Techno-Economic Optimization of the NbTi DTT Feeders

The superconducting (SC) coils of the Divertor Tokamak Test (DTT) facility will be connected to the current leads by a set of SC feeders, currently designed as cable-in-conduit conductors wound using commercial NbTi strands to be cooled by Supercritical Helium at 4.5 K. The feeders are immersed in the magnetic field generated by the SC coil and plasma outside of magnet system, so that the maximum field on the most loaded feeder can reach 4 T at the full rated current (including the self-field effect). Here the performance of the feeder conductors is assessed during a plasma pulse, based on the DTT standard text single-null operating scenario, for the most loaded feeder of the Central Solenoid and of the Toroidal and Poloidal Field coils, computing the minimum temperature margin to current sharing throughout the plasma scenario. Several alternative cabling configurations are analyzed, designed to withstand the nominal current at the peak field with a different number of SC and stabilizer strands. The minimum temperature margin is evaluated as a function of the material, manufacturing and operational costs of the different alternative feeder layouts. Based on such techno-economical characterization, the optimal (cheapest) design of the feeder cables is identified.


I. INTRODUCTION
In the framework of the European Roadmap to Nuclear Fusion [1], the DTT (Divertor Tokamak Test) facility [2] is currently under construction at ENEA, Frascati. The machine is fully superconductive [3], similarly to the largest tokamaks in operation (e.g. KSTAR [4] and EAST [5]), commissioned (JT-60SA [6]) and under construction (ITER [7], SPARC [8]) worldwide. Like in the JT-60SA design, the current to the superconducting (SC) magnets arrives from the power supply at room temperature through the busbar to the current leads, contained in the Cold Terminal Boxes (CTB). The current leads transfer the transport current from their ''hot'' termination at room temperature to their ''cold'' termination at cryogenic temperature, electrically joined to the SC feeders. In turn the feeders, contained inside three cryolines that protrude out of the cryostat surrounding the tokamak in the The associate editor coordinating the review of this manuscript and approving it for publication was Vlad Diaconita . tokamak hall, transfer the transport current to the SC coil, see Fig. 1.
The current design of the feeders consists of cable-inconduit conductors (CICC) [9] wound using commercial NbTi strands to be cooled by Supercritical Helium at 4.5 K [10]. The feeders are immersed in the magnetic field generated by the SC coils and plasma outside of magnet system, so that the maximum field on the most loaded feeder can reach 4 T at the full rated current (including the selffield effect). A first design of all feeders has been already performed in DC condition, checking that the temperature margin to current sharing T CS at the nominal current is > 2K for all feeders [10]. This first design step was quite straightforward, since it was based on a well-established scaling for the strand critical current [11], considering the nominal operating temperature of 4.5 K. In DC condition, the temperature computed along the feeders turned out to be totally acceptable in view of the short length of the feeders and of a small effect of the radiative load from the thermal shield, and Joule losses foreseen in the joint to the coil cables.
However, the design so far has not been checked yet in operative (transient) conditions during a plasma pulse, where on one hand, for the pulsed coils (Central Solenoid CS, and Poloidal Field PF coils), the current and induced magnetic field variation lead to significant heating in the cable due to AC losses, while, on the other hand, the feeders of the DC Toroidal Field (TF) coils -where AC losses are expected to be very small -are subject to nuclear heating [12]. Note that the conductor design in DC conditions could be not optimal for the AC conditions of the pulsed coils, in view of the strongly transient nature of the heat load deposited in the conductor.
The aim of this paper is to perform a techno-economical assessment of the DTT feeder conductors, considering also their transient performance. Based on the DTT standard operating scenario, here the performance of the feeder conductors in operation is assessed in terms of the minimum margin T min CS throughout the standard single-null plasma scenario. In the margin assessment, the radiative load from the thermal shield inside the machine cryostat, as well as the Joule heating in the terminations is accounted for. Several possible alternative designs are considered for the most critical feeder for the CS, PF coils and TF coils. The related variation of the minimum T min CS is investigated as a function of the cost related to the cable design (number of SC and stabilizer strands) and to the cryo-plant burden to remove the operational heat load. The design leading to the minimum cost while still complying with a T min CS > 2K is then identified.

