Analysis and design of the central stack for the SMART tokamak

Fusion Engineering and Design 193 (2023) 113832 Available online 23 May 2023 0920-3796/© 2023 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/bync-nd/4.0/). Analysis and design of the central stack for the SMART tokamak J. Segado-Fernandez a , * , A. Mancini a , b , J. Garcia-Dominguez a , J. Ayllon-Guerola a , c , D.J. Cruz-Zabala a , L. Velarde a , d , M. Garcia-Mu˜ noz a , b , E. Viezzer a , b , C. Navarro c , M. Agredano-Torres a , e , P. Vicente-Torres a a Centro Nacional de Aceleradores, University of Seville, 41092 Seville, Spain b Dept. of Atomic, Molecular and Nuclear Physics, University of Seville, 41012 Seville, Spain c Dept. of Mechanical Engineering and Manufacturing, University of Seville, 41092 Seville, Spain d Dept. of Energetic Engineering, University of Seville, 41092 Seville, Spain e Electric Power and Energy Systems Division, KTH Royal Institute of Technology, 114 28, Stockholm, Sweden ARTICLE INFO Keywords: SMART Tokamak Spherical Central-stack Centering-force Twisting-torque ABSTRACT The SMall Aspect Ratio Tokamak (SMART) is a new spherical machine that is currently under construction at the University of Seville aimed at exploring negative vs positive triangularity prospects in Spherical Tokamaks (ST). The operation of SMART will cover three phases, with toroidal fields Bϕ≤1 T, inductive plasma currents up to Ip=500 kA and a pulse length up to 500 ms, for a plasma with R =0.4 m, a =0.25 m and a wide range of shaping configurations (aspect ratio, 1.4 <R/a <3, elongation, κ≤3, and average triangularity, -0.6 ≤δ≤0.6). The magnet system of the tokamak is composed by 12 Toroidal Field Coils (TFC), 8 Poloidal Field Coils (PFC) and a Central Solenoid (CS). With such operating conditions, the design of the central stack, usually a critical part in spherical tokamaks due to space limitations, presents notable challenges. The current SMART central stack has been designed to operate up to phase 2 and it comprises the inner legs of the TFC, surrounded by the CS, two supporting rings, a central pole and a pedestal. To achieve the plasma parameters of this phase (Bϕ=0.4 T with inductive Ipup to 200 kA), the high currents required, combined with the low aspect-ratio of the machine lead to high forces on the conductors that represent an engineering challenge. The loads expected in the central stack are a centring force up to 1.5 MN and a twisting torque up to 7.4 kNm. This work describes the design of the central stack and its mechanical validation with a multiphysics finite element assessment. Using a combined electromagnetic and mechanical assessment, it is shown that the SMART central stack will meet the physics requirements in phase 2. 1. Introduction Spherical Tokamaks (ST) offer an attractive path to fusion reactors due to the compactness, the high beta (efficiency in the use of the magnetic field for plasma confinement) and the high power density that can be achieved with their low aspect ratio plasmas [1]. Negative Triangularity (NT) is currently a potential game changer offering H-mode like core pressure levels and an L-mode like edge, with no pedestal structure. In NT reactors, the divertor is placed naturally at larger radii, resulting in a larger area available for power exhaust [2]. The SMall Aspect Ratio Tokamak (SMART) is a new spherical tokamak (R =0.4 m, a =0.25 m, A<2) currently being assembled at the University of Seville [3–5]. Fig. 1 shows a cross section of the tokamak with an artistic representation of a negative triangularity plasma. SMART will explore both positive and negative triangularities (−0.6<δ<0.6), high elongation (κ<2.3) and single/double null divertor plasmas. The SMART operation will cover three phases (see Table 1). The first phase aims to test the machine and obtain first plasmas. The second one will focus on the demonstration of the machine capabilities (increasing Ip, Bt and τ ), the addition of a Neutral Beam Injector for plasma heating and the integration of new diagnostics. Third phase will study plasmas with fusion-relevant parameters, similar to those of the main existing ST experiments [6,7] and with the possibility of studying negative triangularity plasmas. This contribution presents the design and analysis of the SMART * Corresponding author. E-mail address: [email protected] (J. Segado-Fernandez). Contents lists available at ScienceDirect Fusion Engineering and Design journal homepage: www.elsevier.com/locate/fusengdes https://doi.org/10.1016/j.fusengdes.2023.113832 Received 29 October 2022; Received in revised form 23 March 2023; Accepted 17 May 2023 Fusion Engineering and Design 193 (2023) 113832 2 central stack. The low aspect ratio gives spherical tokamaks interesting plasma properties, however, the