relevant ν * and ρ * are hardly accessible. In particular, simultaneous attainment of ν * , ρ * and β of an envisaged reactor working point cannot be achieved in W7-X.
Although the step-ladder approach is a powerful tool to measure the reactor-relevance of today's experiments in terms of a number of representative dimensionless (plasma-core) physics and engineering parameters, a number of additional constraints exist which cannot be incorporated into such a representation. In particular the physics and technology of the divertor and plasma exhaust is governed by very different similarity conditions. Nonetheless, it is possible to define global parameters which are not necessarily dimensionless but which can be employed to characterise the required step-size to reactor conditions. For example, a commonly employed figure of merit which measures the challenge for the exhaust system is the parameter P / R.
An additional important challenge for stellarators, which is not directly covered by figure 1, is the confinement of fast particles and their interaction with Alfénic instabilities. Therefore we introduce an additional dimensionless quantity α f p, which serves as figure of merit to describe the importance of fast particles in comparison with the background plasma. The normalised alpha particle pressure α f p, is therefore defined as the ratio of the fast particle pressure in relation to the pressure of the background plasma where ∼ p nT back is the plasma pressure in its usual definition and the alpha particle pressure ∼ as characteristic time interval in which the alpha particles remain 'energetic', the density of the alpha particles becomes in the relevant temperature regime of 10-20 keV by ∼ n T 2 2 and substituting in equation (5), a scaling for the normalised alpha particle pressure can be obtained with which allows us to represent α f p, in the dimensionless stepladder approach. However, as intrinsically assumed, this scaling is only correct as long as the heating power is dominated by the fusion alphas.
Last, but not least, we consider the fusion triple product τ nT E which is a measure for the burn or ignition of a fusion device. It is generally accepted that τ nT E must reach a certain value above which the plasma can be considered to be ignited. According to the above introduced step-ladder methodology, isocontours for P / R, α f p, and τ nT E are given within the dimensionless engineering parameter space in figure 2.
It can be seen in figure 2, that for either of the presented 'challenges' regarding exhaust, fast particles and fusion burn, substantial gaps exist in the chosen representative figures of merit. Step-ladder plots for ITER-like tokamaks (left) and the HELIAS line (right). The left side shows operation windows of ASDEX Upgrade (AUG), JET and ITER in dimensionless engineering parameters with isocontours of dimensionless physics parameters at constant n * . The right side shows the same for the HELIAS line. The W7-X operation windows refer to operation phase 1 (OP1) and 2 (OP2) for X2 and O2 heating, respectively, where n * has been adapted to ECH cut-off densities and 'HELIAS 5-B' is an engineering-based reactor study [13]. The dotted line on the right side is the projection of the collisionallity of W7-X into the plane of HELIAS 5-B.
Comparing figure 2 with the values presented in table 1 one realises some deviations. For example, the difference of P/R is less in the dimensionless plot, while the difference in τ nT is greater than in the table. The renormalisation factor has been fixed in the dimensional analysis, however detailed 1D transport simulations have shown [43] that the renormalisation factor is quite different for W7-X and a HELIAS. Furthermore, the dimensionless extrapolation uses the empirical confinement time scaling ISS04 and is thus dependent on the scaling relations therein. It has also been shown in [43], that the transport regimes change from W7-X to a power plant and that for an ignited plasma the heating power is no longer an external variable, but rather determined by plasma volume, beta, and magnetic field. Taken together, this causes the underlying scaling relations of the confinement time scaling to change. While this can be reflected in table 1 for single design points, it is much more complicated to accurately account for such effects in the dimensionless scaling which covers several orders of magnitude in different parameters. However, the conclusions which can be drawn from figure 2 remain intact, but absolute values should be taken with care.
The existence of the gaps for the HELIAS-line leads to the conclusion that the experimental program of W7-X needs to demonstrate the physics of high-beta discharges at lowest ρ * and ν * (high-performance discharges). Since substantial gaps in ρ * and ν * exist with regard to HELIAS reactor plasmas, it is mandatory to develop predictive capabilities about any issues related to collisionality and gyro-radius effects. Examples are the interplay of neoclassical and turbulent transport and the confinement of fast particles and their excitation of Alfénic instabilities.
Overall, the step from W7-X to a power plant contains significant extrapolations of a number of physics and engineering parameters. While a further increase of β is not foreseen and an envisaged increase of the magnetic field by a factor of about two appears to be sufficient, quantities such as plasma volume, stored magnetic energy, energy stored in the plasma and power levels increase substantially. Associated with the high power levels of a power plant is the fact that the plasma heating is governed by alpha-particles which entails not only additional physics effects, but also adds requirements to the design of the device. Finally, the handling of high neutron fluxes and fluences generated by a D-T fusion plasma introduces an entirely new level of complexity.