II. METHODOLOGY
The techno-economic optimization performed here is based on one side on the evaluation of the conductor performance in terms of compliance with the hot spot temperature criterion and minimum temperature margin criteria. The hot spot temperatures, T HS , have been calculated by solving the adiabatic hot-spot model [13] in (1): where T op is the operating temperature, ρ is the electrical resistivity of the Copper (Cu) (Residual Resistivity Ratio = 150),c is the averaged heat capacity per unit volume, and J Cu is the current density after quench. In the calculation, it is assumed, conservatively, that all the current flows in the Cu cross-section A Cu . The temperature-and field-dependent resistivity of Cu is taken from [14] and [15]. The delay time starting from the origin of the quench until the beginning of the current discharge is set to 1.5 s, whereas the characteristic time constant of the circuit following a quench is set to 5 s. The averaged volumetric heat capacity is calculated as in (2), where θ is the angle between the feeder axis and the strand axis and A TOT is the total cross-section: The heat capacity data per unit volume (c p ) are taken from [16], [17], and [18] for solids and from [19] for the Helium (He). The adopted criterion on T HS is such that during a quench it should not exceed 150 K (T HS,1 ), accounting for the heat transfer to the (stagnant) helium. If only the Cu and NbTi are considered (A He = A SS = 0), then the maximum allowable adiabatic hot spot temperature is set to 250 K as done in ITER (T HS,2 ).
The temperature margin to current sharing T min CS is defined on the basis of the local current sharing temperature T CS (x) and of the local strand temperature T St (x) as In (3), x is the local coordinate along the feeders and L is their length. The thermal-hydraulic analysis for the performance assessment has been performed using the software OPENSC 2 [20]. A mass flow rate between 0.1 g/s and 10 g/s of Supercritical Helium (SHe) at 0.5 MPa and 4.5 K has been considered as coolant, in all cases entering the conductor from the high-field side. Joule heating is accounted in the 0.47 mlong joints (joint resistance = 5n ) located at both inlet and outlet of the feeder. Radiation from the thermal shield at 80 K has been conservatively considered on the 70% of the external surface of all feeders (emissivity ε = 0.89), while conduction heating from feeder supports is neglected in view of the lack of information about the mechanical support of the feeders.
On the other, more economical, side, a cost function for the feeders (C tot ) is built here, based on features that are related both to their manufacturing (C SC+Cu ) and to the operating costs (C cryoplant ) as in (4).
The manufacturing costs are related to the manufacture complexity and are split here in costs per unit length for a NbTi strand (C NbTi ) and a segregated copper strand (C Cu,segr ), to be multiplied by the number of SC strands N SC and copper strands N Cu,segr , respectively, and the cost of the cabling per unit length C cabl−jack : The actual values considered here for the specific costs of the strands are 150 = C/kg for the NbTi and 42 = C/kg for the segregated copper, whereas the average linear density is 4.2 kg/km and 4.7 kg/km for a NbTi and a Cu strand, respectively. The cabling is rated to 400 k = C/km for a conductor with 5 cabling stages.
As far as the cryoplant is considered, C cryoplant is given by the sum of three contributions, and namely the cost of heat removal at cryogenic temperature C power , the maintenance cost C maint and the pumping cost C pump . The last two are considered negligible in this analysis since the contribution due to the feeder to the total maintenance and pumping costs can be considered negligible when compared to that due to the cooling of the rest of the magnets, so that The contribution of C power is proportional to the average power to be removed at cryogenic temperature from the feeders P ave . Note that, if we consider an inverse thermodynamic cycle operating between the ambient temperature T amb and the cryogenic temperature T op , the power removed at cryogenic temperature gives the electrical power P feeder that is needed to provide such cooling if the inverse cycle has an efficiency η (here 20% as suggested in [21]): The annual operating costs of the cryoplant are then given by (8), where θ represents the operating hours/year and e the electricity cost.
The methodology followed for the optimization of each feeder is depicted in the flow chart in Fig. 2.