inner-radial compactness supposes a technical challenge. The reduced space available for the Toroidal Field Coil (TFC) inner leg and the Central Solenoid (CS), added to the high currents and magnetic fields generated, make the mechanical design of the central stack a complex task. Several of the main spherical tokamaks (i.e., NSTX [8] or Globus-M2 [9]) have reported failures related with this component due to the difficulty of managing the high ElectroMagnetic (EM) loads generated within this very tight space, which is restricted strongly by the aspect ratio (in SMART, with R =0.4 m and a =0.25 m, only 0.15 m in radius is free for the TFC and the CS). The work presented here covers the design of the SMART central stack assuring that it withstands the expected EM loads up to phase 2 for 1k cycles at full performance and 200k cycles at baseline performance. The parameters of phase 3 will require a completely new design to manage the extreme EM loads that will be caused by the larger magnetic field/current envisioned. A general description of the Central Stack is given in Section 2. The EM analysis of the system is presented in Section 3 and the structural verification in Section 4. A summary is given in Section 5. 2. Central stack design The SMART central stack is composed by the TFC inner legs and the CS creating an individual component separated of the Vacuum Vessel (VV). Fig. 2 presents a cross section, with the TFC inner legs (orange), the CS (brown) and the epoxy moulding (pink) which solidifies the assembly. The main dimensions are also given in the figure to highlight the tight space available for each component. This stack will be inserted in the 300 mm inner diameter VV central column. The arrangement of the conductors maximizes: the TFC area with square conductors, comprising 48 bars with a section of 480 mm 2 each; the solenoid flux swing, fS∼A⋅B, for a given magnetic field B, maximizing the cross-sectional area A by positioning the solenoid at the outward radius of the column. The solenoid is composed by 230 turns arranged in two layers and a conductor cross section of 105 mm 2 [5]. The design limit parameters of the SMART central stack are shown in Table 2. The double flux swing of 224 mV⋅s is expected to be enough to ramp the plasma current up to 200 kA and sustain the flat-top for 150 ms. Longer pulses are feasible with other start-up (e.g., helicity injection [10], radio frequency [11]) and current drive schemes (e.g., bootstrap current, neutral beam current drive [12]). In an optimised scenario in the SMART tokamak, it is expected to have 45% of non-inductive current drive, with 30% of bootstrap current and 15% of neutral beam current drive [13]. The central stack is shown in detail in Fig. 3. It is 2.6 m in height, 296 mm in diameter and 800 kg of weight. Explaining it from the inward parts of the column, the central pole is the core of the system, being a SS316L calibrated bar of 48 mm of external diameter and 7 mm thickness. It is supported by a pedestal. To avoid the consumption of flux swing, the central pole is longitudinally cut in its whole length. A PEEK block is inserted in the groove as mechanical support and electrical break. Two SS316L torque rings (up and down) are bolted to the central pole and will restrain the TFC inner legs in their position during assembly and operation. Two spacer rings of epoxy G10 are also included to guide the bars during assembly. The 48 TFC inner legs are Oxygen Free (OF) copper bars with 480 mm 2 provided by Luvata [14]. The electrical insulation in these bars is performed with a 50 μ m kapton layer and a 200 μ m TUFQUIN TFT layer [15] having an insulation strength of 20 kV while a maximum of 2 kV is expected during operation. The solenoid has 230 turns arranged in 2 layers and it is wrapped around a 2 mm thickness SS316L cylinder. As the central pole, the cylinder is longitudinally cut to avoid flux consumption. The solenoid conductor is an OF copper hollow conductor with 105 mm 2 and 4 mm diameter hole for cooling provided also by Luvata. The insulation is made by a 185 μ m kapton layer giving 50 kV of insulation strength while a maximum of 6 kV is expected during operation. The components inside the wrapping cylinder (TFC bars, rings, pole, etc.) will be solidified with epoxy (SR1720) [16] to give mechanical stiffness to the assembly. Once manufactured and assembled in the VV central column, the central stack will be fixed in position with the torque arms (aluminium 7075 T651), that will be bolted to the VV lid ribs. Finally, the electrical connection between the inner and outer TFC legs will be carried out with lamellae flexible joints. They decouple mechanically the inner and outer TFC legs, Fig. 1. SMART cross section with negative triangularity plasma. Table 1 SMART operational phases. Phase 1 Phase 2 Phase 3 Ip(kA)100 200 >500 Bt(T)0.1 0.4 1 τ ft (ms)100 150 500 PECRH (kW)6 (2.45 GHz) 6 (7.5 GHz) 200 PNBI (MW)– 1 1 Fig. 2. Central Stack cross section. J. Segado-Fernandez et al. Fusion Engineering and Design 193 (2023) 113832 3 which have different behaviours due to differential thermal expansions or the EM loads. Similar solutions with lamellae flexible joints have already been implemented in other machines [17–19]. 