For the advancement of the tokamak-line the ITER device is seen to play a key role in figure 1 bridging the gap between JET and DEMO. Similary for the advancement of the stellarator line, an intermediate-scale HELIAS may be envisaged to bridge the gap between W7-X and a HELIAS power plant. Therefore, the conclusion of this analysis is to introduce a burning-plasma HELIAS as a reasonable next step after W7-X. The main purpose of such a device would be to investigate the burning plasma physics and to a limited extent also the associated technologies while the risk related to the extrapolation from W7-X results is kept at an appropriate level. As outlined in [16], this intermediate-step burning-plasma HELIAS would rely on the parallel development of the tokamak line. In particular, it is assumed that after such an intermediate device, the following development step might already be on the commercial power plant level. This scenario, however, requires that validated technology solutions are available for a HELIAS power plant without the need for another major experimental verification. From the physics and engineering point of view, as presented in figures 1 and 2, this argument is substantiated by the fact that the operating point of HELIAS-5B already represents an ignited plasma.
On this basis a set of high-level requirements can be derived which a potential intermediate-step HELIAS device must fulfill in order to bridge the gap from today's experiments to commercial fusion for the HELIAS line. A tentative list of these high-levels goals is summarised in the next section.
Some specifications, however, are still ambiguous. For example, it remains to be shown by detailed theoretical studies which value of α f p, must be achieved by an intermediate HELIAS device to allow a meaningful experimental study of the important fast particle effects. Generally speaking, more in-depth studies are necessary to substantiate the list of highlevel requirements presented below.

High-level requirements for a next-step stellarator
An intermediate device is assumed to bridge the gap between W7-X and a HELIAS power plant. The high-level objective of such a device is to demonstrate and investigate the physics of a burning plasma and the corresponding confinement and control of fast alpha particles.
In this sense an intermediate step stellarator is very much comparable with the general requirements for ITER [12]. New aspects would be the stellarator-specific physics and f p, and τ nT E which serve as figure of merits for the challenges regarding exhaust, fast particle confinement and fusion burn, respectively. The W7-X operation windows refer to operation phase 1 (OP1) and 2 (OP2) for X2 and O2 heating, respectively, where n * has been adapted to ECH cut-off densities and 'HELIAS 5-B' is an engineering-based reactor study [13]. Also shown are values for the fusion gain Q whose contours coincide with the contours from the triple product.
3D engineering issues. Especially the divertor concept must be able to handle the heat and particle exhaust of a burning 3D plasma. Nonetheless, an intermediate step HELIAS is expected to have far fewer requirements and constraints than a HELIAS reactor on the power plant scale. Also with regard to accessibility, an intermediate step HELIAS can be regarded to be more a scientific experiment than an electricity generating plant. Consequently, an intermediate-step HELIAS is a device which uniquely allows for an optimisation of 3D reactor scenarios by fully investigating the plasma physics properties of 3D burning plasmas. Based on the step-ladder analysis of the last section, a tentative list of high-level specifications can be defined which is summarised in the list below: • sufficient fast-particle pressure (to assess, e.g. the effect of Alfvénic instabilities) • high plasma β (∼ 4% to enable fast-particle confinement and to demonstrate high-performance operation) • ρ * and ν * must be sufficiently close to reactor conditions • steady-state operation to allow for reactor scenario development (e.g. exhaust) • optimised magnetic configuration with respect to neoclassical and turbulent transport of the main plasma, impurities as well as for fast particle confinement • availability and feasibility of modular magnet system • reliable divertor concept and operation (e.g. impurity control and (partial) detachment with high SOL radiation to reduce the divertor heat load to acceptable levels) The definition of such high-level goals is important, since these form the guidelines and constraints for the development of design concepts. In particular, the specifications listed here, serve as input for the systems studies of next-step HELIAS devices as will be discussed in the sections below.

Systems studies of possible next-step scenarios
A well-established method to investigate the impact of engineering and physics parameter variations on a conceptual design are so-called 'systems studies'. In the design phase of a nextstep HELIAS device such studies allow the investigation of a wide parameter range and its impact on the design of the device. Ultimately, such an investigation allows one to show the robustness of a design point and optimise it with respect to the high-level goals taking into account trade-offs between different parameters and limitations. To conduct such systems studies usually 'systems codes' are employed, which are in this context simplified, yet comprehensive models of an entire fusion power plant. While this approach has a long tradition for tokamaks, heliotrons and compact stellarators, only recently have systems code models been developed for the HELIAS concept [44] including descriptions for the 3D topology, the modular coil set, and the island divertor. These models were implemented in the European systems code PROCESS [45] and tested succesfully [46].
First design window analyses of helical devices were originally carried out for the heliotron concept [47]. Following the developments described above, systems studies have also recently been carried out for HELIAS reactor concepts [18]. In the following the same methodology is applied for different design concepts of an intermediate-step stellarator of the HELIAS line. Having the purpose to bridge the gap between W7-X and a HELIAS power plant, such a device must fulfill the high-level requirements outlined in the previous section.
However, the systems code PROCESS employs empirical confinement time scalings to extrapolate the confinement time, i.e. the plasma transport, to power-plant-sized devices. But as already outlined in the strategy presented in [44] and discussed in [43] empirical confinement times are not sufficient to confidently predict the confinement properties of a HELIAS power plant. Therefore, in addition to the systems code approach, a dedicated 1D transport code [48] is employed to calculate and estimate the neoclassical and turbulent transport and thus provide a more sophistacted estimation of the confinement in a HELIAS power plant and intermediate-step burning-plasma stellarators.