III. ALTERNATIVE FEEDER CONDUCTOR LAYOUTS
The first design of the DTT magnet feeders, together with their routing in around the tokamak, has already been described and discussed in [10]. For the 6 CS modules, 2 feeders per module are present and sized to transport a current of 32 kA at the peak magnetic field of 4 T. For the 6 PF coils, 2 feeders per coil are foreseen and sized again to transport a current of 32 kA but at a lower field (3.1 T). The 18 TF coils are connected in series in groups of 6 coils: they present 3 × 2 feed-and-return feeders and 3×5 jumpers, connecting two TF coils. The transport current for the TF coils feeders and jumpers is 42.5 kA, with a peak field of 1.4 T. All the feeder conductors are designed as 5-stages twisted cables, assembled using commercial NbTi strands (with 1914 0.011-mm SC filaments) with a diameter of 0.82 mm and, if needed, pure Cu segregated strands as stabilizer. All cables are contained in rectangular SS316L conduits (see Fig. 3) with different dimensions, according to the final number of strands, and void fraction around 35%, resulting in classical 1-region CICC, for which a 3-mm prepreg fiberglass insulation layer is foreseen.
From preliminary analysis of the feeder DC performance [10], the 16.6 m-long CS3U2 feeder, the 7.3 m-long PF61 feeder and the 3.25 m-long TF jumpers turned out to be the most critical ones, i.e. the ones with the minimum temperature margin to current sharing T min CS , defined as the minimum local difference between the current sharing and the cable operating temperatures.

A. CS FEEDER LAYOUTS
Three alternative layouts (B, C, D layouts in Table 1) for the CS feeders were developed and analyzed on top of the baseline layout (layout A in Table 1) already presented in [10].  The alternative layouts are developed based again on the scaling from the critical current in [11], but with a progressively reduced number of SC strands N SC and increasingly higher number of segregated Cu strands N Cu,segr . While the first and the last of the cabling stages are kept fixed to the classical twisting pitch of 3 triplets of (SC/Cu) wires, and 6 petals, respectively, the intermediate stages are modified from the original 5 × 5 pattern (layout A) to 3 × 5 (layout B), 4 × 5 (layout C) and eventually 3 × 3 (layout D). As a consequence of the almost constant void fraction of the conductor, the dimensions of the conductor (h and w in Table 2, see Fig. 3) also vary.

B. PF COIL FEEDER LAYOUTS
Two alternative layouts (B1 and C1 in Table 2) were developed and analyzed for the PF coils, in addition to the baseline layout (A1 in Table 2) [10]. Again, the number N SC in decreasing throughout the alternatives, and they also differ for N Cu,segr and for the conductor cross section dimension. For these feeders, the cabling pattern was varied from the original pattern of (1 SC + 2 Cu) 3 × 3 × 3 × 6 (layout A1) modifying the last two stages in 3 × 5 (layout B1) and 4 × 4 (layout C1).

C. TF COIL FEEDER AND JUMPER LAYOUTS
The same alternatives analyzed for the PF coils were retained for the analysis of the TF feeders as well.