3. Electromagnetic analysis The Electromagnetic (EM) assessment of the SMART central stack has been carried out with a Finite Element Method (FEM) model using ANSYS Maxwell. The objective of the assessment is to obtain the EM load generated during the operation of the machine. In this assessment, the main EM effects are the interactions of the electric currents with the magnetic fields generated, therefore, only magnetostatic effects are assessed. To simplify the model, the passive components (i.e., Vacuum Vessel, in-vessel coil casings) have been neglected, since the induced current in these component are not relevant in this analysis, because the forces that might be created in them will not interfere with the central stack. Specific transient models have been used to check the structural integrity of these components during dynamic events [4,20]. The geometry considered in this model is the complete magnetic system of SMART, which includes 12 TFC (4 turns each), the central solenoid, two pairs of divertor coils and two pairs of poloidal field coils. Fig. 4 shows the magnetic system and the field generated at one instant of the phase-two baseline equilibrium, later described. Since the objective of this simulation is to obtain the EM load in the central stack conductors, the supporting component and all the details (insulation, screws, fillets, etc.) are neglected to reduce the computational cost of the model. The current input for each coil is obtained from the phase 2 reference scenario [3] and from the design limit scenario, obtained as the phase 2 baseline scenario with the current multiplied by a factor of 2.5 [21]. Fig. 5 shows the current waveform considered in each coil for the design limit scenario. The simulation time (highlighted with the dashed grey line) is −5 ms, a pre-breakdown instant. At this time, the solenoid and the divertor coil 1, have their maximum current pointing into the same direction, adding their magnetic field. This time will be the most relevant for the EM load in the central stack conductors, since the magnetic field crossing it will be maximum. The TFC current is not shown in the plot because it is constant during the whole pulse (16.8 kA for 0.4 T). With this setup, the forces generated in the TFC inner legs and the solenoid were obtained. They can be divided in two groups, In Plane Loads (IPL) and Out of Plane Loads (OPL). They are shown qualitatively in Fig. 6. •IPL: this load is equivalent to the magnetic pressure. It is generated by the interaction between the coil current with its own magnetic field. It tries to expand outwardly the TFC and is proportional to the magnetic field strength, being maximum in the centre column and decaying as 1/R. The IPL in the TFC inner legs is equilibrated between each bar and its opposite, trying to compress them to the central pole, that equilibrate the whole load. Regarding the solenoid, the IPL expands it radially in the outward direction. This load is equilibrated by the solenoid itself. •OPL: in the TFC inner legs, this load is generated due to the interaction of the vertical current with the radial field in the solenoid ends. The addition of the OPL in all the TFC inner legs results in a torque in the central stack. This OPL is self-equilibrated since it generates equal and opposite torsion loads in the upper and lower part of the column. To reduce the structural requirements of the central stack, the torque rings have been included. They connect the system through the torque arms to the Vacuum Vessel, where part of Table 2 SMART Central Stack design limit parameters. Design limit Solenoid max. current (kA) 10 Double flux swing (mV⋅s) 224 TFC current (kA) 16.8 Bt(T) 0.4 Fig. 3. SMART central stack. Fig. 4. Magnetic system of the SMART tokamak with the magnetic field generated during the phase 2 reference pulse. J. Segado-Fernandez et al. Fusion Engineering and Design 193 (2023) 113832 4 the torque is reacted. With a specific numerical model, it has been estimated that about 50% of the torque takes the previous path (ring, arm and Vessel), while the other 50% is reacted by the column itself. In the solenoid the OPL is generated due to the interaction between the current and its radial field at the ends, generating equal and opposite compressive loads at both ends, again reacted by the solenoid itself. Fig. 7 and Fig. 8 show the load generated in the TFC conductors and the solenoid, respectively, depicting the two main force components discussed before. As it can be seen in Fig. 7, the load in the TFC bars is mainly IPL, with the OPL just at the end of the solenoid. In Fig. 8, the solenoid force distribution show that the compressive load is just at the ends, being radial in the rest of its length. Table 3 summarises the maximum absolute value of each type of load generated in the TFC inner legs and in the solenoid during the design limit scenario. 