Since the step from W7-X to a HELIAS power plant is rather large both in engineering and physics quantities, a number of different devices could be envisaged to fit the stated goals. In the following studies the focus is put on two cases. The first case represents the smallest possible device, which could be realised on a near-term time scale using mostly today's technology, in the following called 'option A'. The second case, which can be seen as an upper boundary, is meant to be a DEMO-like design which employs reactor-ready technology and should consequently produce a net amount of electricity. Since there are still possibilities for a design compromise between those two cases, the DEMO-like concept is referred to here as 'option C' (i.e. 'option B' would be a compromise between these two options but is not investigated in this work).

Workflow
Before the individual options are presented in detail, the general workflow which is followed in this work is introduced; see figure 3 for the flowchart.
Generally, the first step is to define a number of high-level requirements which directly influence certain parameters and in addition serve as limits and constraints in the subsequent calculations. With the general inputs defined, the next step is to carry out simulations. One could either start with systems studies and make assumptions on the transport or start with transport simulations and make assumptions on the size of the device. In any case, both tools need to be coupled by iterations. E.g. starting from systems studies, engineering parameters such as the size and the magnetic field can be narrowed down which serves as input for the transport simulations which in turn provide plasma parameters such as the temperature and the confinement time. This in turn, is fed back to the systems studies improving the modeling. After a few iterations back and forth between the systems studies and the transport simulations, a consistent design is obtained. The 'final' set of major input parameters for the systems studies is summarised in table 2.
In the next section, this approach is used for option A. First the systems studies are discussed and afterwards the transport simulations. However, one has to keep in mind, that these are not separated but are actually interconnected and the results presented are an outcome of several iterations back and forth between both tools.

Option A
As the rationale for option A is to be a small device which should be realisable on a fast track, i.e. shortly after W7-X has demonstrated the achievements of optimisation and steadystate operation, the device should mostly employ today's technology or technology expected to be ready in the near future. This option can thus be regarded more as a scientific experiment to clarify the gaps in physics mentioned earlier. In this approach it is expected that reactor-relevant technology is developed for a tokamak DEMO which should then be transferable to the HELIAS line.
Under this guideline, a subset of goals can be defined in addition to the high-level goals of the last section. Being more a scientific experiment on a near time-scale, it is not a requirement for this option to produce electrical power. Rather, a fair amount of fusion power is required to achieve plasma parameters relevant for reactor conditions. To be more precise, not the amount of fusion power is the real design constraint for option A, but the required alpha pressure in terms of α f p, and the fusion gain Q. However, as a detailed specification for these parameters is still lacking and subject of ongoing research, the fusion power as been taken as proxy for the design constraint.
Using transport simulations (see section 4.2.2) and varying density and heating power, it was found, that the achievment of = P 500 fus MW for option A provides sufficiently high values of α f p, and Q. If the plasma is driven with 50 MW of external heating power, Q = 10 is achieved which is also the goal for ITER. At the same time the normalised alpha pressure in the centre of the plasma reaches values of = α f 7 p, ,0 % compared to 11% in option C and 18% in HELIAS 5-B. However, it remains to be shown by theoretical studies whether these values are sufficient to study the properties of a 3D burning plasma. Once more precise predictions are available, α f p, and Q will be used as constraints in future design studies.
Consequently, a blanket is not assumed and only a shield is considered to protect the coils. Without the blanket, space should be available to have an aspect ratio similar to that of W7-X with A = 10.5. To further save costs, NbTi superconductor technology is assumed for option A. The device will be designed for steady-state operation as this is one of the great advantages of the stellarator concept. Based on helium cooling technology, about 100 MW of pumping power are assumed [49]. High-pressure gaseous helium cooling has advantages in terms of safety considerations [50] and in view of power plant requirements. On the physics side, 5% Helium is assumed in the plasma as 'ash' and the volume-averaged temperature is fixed to = T 7 keV. Correspondingly, the renormalisation factor representing the confinement enhancement with respect to the empirical confinement time scaling law ISS04 was limited to (i.e. the systems studies have been iterated in combination with detailed transport simulations, discussed in section 4.2.2). For comparison, the confinement enhancement in W7-X is expected to be on the order of ≈ f 2 ren W7X [48]. For the controlled particle and energy exhaust, the island divertor concept is assumed which was succesful during operation of W7-AS and will be further qualified in the later operation phases of W7-X. The island divertor model assumes cross-field diffusion and radiation around the X-point in combination with a geometrical represenation [44]. The heat-load limit on the divertor is specified to be = q 5 div max MW m −2 which has been proposed as the limit for power plants considering the material constraints under high neutron fluences [51]. Due to the low neutron fluence in option A one could also discuss a higher limit. As input for the divertor model the perpendicular heat diffusion coefficient was set to χ =  Table 2 summarises the para meters of option A and compares them to option C (described later).

Design window analysis-option A.