A. EVALUATION OF THE AC LOSSES
The reference model for the AC losses adopted here is sketched in Fig. 5, where the coupling currents in the wires with twisted filaments are shown.
The overall AC losses are then given by the sum of the contribution of the coupling losses M c , of the hysteresis losses  M h and of the dynamic resistance losses V d as [23]: The three contributions are detailed in (10)- (12).
being d the filament diameter, the reduced current i defined as the ratio of the transport current I t to the critical current I c and B * p defined by (13) as a function of the full-penetration field of the composite conductor B p [23] in (14): In (12)- (14), D is the composite diameter. In (11), the penetration field of the filament b p , is defined as: being d the filament diameter. VOLUME 11, 2023 The magnetic field B is obtained solving numerically the Ogasawara equation [23], [24]: (16) in which B e represents the changing external field, whereas the decay time constant of the induced coupling currents τ , is defined as: where l p is the twist pitch, and ρ et the effective resistivity of the Copper stabilizing matrix. Note that the coupling time constant is a crucial parameter in the calculation of the coupling loss. In a CICC, the coupling currents loss account for the multiple induced currents loops with a broad range of time constant, affecting different volume fractions of the cable [25]. By using a single time constant, we implicitly assume that only one contribution is dominant at all time. This parameter is affected by a certain degree of uncertainty, due to the experimental difficulty of determining its value accurately. In principle, τ is expected to be different in the two types of feeders, since it depends on the composite and cable layouts. However, in the simulations the same value (150 ms) has been used, based on the values previously measured on other CICCs with similar layouts.

B. EVALUATION OF THE NUCLEAR HEAT LOAD
The nuclear heat load has been considered only for the TF feeders, and conservatively taken as 0.1 mW/cm 3 , in agreement to the values on the outermost part of the TF casing, as shown in [26].

V. RESULTS
The computed results on the alternative cable configurations for the different feeders is first performed in terms of T HS and then in terms of T min CS in operation. Eventually, the economic performance is assessed to identify the best options.

A. EVALUATION OF T HOTSPOT
The computed values of the hot-spot temperatures, computed accounting for, or neglecting, the heat sink constituted by the helium, are reported in Table 3, showing that for all the adopted layouts the constraint of 150K for the ''wetted'' conductor is always satisfied, while the constraint on the ''dry'' conductor (T HS,2 < 250 K) is largely not met for the second layout (B1) of the TF jumper, and just slightly overcome when the layout C1 is considered. All the alternative layouts for the CS and PF coils feeders show hot spot temperature values well below the design criteria.

B. HEAT LOSSES
From the computed magnetic field and magnetic field variation, according also to the transport current shown in Fig. 6a, the computed AC losses per unit length and single SC strand  turned out to be constant for all the configurations of each feeder, and they are shown in Fig. 6b. Note that the scale of the y axis is logarithmic, and the deposited power can reach almost 1 W/m at the plasma breakdown in the CS feeder.
The resulting power, averaged on the entire plasma pulse, is shown in Figs. 7-8. More in detail, in Fig. 7a the average power for the different configurations of the CS3U2 feeder is shown. The dominant contribution for the CS feeder is given by the AC losses, which can vary up to a factor of 3 for the different configurations, in view of the very large difference in N SC they present, see Table 1. The impact of the AC losses is significantly reduced when one considers the different configurations of the PF61 feeder (see Fig. 7b noting the different scale if compared to Fig. 7a), where the global losses are dominated by Joule power. The AC  loss contribution becomes almost totally negligible, if the TF feeder is investigated (see Fig. 8, where the scale in the y axis is logarithmic). For the TF feeder, indeed, the static load is by far the dominant component, as expected.

C. PERFORMANCE ASSESSMENT
The computed minimum temperature margin along each feeder, considering different configurations and different possible values for the nominal mass flow rate are reported in Fig. 9.
As far as the CS3U2 feeder is concerned, the value of T min CS is always computed when the losses are highest (breakdown) independently on configuration and flow rate (provided it is > 0.5 g/s). Being the losses per cycle proportional to N SC , the temperature margin turns out to be quite insensitive to it, as visible in Fig. 9a, where the margin varies by 15% throughout the entire parameter space explored in The behaviour of the PF61 feeder and TF jumper is different in that respect (see Figs. 9b,c), since there is a larger effect of the coolant flow rate in the temperature margin. Note, however, that in these two cases the amount of SC material in the cable has been varied in a much smaller range, if compared to the configurations analysed for the CS3U2 feeder. For the TF jumper, moreover, only for mass flow rates ≥ 5 g/s guarantee the margin > 2 K for all configurations (Fig. 9c).
The hydraulic performance of the different conductor layouts is reported in Fig. 10 for the sake of completeness. For all the layouts of the TF/PF coils feeder, as well as for the layout D of the CS feeders, the pressure gradient reaches about 1 kPa/m if the Katheder correlation is used [27]. Note that the computed values is, at a mass flow rate of 10 g/s, 1 order of magnitude larger than the reference values typically computed for the (ITER-like) tworegions CICCs, where a low-impedance relief central channel is present [28], [29]. The much larger pressure gradient is largely compensated by the short lengths into play (max 17.6 m for the CS feeders and < 12 m for all the others).