4. Structural analysis In order to check the structural integrity of the system, a coupled multiphysics assessment was set up. The results (volumetric forces) of the EM analysis in the central stack conductors were imported into ANSYS Mechanical. This is performed by interpolating the loads from the original mesh (in ANSYS Maxwell) to the final mesh (ANSYS Mechanical) using a specific module of the ANSYS suite. The fidelity of the interpolation between both modules has been checked, obtaining errors lower than 5% in all the cases. This model considers all the structural components of the central stack and neglects the components of the magnetic system that do not belong to the central column, i.e., TFC outer leg, PFC and divertor coils. The analysis of the solenoid is not presented here and will be published in a follow-up article. A simplified model geometry, in contrast to the detailed realistic geometry presented before, is used for the structural analysis. Comparison of the simplified and full geometries is presented in Fig. 9, where the coil insulation, bolts or small details have been simplified. The boundary and contact conditions of the model are presented in Fig. 10. The model has a frictionless contact in the lower part of the central pole (pedestal connection) and frictionless contacts in all the torque arms clamps. They simulate the contact with the VV lid ribs without constraining excessively the model. The contacts between all the components of the model are performed by the creation of a unified mesh with a shared topology approach. Since all the components are joined together by means of the epoxy moulding, this constraint is considered realistic and efficient. Only the torque rings are not included in this shared topology, to have more control of their meshes, since they Fig. 5. SMART current limit scenario waveform. Fig. 6. EM Loads generated in the Central Stack. (Left) In Plane Loads (IPL); (Right) Out of Plane Loads. (Detail) Torque ring. Fig. 7. Volumetric force acting on the Toroidal Field Coil (@−5 ms). J. Segado-Fernandez et al. Fusion Engineering and Design 193 (2023) 113832 5 are the most important structural components of the system. The contact between the rings and the rest of components is made with a bonded contact, which is a good approximation provided the behaviour of the epoxy. The resulting mesh is depicted in Fig. 11, where the most refined component, the torque ring, is shown. The other components have been refined in its surroundings. To improve the analysis of the torque rings, a sub-modelling technique has been applied to refine further the mesh without increasing in excess the mesh of the general model. The structural criteria of the SMART project is based on the ITER Structural Design Criteria for In-vessel Components (ITER SDC-IC) [22] and is adapted to the scope of this project. The design rules for the Fig. 8. Volumetric force acting on the Solenoid (@−5 ms). Table 3 EM loads generated in the TFC inner legs and in the solenoid. Design limit TFC IPL 1.5 MN TFC OPL 7.4 kNm Solenoid radial load 1.6 MN Solenoid compressive load 120 kN Fig. 9. Comparison between real and simplified geometry for the FEM model. Fig. 10. Boundary and contact conditions of the structural model. Fig. 11. Mesh of the complete structural model and detail of the torque ring. J. Segado-Fernandez et al. Fusion Engineering and Design 193 (2023) 113832 6 monotonic damage are: •Membrane stress <S m •Membrane +Bending stress <1.5 S m •Membrane +Bending stress +Peak stress <2 S m Being S m the allowable stress limit of the materials, defined as S m = min {2/3 S y || 1/3 S u }, where S y is the yield strength and S u the ultimate strength of the materials. For the cyclic damage, the rule considered is: •Δ ε <Δ ε m-1k – for more than 1k cycles at the design limit performance (Bt=0.4 T & Ics =10 kA). •Δ ε <Δ ε m-200k – for more than 200k cycles at the phase 2 baseline scenario performance (Bt=0.3 T & Ics =4 kA). The maximum total strain range Δ ε is obtained with Eq. (1)[23]. Δ ε (%) = 100(Δ σ ⋅[2(1+ ν ) 3E]+[Δ σ K]1 m)(1) Being Δ σ the maximum stress range, ν the Poisson ratio, E the Young modulus and K and m coefficients for the cyclic stress-strain relation (obtained in [23] for the SS316L). To obtain Δ σ with a FEM model, the maximum stress value Smax of the model is used. Considering that the stresses go from zero to Smax, Smax =ΔSmax. Since this value is obtained with a linear-elastic model, to obtain the elastic-plastic stress range that should be used in the fatigue assessment, the Neuber’s rule has been applied with Eq. (2) [24]. Δ ε Δ σ =ΔS2 max E(2) With the Neuber’s rule is obtained a new maximum stress range Δ σ that is lower than Smax as it considers the plastic behaviour of the material. The material properties are presented in Table 4. For the design limit scenario, the system presents moderate stresses in all the components, with values below all the limits. The most demanded elements are the torque rings. The Von-Mises stress distribution in the lower torque ring is shown in Fig. 12, where the complete ring and the sub-model are shown. The stresses in this component have been linearized along the path P1 drafted in the figure. These stresses are presented and compared with their respective limits in Table 5. The cyclic damage has only been studied in these torque rings. The rest of the components have very low stresses and the fatigue is not considered an issue. The results of the fatigue assessment are shown in Table 6 for both, the design limit and the phase 2 baseline scenarios. Finally, the deformation around the central stack axis is shown in Fig. 13. As discussed in Section 3, the OPL generates a torque that tries to squeeze the central stack around its axis. The plot shown has a deformation scale factor of 500, to allow the appreciation of the turn. The upper and lower deformation is almost the same, being different for some asymmetries of the model and the mesh, but the difference is lower than 10%. The maximum angle that the central stack will turn is lower than 1 mrad. 5. Conclusion The design of the central stack for the SMART tokamak has been presented attending to the conductor arrangement, the mechanical supports and the electrical insulation. The structural verification of the system has been performed with a multiphysics FEM model that coupled an EM analysis in ANSYS Maxwell with a structural analysis in ANSYS Mechanical. The system withstands the EM loads generated within acceptable levels in all the components. The torque rings react to the out of plane torque generated in the TFC inner legs and are the most demanded elements, but their stresses are below all the design limits. The fatigue damage has been studied in the central stack and it meets with big margins the limits established for more than 1k cycles at the design limit performance (Bt=0.4 T & Ics =10 kA) and more than 200k cycles at the phase 2 baseline scenario (Bt=0.3 T & Ics =4 kA). During the operation, an experimental monitoring system will be implemented in the machine to check the structural behaviour and compare with the results of these numerical studies. Future work along this line will focus on the design and development of the SMART central stack for the operation of phase 3 (Bt=1 T; Ip>500 kA; τ ft =500 ms). Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Table 4 Material properties of the central stack components. Material Component E (GPa) S m (MPa) AISI SS 316 L Torque Rings & Central Pole 200 147 Aluminium 7075-T651 Torque Arms 71.7 190 OF Copper TFC Inner Legs 117 37 Epoxy SR1720 Moulding 4 15 PEEK Insert 3.9 32 Fig. 12. Von Mises stress distribution generated in the torque ring in the design limit scenario. The detail shows the stresses in the sub-model. Table 5 Structural verification of the torque ring against monotonic damage for the design limit scenario. Torque Ring Design limit scenario Memb. (MPa) Memb.+Bend. (MPa) Memb.+Bend.+ Peak (MPa) Rule <S m <1.5 S m <2S m Stress Limit SS316L [10] 147 221 294 Path P1 48 120 144 Table 6 Structural verification of the torque ring against cyclic damage for both the design limit scenario and the phase 2 baseline scenario. Torque Ring Design limit scenario 1 k cycles 200 k cycles K (MPa) 798.3 m 0.339 Rule <Δ ε m Strain limit (%) 0.698 0.250 Strain (%) 0.204 0.025 J. Segado-Fernandez et al. Fusion Engineering and Design 193 (2023) 113832 7 Data availability Data will be made available on request. Acknowledgements This work received funding from the Fondo Europeo de Desarollo Regional (FEDER) by the European Commission under grant agreement numbers IE17–5670 and US-15570. References [1] M. Gryaznevich, et al., Achievement of Record b in the START Spherical Tokamak, Phys. Rev. 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Handrock, Fundamentals of Metal Fatigue, Prentice Hall, New Jersey, 1990. Fig. 13. Central Stack circumferential deformation (y axis of cylindrical coordinate system). J. Segado-Fernandez et al.