For the design window analysis of option A, the main engineering parameters (i.e. the major radius and the magnetic field strength on axis) were systematically varied within a predefined range of R = 12-15 m and B t = 4.0-5.6 T. Both the high-level and the above-mentioned subsequent goals have been taken as constraints / limits and held constant in the systems studies. Thus, every design point is set to reach 500 MW fusion power. To achieve this while varying device size and magnetic field, the density, the external heating power and the confinement enhancement factor were used as iteration variables. The corresponding result for option A is shown in figure 4 where isocontours of the volume-averaged thermal plasma β , the average neutron wall-load Γ NWL , and external heating power are highlighted as important parameters.
It should be noted that due to the 3D topology and the resulting higher complexity of the systems code models, the calculation time for a single run of a HELIAS design point is on the order of a few minutes on a modern CPU. For the design window analysis presented here a resolution of × 16 16 for the varied engineering parameters was chosen corresponding to ∼ 1 d calculation time per figure [52].
As can be seen from figure 4, reasonable beta-values in the range of 3-5% can be obtained in the engineering parameter range considered (blue lines). While the beta-limit is a strongly limiting factor for the HELIAS reactor studies, it's importance for the intermediate-step stellarator, option A, is rather low. Linear stability predicts the beta-limit to be in the range of β = 4.5%, but stellarator experiments have demonstrated the capability to operate above this limit [53] such that beta may be ultimately limited by stochastisation of the plasma edge and corresponding destruction of flux surfaces and shrinking of the plasma volume. However, these effects are much reduced in a HELIAS due to the optimisation of the magnetic configuration. Such a beta-limit has been predicted to be in the range of 5-6% [54]. In the design window analysis of option A, the isocontours of the external heating power and beta are nearly parallel. Already at β = 4.5%, an external heating power of 50 MW is required. It would not seem desirable to select a design requiring more heating power which reduces the fusion gain Q, and the beta-limit therefore does not play a role.
However, since the plasma is maintained by external heating using ECRH, the cut-off density of O1-mode heating must be taken into account. The magnetic field provides a highly localized resonance for O1-mode ECRH heating at B t,max near the magnetic axis. As the considered magnetic configurations have a mirror term for the magnetic field strength of around 10% in the plasma center, the (cold) resonance is . For example at B t = 4.5 T the resonance is at 5 T which would be exactly the O1-resonance for the 140 GHz W7-X gyrotrons. The cut-off for O1-mode heating is then ⋅ 2.4 10 20 m −3 which leaves about 10% of margin with respect to central densities on the order of ⋅ 2.2 10 20 m −3 . Access to lower fields than B t = 4.5 T is therefore problematic as the cut-off density decreases with B 2 , i.e. at B t = 4.0 T it drops to ⋅ 1.85 10 20 m −3 .
As outlined above, the systems studies have been iterated in alternation with 1D transport simulations and the confinement enhancement factor was set accordingly to ⩽ f 1.8 ren . Since considerable external heating power is used to maintain the plasma, the confinement has a relatively small effect on the beta contours. However, the required external heating power is very sensitive to f ren as an overall degradation of the confinement from = f 1.8 ren to 1.6 would double the required heating power, e.g. from 50 to 100 MW. This illustrates how critical it is to accurately predict confinement. While advanced optimisation procedures should ensure that the magnetic configuration for an intermediate-step stellarator has good confinement properties, recent advances in gyrokinetic simulations of stellarator geometry [55] and the comparison with upcoming experimental results of W7-X are anticipated to increase the predictive capability of transport codes.
The average neutron wall load Γ NWL (orange) varies only moderately over the engineering range considered. This is clear as the fusion power is constant and only the first wall area is changing with size, i.e. decreasing the device size by 1.5 m from 13.75 to 12.25 m increases the neutron wall load from 0.4 to 0.5 MW m −2 . Consequently, the neutron wall load is a factor three lower than in a HELIAS power plant, but still high enough for e.g. material testing, especially as the device could be designed for steady-state. However, without further material qualifying, the lifetime of componentes and the device is limited by the neutron damage in terms of displacements-per-atom (dpa). Isocontours of other parameters are not shown in figure 4 to retain clarity. E.g. the radiation fraction, which is required in the scrape-off-layer (SOL) to reduce the heat load of the divertor to 5 MW m −2 must be for the maximum considered size on the order of 40% and increases to 50% for the smallest device sizes. Impurities in the plasma core for additional radiation have not been considered here but will be included in future studies.
Another engineering parameter which is often of interest is the stored magnetic energy in the coil system which is a proxy for the required support structure. For the smallest device size at low field this value is on the order of = W 30 mag GJ and increases up to 50 GJ for the highest field and largest size.
The systems studies suggest that NbTi can be used to achieve the desired fields, however the maximum field on the surface of the coils is for e.g. R = 14 m and B t = 4.5 T on the order of ≈ B 10 max T. To push NbTi to such a high field, super-critical helium cooling at 1.8 K is needed requiring a higher effort for the cooling systems. It should be noted, that the NbTi critical current density scaling was obtained from W7-X and the calculations for the maximum field on the coil subsequently verified against W7-X. The device considered here, however, is nearly a factor three larger than W7-X (in terms of the major radius) which may result in some deviations and an error of about 10% is easily imaginable, but is sufficient to distinguish between the requirements for normal (4.2 K) and critical helium cooling (1.8 K). For comparison, in the more detailed 'HSR 4/18i' HELIAS study [4] NbTi could be employed with normal helium cooling with 4.5 T on axis by trapezoidally shaping the winding pack and thereby reducing the maximum magnetic field on the coils. A more detailed engineering study is required to clarify this aspect for option A.