D. ECONOMIC ASSESSMENT
The capital cost of the different cable layouts from (3) gives the results reported in Fig. 11. It is clear that the alternative configurations for CS feeder conductors can allow saving up to 50% of the capital cost (Fig. 11a), while still keeping the temperature margin above 2 K, at all the considered mass flow rates > 2 g/s. The saving for the PF feeders could achieve only ∼ 10%, but with some additional room for improvement (Fig. 11b), especially if the nominal mass flow rate is targeted, for which the temperature margin is 2.5 K. No effect on the conductor cost of the alternative configurations for the TF jumpers is found (Fig. 11c), also keeping in mind the poor performance in terms of T HS,2 of the two alternative layouts. Note that the different capital cost for the TF coil jumper, compared to the PF coil feeder, derives from the different lengths of the two conductors, while the cost per unit length is obviously the same, and very similar to that of the layout D of the CS feeders.
Moving to the operational costs of the cryoplant, we consider one year of operation, with a constant electricity cost of 0.3 = C/kWh. For the CS3U2 and PF61 coil feeders an operation time of 1000 h/y is considered, while for the TF jumper an operation time of 180 d/y is accounted for. The results in terms of cost of operation of a single feeder are reported in Fig. 12, where the cost related to the pumping power of the coolant has been neglected since the total mass flow rate for the feeders is small compared to that of the magnet system. The cost associated to the CS3U2 feeder are strongly influenced by the alternatives (Fig. 12a) since the AC loss power is strongly related to N SC , which varies by a factor of 4 among the different alternatives. For the same reason, the cost of the other feeders is almost unaffected changing the configuration (Fig. 12b, c). Note that the operational cost of the TF jumper is one order of magnitude higher than that of the feeders of the pulsed coils, in view of the much longer operational time foreseen for the TF coils. This aspect becomes even more critical keeping in mind that the largest fraction of the power to be removed form the TF jumper is the Joule load on the joints, and that the TF jumpers and feeders are much more than the feeders of the pulsed coils (namely 15 jumpers and 3 × 2 feeders).

VI. CONCLUSION
A techno-economic assessment on different cable alternatives for the DTT feeders has been performed, evaluating different key performance indicators, and namely the capability to meet the criteria on the maximum hot spot temperature, the capability to meet the criterion on the minimum temperature margin during operation, the hydraulic performance and the capital and operational costs.
The results highlight that there is room for ∼ 50% saving in the capital cost for the pulsed CS feeders found, moving from the original layout (A) to layout D, reducing to 25% of the number of SC strands and introducing segregated-copper strands. Also, the operational cost could be dramatically reduced if layout D is implemented for the CS feeders instead of the original one.
As far as the PF coil feeders are concerned, a saving of 5% in the capital cost can be achieved by moving from the original layout (A1) to a cable again with a reduced number of SC strands (layout C1).
Notwithstanding a comparable capital cost per unit length of the cable, the TF coil feeders are anticipated to have a 20× operational cost, when compared to the others. The original design for the TF coil feeders has been confirmed here to be the best among the alternative configurations considered, guaranteeing the highest minimum temperature margin without significant increase of the operational costs.