The results of the design window analysis for option A may suggest higher fields to reduce the device size. But with higher field on-axis also the maximum field at the coils increases. According to the argument above it is unlikely that NbTi can be employed for fields up to 5.5 T. Nb 3 Sn could be used to achieve this, but this would considerably increase the costs of the magnets and negate the savings due to reduced device size.

1D transport scenario-option A.
In order to make predictions about the expected confinement in next-step devices such as an intermediate-step stellarator, a 1D transport code [48,56] is employed which solves the power balance for the electrons and ions and calculates the neoclassical energy fluxes given DKES [57,58] data sets. Additional anomalous energy fluxes are considered at the plasma edge based on experimental data from W7-AS [59][60].
In order to carry out predictive transport simulations for an exemplary design for option A, a suitable magnetic configuration has to be defined. As dedicated configurations for such a next-step device are still a topic of ongoing research, the existing W7-X 'high-mirror' configuration was selected due to its reactor-relevance. The DKES database has been prepared for a β = 4% equilibrium to account for finite beta effects. The dimensionless nature of the DKES approach allows a linear upscaling of the magnetic configuration. The configuration has been scaled by a factor 2.5 which corresponds to the design point found in systems studies with a major radius of R = 14 m. The magnetic field on-axis has been set to 4.5 T accordingly. Additionally, 50 MW of ECRH steady-state external heating power are assumed with central deposition modeled by a Gaussian profile to reach the desired fusion power of 500 MW. The associated 100 MW of internal alphaheating are self-consistently taken into account in the code.
For the density a 'standard' profile has been selected and kept constant to avoid a fuelling scenario which requires detailed knowledge of particle sources and sinks. In fact, density control in large stellarators is generally problematic and requires central sources such as pellet injection to avoid hollow density profiles [28]. This is beyond the scope of this work, but will be investigated in future studies.
Regarding the anomalous transport, as so far no better quantitative assessment exists, the anomalous heat conductivity has been described by in terms of the empirical ISS04 scaling. As already stated, this result, including the density and temperature profiles and values, have been taken as input for systems studies of option A.

Option C
While 'option A' represents a bounding scenario for a small, fast-track intermediate-step stellarator, 'option C' in contrast is meant to be an upper boundary scenario for a large, DEMO-like device employing reactor-ready technology. Consequently, a pre-requisite of option C is the research and development of reactor-relevant technology similar to a tokamak DEMO [16] which is usually defined as a device demonstrating an integral workable solution (i.e. concerning all components) for a fusion power plant. DEMO must not be economically competitive but allow extrapolation to commercially attractive applications. The essential difference between option C and a tokamak DEMO would be the fact, that the tokamak line can rely on the burning plasma experiment ITER. Option C, in contrast, would be a direct step from W7-X and as explained ealier, the step in physics and engineering parameters larger than that from ITER to DEMO.
As for option A, a set of concept-specific sub-goals can be defined for option C which need to be realised in addition to the high-level requirements outlined in section 3. Under the premise of a DEMO-like device, option C should produce a reasonable net amount of electricity, set here at 200 MW, to demonstrate the power plant capability of the concept. Consequently, a full blanket and shield are required and enough space must be foreseen to accommodate these components. As a result, the aspect ratio is increased to A = 12 compared to A = 10.5 for option A. This value is based on the HELIAS 5-B engineering study [13] where the aspect ratio was raised to A = 12 to accomodate enough space for blanket and shield. The power conversion system of thermal to electric energy is mainly dependent on the chosen coolant which determines the thermal conversion efficiency η th . Common technologies employ either pressurized water or gaseous helium cooling. Water cooling is a well established technology requiring a moderate amount of pumping power but has a lower efficiency compared to helium. In turn, helium cooling requires a much higher pumping power. A detailed discussion of the advantages and disadvantages of both systems is still ongoing in the fusion community. In this work, the Brayton power cycle with helium cooling technology has been chosen for the cooling system due to the possibility of working at higher temperatures and avoiding the unresolved safety issues regarding water cooling [50]. This is also consistent with the European 'helium-cooled pebble bed' (HCPB) blanket concept [61]. Additionally, the higher thermal conversion efficiency, η = 0.4 th , compensates for the higher pumping power, = P 150 pump MW, assumed here [49,62].
Further, Nb 3 Sn is foreseen as superconductor, which could also be a possible conductor for a HELIAS power plant. Similar to option A, the device will be designed for steadystate operation. According to the detailed predictive physics transport simulations, see section 4.3.2, which have been iterated with the systems studies, the helium 'ash' is set to 5% and the volume-averaged temperature to = T 9 keV. Correspondingly, the renormalisation factor representing the confinement enhancement with respect to the ISS04 confinement time scaling law was limited to It may seem surprising that the confinement enhancement factor from option C is different to that from option A. However, this is due to the paradigm change of the underlying scaling relations. In the regression of the empirical confinement time scaling it is assumed that the heating power P is an independent parameter. Under fusion conditions, however, alpha particles heat the plasma and the heating power is, therefore, no longer a free parameter. Instead, it is interconnected to the plasma volume, plasma beta, and the magn etic field. As such, τ E scales differently for a reactor than for an experimental scenario where the heating power can be externally adjusted as an independent parameter. This has been explained in detail in [43]. The sub-goals of option C are summarised in table 2.

4.3.1.
Design window analysis-option C. Again, the highlevel requirements and the above-mentioned sub-goals have been taken as constraints for the design window analysis of option C. This time the major radius was varied in the range R = 15-20 m and the magnetic field on-axis between B t = 4.5-5.6 T while the density, the confinement enhancement factor as well as the external heating power were taken as iteration variables. The corresponding result for option C is shown in figure 6 where isocontours of the volume-averaged thermal plasma β , the average neutron wall-load Γ NWL , and external heating power are highlighted.
A first result which can be inferred from figure 6 is the fact that, under the given confinement and size constraints, the design points within the systems study are not ignited. The black curves show the required external heating power which is needed to fulfill the power balance. Again, the betacontours (blue) run approximately parallel to the heating power contours. The plasma beta takes reasonable values of … 4 5% in the range between 50 and 100 MW external heating power. Consequently for option C, the beta-limit also does not play a large role unless one would be restricted in the achievement of higher field strengths. But as outlined above, Nb 3 Sn superconductor is envisaged from the beginning for this option allowing a higher maximum field on the coil and therefore magnetic field strengths of up to 5.5 T on-axis should be unproblematic. In particular for R =18 m and B t = 5.5 T, the maximum magnetic field on the surface of the coils is about ≈ B 12 max T which is consistent with Nb 3 Sn technology and normal Helium cooling (4.2 K). As already shown in the systems studies for HELIAS power plant devices, the contours of construction cost are rather flat with respect to the magnetic field, i.e. it is very desirable to employ a high field for option C.
At a field of about 5.5 T on-axis (6 T including the mirror term), the ECRH cut-off is at ⋅ 3.5 10 20 m −3 , and therefore not a concern for the systems studies and the achievable density. Even in the centre of the plasma, a density not higher than ∼ ⋅ n 2.0 10 e 20 m −3 is required, see section 4.3.2. Since the considered range of device sizes is greater for option C than for A it follows that the average neutron wall load Γ NWL (orange) also has a broader variation over the whole design window analysis between 0.5-1.0 MW m −2 . This is mostly due to the change of first wall area with changing major radius. However, as seen from figure 6, the isocontours of the neutron average wall load are not horizontal lines as for option A, but rather decreasing with increasing magnetic field. This is simply due to the fact, that for lower magnetic field the confinement time is lower and the required heating power must increase. As the net electric power is held constant, the density and fusion power must increase to provide additional gross electric power to sustain the additional heating. Thus, the higher fusion power for lower magnetic field leads directly to an increase of neutrons. At 4.5 T the required fusion power is about 1400 MW and can be reduced to 1100 MW for 5.5 T on-axis at a constant net electric power of 200 MW.
For the same reasons also the required radiation fraction in the SOL varies over a wider range from 60% for the largest device and field up to 80% for the smallest. And the stored magnetic energy in the coil system varies vice versa from 60 GJ to 130 GJ.
Similar to option A, the required external heating power is rather sensitive to changes in the confinement enhancement factor f ren , which was set here according to the 1D transport simulations to / ⩽ τ τ . However, for option C not only the external heating power would change but also the betacontours would shift to lower fields as for option C considerable heating power is coming from the fusion alphas. The transport simulation for option C are discussed in the next section.

1D transport scenario-option C.
The same methodology for the predictive transport simulations is applied here which was already used for option A. Again, the W7-X 'highmirror' configuration was selected for its reactor relevance. However, the aspect ratio of this magnetic configuration is with A = 10.5 not the same as the one used in the systems studies of option C with A = 12. Therefore the configuration has been scaled such, that the plasma volume corresponds to the design point with R = 18 m. It is clear that this is not completely consistent, but is nevertheless a reasonable approximation. Dedicated magnetic configurations for an intermediate-step HELIAS will be further optimised and are therefore expected to have better confinement than the results derived based on the W7-X 'high-mirror' configuration.
For the simulation a high field has been chosen with B t = 5.5 T and the external heating power by ECRH adjusted to 50 MW with a Gaussian profile and central deposition. The alpha heating power is self-consistently taken into account in the simulations. Again as for option A, a standard flat density profile has been used and kept constant and the anomalous heat conductivity-described by The simulation results were taken as input for the systems studies of option C and have been iterated until both the design window analysis and the 1D simulations were in agreement.

Step-ladder including options A and C
With the presented design window analysis of options A and C and the corresponding parameters, it is now possible to include these cases in the step-ladder approach of the Wendelstein line, see figure 8.
One can see, that an intermediate-step stellarator helps to strongly reduce the gap between W7-X and a HELIAS power plant (one should keep in mind that the figure is logarithmic). Thus, the step between W7-X and option A is similar to the step between W7-AS and W7-X or to compare it with the tokamak line, similar to the step between JET and ITER.

Economic comparison
As the options presented here for an intermediate-step stellarator represent boundary cases with quite a conceptual difference between option A and C, it is meaningful to carry out an economic comparison in order to rate the effect of the respective sub-goals on the construction costs.
The current version of PROCESS accommodates a basic cost-model with which it is possible to estimate the construction costs of a design point based on the total sum of material costs. In fact, the systems code PROCESS can calculate for each component of a fusion device the size. Each component is described by a material or even several materials. Based on the size of the components and the material densities the total weight for each material can be estimated. Every mat erial in turn is associated with a specific cost-perweight which allows estimation of the costs of each component and in total the direct costs of the device as a sum of all individual comp onents. The direct costs are complemented by indirect costs which are a flat rate of the direct costs and represent together the total construction costs. A cost penalty for the complexity of components is not yet included in the model (costs of certain components may thus be underestimated). The PROCESS cost model has been benchmarked with the dedicated cost analysis code FRESCO which showed a reasonable agreement for the total costs of a tokamak test case with about 20% difference [63]. The cost estimates are obtained from the PROCESS cost model and will be given  Step-ladder plot for the HELIAS line. The figure shows operation windows of W7-AS and W7-X in dimensionless engineering parameters with isocontours of dimensionless physics parameters at constant n * . The W7-X operation windows refer to operation phase 1 (OP1) and 2 (OP2) for X2 and O2 heating, respectively, where n * has been adapted to ECH cut-off densities. 'HELIAS 5-B' is an engineering-based reactor study [13]. The dotted line is the projection of the collisionallity of W7-X into the plane of HELIAS 5-B. In addition, the design window of the intermediate-step stellarator options A and C are shown in red. here as 'PROCESS currency units' (PCU) since the cost analysis is carried out for all devices in the same framework allowing a relative comparison between the individual devices while absolute values should be taken with care. For this comparison, favourable design points are selected from each design window analysis and compared in a costbreakdown. For option A, a medium-sized low-field device was selected with R = 14 m and B t = 4.5 T while for option C, a high-field, larger device seems to be a favourable design point with R = 18 m and B t = 5.5 T; important parameters are summarised in table 3. The total construction cost of both these design points have been broken down into their major contributions, which are the magnets, the blanket (including the shield), the buildings, the equipment and indirect costs. The results are shown in figure 9. Additional to these design points, the total construction costs of a HELIAS power plant and an 'equivalent' tokamak (Model B of the European PPCS study [25]) are presented as reference which have been discussed in [18].
It should be noted that the 3D complexity of the stellarator will most likely increase the magnet costs, but this has not been taken into account here. However, while the modular coils of a HELIAS are rather small (even for power-plant size they are comparable to the ITER TF-coils [15]), the poloidal and toroidal field coils of the tokamak case are much larger. That means, while the HELIAS coils can still be produced by industry and shipped to the construction site, the tokamak coils, on the other hand, must be built on-site or transported by 'unconventional' means. This requires a dedicated facility increasing the magnet costs for the tokamak, but which so far is also not taken into account. Thus arguments for cost increases can be found for both concepts and should be considered in future studies.
A very striking result from this comparison as seen in figure 9 is the fact that the cost difference between the boundary cases option A and C is about a factor two. In particular the magnet costs contribute to this difference which are much higher for the DEMO-like device than for the near-term step. This is attributed to two reasons. First, option C is a larger device with higher field and requires therefore a higher amount of superconducting material and second, the costs for Nb 3 Sn are considerably higher than for NbTi. This confirms the strategy to employ NbTi for the near-term device.
The costs for the blanket are of course higher for option C which foresees a full blanket concept in contrast to option A with solely a shield. However, in this analysis the total blanket costs are a rather small fraction of the total construction costs. It is unclear if this is an underestimation compared to the other costs since the blanket is also a complex component for a HELIAS device. In addition, little practical experience exists. As already stated above, the complexity of components is not yet considered for the costs, but is relevant for future studies. The upgrade of the cost model is an ongoing and continous process.
Also the building and equipment costs are higher for option C which is understandable as option C requires more buildings and equipment for the power conversion systems in order to produce a net amount of electricity.
In comparison to a HELIAS power plant design point, option A would require only a third of the construction costs, while option C reaches two-thirds of the costs of a power plant. If one were to model an idealised version of ITER [64] in PROCESS, the construction costs would lie nearly in the middle between the exemplary design points of HELIAS option A and C.
Although PROCESS has been developed for modelling of power plant devices, it is possible to also model W7-X. However, the uncertainties associated with this analysis are rather high. With respect to the cost analysis presented in figure 9, option A would be about three times more expensive than W7-X.
Using the actual costs of the W7-X construction (until 2014) as a reference for real costs and applying this scaling to the costs of ITER given by PROCESS, one realises that the PROCESS ITER costs scaled as real costs are about a factor three lower than the current estimate of the actual ITER costs Figure 9. Total construction costs obtained from the PROCESS cost model in 'PROCESS currency units' (PCU) broken down to major costing accounts for exemplary design points of option A, option C as well as for a HELIAS power plant and an exemplary tokamak reactor (similar to Model B of the European PPCS study [25]). [65]. How much this discrepancy can be attributed to the limitations of the PROCESS cost model and how much of this is due to the project structure and first-of-a-kind nature of the ITER enterprise is unclear.

A remark on tritium
As option C should be designed with a tritium breeding ratio larger than one, the tritium supply should be self-sufficient apart from the start-up inventory. Tritium supply for option A, in contrast, needs to be supplied from external sources due to the lack of a blanket. Comparing with the ITER fusion burn phase, tritium consumption could be on the order of one kilogram per year [66] for ∼ 5 years.
Nonetheless, in either of the presented options for an intermediate-step stellarator, a tritium start-up inventory is required to initiate operation of the devices. One of the main commercial tritium sources are the Canada deuterium uranium (CANDU) type pressurised heavy-water reactors which have a total supply capacity of several kilogram tritium per year. The shutdown of the CANDU type reactors would thus have a great impact on the tritium supply. However, recently discussions started regarding a 30 year life-time extensions of these reactors [67] potentially improving the situation for tritium supply in the upcoming decades. Once a 'fleet' of fusion power plants is running, the surplus of produced tritium can be used for the start-up of new fusion power plants. Apart from that, other possibilities exist to breed tritium commercially [66].
Costs for tritium have not yet been taken into account in the cost assessments since the estimation of the tritium start-up inventory of a stellarator power plant are still too vague. The resulting contribution of the tritium start-up inventory to the total construction costs and, for option A, also the operation costs cannot be calculated.

Summary and conclusions
This work is thought of as a starting point for a more in-depth discussion of a research strategy leading from Wendelstein 7-X to a HELIAS power plant. The experimental results of Wendelstein 7-X, which has just started operation, will of course play an essential role in the continuing refinement of this analysis. In particular, the better understanding and modelling of turbulence as well as the verification of stellarator optimisation will allow a more refined prediction of the confinement in next-step devices. Further aspects are the investigation of suitable plasma scenarios with impurity and density control (pellet injection) and the plasma stability at high β (5%).
Looking at the extrapolation from W7-X to a power plant, three approaches or viewing perspectives have been presented. They shed light on the level of extrapolation required or in other words they indicate the gaps in physics and engineering parameters which have to be bridged. Selected physics and engineering parameters (e.g. energy of the magnet system, stored energy in the plasma, heating power, P/R, fusion power gain, triple product), already show increases by orders of magnitude when going from W7-X to a power plant. Other quantities (plasma β, average magnetic field) need no or only moderate extrapolation which is a particular property of the HELIAS concept. Considering the scientific progress which has been made since the optimised design of W7-X was frozen, a further refinement of the optimisation seems possible and also meaningful. This concerns, in particular, the fast-ion confinement and the inclusion of the turbulent transport in the optimization procedure. Finally, combining dimensionless physics quantities with dimensionless engineering parameters and employing empirical confinement scaling laws show the necessary steps between different experiments or fusion devices in a more rigorous way. Comparing the HELIAS development to the tokamak line, from ASDEX Upgrade and JET to ITER and a tokamak DEMO, it becomes clear that between W7-X and HELIAS 5-B the step or gap is much larger than between JET and ITER or ITER and DEMO.
Taking these arguments together, two possible options for filling this gap are investigated. Based on a tentative list of high-level requirements, guidelines for the conceptual study of an intermediate-step HELIAS are developed. The two options represent different levels of sophistication and basically can be considered as bounding cases for such a device. Option A is defined as a reasonably small fast-track device, while option C is a DEMO-like device with net electrical power output. For option A, the fusion power is fixed to a value comparable to ITER (500 MW). Selecting an example within the design window analysis, this suggests a device with a major radius of 14 m, an average magnetic field on axis of 4.5 T and a fusion power gain of Q = 10. The moderate magnetic field allows the use of conventional NbTi superconductor. This may require supercritical helium cooling but needs a more detailed engineering assessment. For option C, a fixed net electrical power of 200 MW is assumed. This results in a larger device (R = 18 m) with a larger aspect ratio (A = 12 instead of 10 for option A), a larger magnetic field (5.5 T) and a significantly higher fusion power of 1100 MW. The higher magnetic field requires a different type of superconductor. Nb 3 Sn, as used for the ITER toroidal field coils, would fulfil this requirement. With a fusion power gain of Q = 20, this device would still not be ignited.
A first cost assessment indicates that option C is more expensive by approximately a factor of two, ignoring the costs for tritium. Option C requires a start-up inventory, while option A depends on a continuous tritium supply as it does not have a breeding blanket.
As the options A and C represent bounding cases, of course any compromise between them is conceivable. The further development and refinement of the conceptual design of an intermediate-step HELIAS will depend on the validation of the optimisation principles by W7-X, on the advancement of the theoretical understanding of confinement and stability of optimised stellarators and on the capability to extrapolate to a fusion power plant. Moreover, the exact design will also depend on the general development of fusion technologies and how easily these can be transferred to such a device.