Exploration of ITER operational space with as-built stiffness of central solenoid modules

The as-built stiffness in the ITER central solenoid (CS) modules (CSM1 thorough to CSM4 are currently manufactured) determines the range of vertical compression forces that can be tolerated by the CS modules during ITER operation. Since the as-built stiffness of the CS modules manufactured (∼32 GPa and ∼34 GPa for CSM1 and CSM2, respectively and similar for the other modules) has been reduced from the design value (53 GPa), the CS axial (vertical) force criteria have been updated assuming a conservative stiffness (25 GPa) with margins for all six CS modules. Initial analysis using the updated CS force criteria has revealed that this reduction affects only the plasma initiation with fully charged CS in the ITER 15 MA Baseline DT scenario, resulting in a slight reduction of poloidal magnetic flux, from 117.5 Wb to 116.2 Wb at initial CS magnetization. Therefore, the 15 MA Baseline scenario has been re-developed with an updated plasma start-up, and then the entire evolution of the CS and poloidal field coil parameters has been validated against all the coil currents, fields and forces criteria. To explore potential risks and opportunities for further optimization of scenarios, the equilibrium operational space (the plasma internal inductance versus the poloidal magnetic flux produced by the coils) at flat-top burn has been analyzed using the CORSICA and DINA codes. The three major ITER reference DT operation scenarios, 15 MA Q = 10 Baseline, 12.5 MA Q > 5 Hybrid and 10 MA Q ∼ 5 Steady-State, satisfy all the coil criteria including the CS force updated reflecting the as-built stiffness. The evolution of the plasma discharge parameters within the equilibrium operational spaces provided a guidance for potential optimization with margins.


Introduction
The first ITER central solenoid (CS) modules recently manufactured are identified, in their cold-tests, to have a lower stiffness than the assumed values for their design [1,2].The average vertical Young's Modulus, which is a measure of the elasticity, is reduced from the design value of 53 GPa to the measured values (∼32 GPa and ∼34 GPa for CSM1 and CSM2, respectively).In addition to this reduction in the asbuilt vertical stiffness, small margins are added to the average vertical Young's Modules and the uncertainty associated with the mechanical properties of future coils and a foreseen settling of the stack is considered into the stack tie-plate preload.To replicate the soft behavior in the structural analysis models, the average vertical Young's Modulus and the minimum permitted 4 K tie-plate preloads are finally specified as 25 GPa and 190 MN, respectively, and then the CS axial (vertical) force criteria are updated.The updated CS force criteria have been applied to the major ITER DT operation scenarios, such as 15 MA Baseline, 12.5 MA Hybrid and 10 MA Steady-State, firstly to identify when the scenarios violate these criteria and then to revise the scenarios and/or scenario segments to be compliant.The feasibility of the ITER coil systems is also investigated by analyzing the equilibrium operational space, defined by the poloidal magnetic flux produced by external coils (poloidal flux linkage) and plasma internal inductance, to extend the analysis beyond the representative operation scenarios which covers only a subset of the foreseen plasma operation.Although advanced optimization of operational scenario within the operational space is beyond the scope of this paper, it is worth to mention that several advanced methodologies, such as machine learning and Bayesian optimization, are available in various literatures [3][4][5][6].
In section 2, the CS axial force criteria updated with the asbuilt CS module stiffness, briefly summarized in appendix B together with other coil criteria, are applied to investigate their violations in the previously developed 15 MA Baseline scenario (engineering-oriented DINA scenario) and to revise the plasma initiation where minor violations were identified.The 15 MA Baseline scenario is then re-developed including the revised plasma initiation and to stay within all the coil current, field and updated force criteria.However, this demonstration of a single representative ITER operation scenario within the applied criteria would be insufficient to cover the wide range of variant scenarios to be explored during the experimental research in ITER.Besides, the analysis on a specific scenario does not provide useful information in terms of scenario optimization within the equilibrium operational space.Therefore in section 3, the equilibrium operational space, defined by the poloidal flux produced by coil currents versus the plasma internal inductance, as previously studied in [7,8], is identified by applying the updated CS force criteria.The CORSICA [9] constrained equilibrium (CEQ) package and the DINA [10] equilibrium analysis workflow are chosen as in-house analysis tools of the ITER Organization to apply continuous identification of as-built properties of the ITER tokamak components.In section 4, equilibrium operational spaces of the other reference ITER DT operations, such as the physics-oriented CORSICA 15 MA Baseline, 12.5 MA Hybrid and 10 MA Steady-State, have been identified and the evolution of the plasma discharge parameters (poloidal flux linkage versus internal inductance) has been analyzed.Note that the plasma initiation phase is not included in these CORSICA scenarios due to the lack of plasma initiation models.Instead, the plasma is assumed to start after the similar plasma initiation (re-)developed by using DINA.

Re-development of the plasma initiation phase within the CS axial force criteria updated including as-built CS module stiffness
The CS axial force criteria updated using the average vertical Young's Modulus of 25 GPa and the minimum permitted tieplate preloads (at 4 K temperature) of 190 MN are summarized in appendix B and a schematic view of the ITER coils and forces are shown in figure 1. Application of the updated CS force criteria to the previously developed ITER operation scenario with full CS initial magnetization (used in 15 MA Baseline DINA scenario) has revealed that the axial force on the lowest gap (F gap 0 ) violates its limit during the first 0.6 s of the plasma initiation phase, as shown in figure 2. To avoid this violation, the plasma initiation phase has been re-developed using DINA [10] and TRANSMAK [11].The original design goal of this initiation phase, maximization of the poloidal magnetic flux at the start of CS initial magnetization for the achievement of a long enough flat-top burn duration (∼500 s), and the original design assumptions, such as prefilled main fuel gas (D) and impurity (Be) species, inboard-side gas breakdown region and circular cross section (minor radius of 1.6 m), toroidal electric field at the center of breakdown region (∼0.3V m −1 ) and ECH power absorption (∼2 MW), have been unchanged.TRANSMAK is firstly used to design waveforms of the CS/PF coil systems, including 11 currents in the CS and PF circuits, eddy currents in the conducting structures, 7 resistances of the Switching Network Units in the CS circuits and PF1 & PF6 coils, and 11 feedforward voltages of the CS and PF circuit converters.Then DINA is used for simulation of the plasma initiation using the designed waveforms, in particular, to compute 2D free-boundary plasma evolution as the plasma current becomes higher than 0.1 MA.If the coil currents finally obtained in the DINA free-boundary modeling violate certain criteria, TRANSMAK reference waveforms are revised either to avoid the violations or to maximize the margin.Note that here we assume the plasma current increases with positive values during the current ramp while the magnetic poloidal flux produced by the PF system in the plasma region has maximum positive value at the start of CS discharge and then decreases to a negative value during the current ramp-up.It should be also noted that there are automated approaches attempted to optimize the plasma initiation design using either an iterative modeling [12] or an inverse reconstruction of magnetic fluxes [13], and these would be useful to improve the current method of designing ITER pulses.The re-developed plasma initiation (green curves) is compared with the original initiation (blue curves) in figure 2 and the CS and PF coil currents at the initial magnetization are shown later in table 4. All the updated axial forces on the CS gaps were maintained within their criteria.The main modification applied to the original initiation is the reduction of current (from 41.8 kA/turn to 36 kA/turn) in the CS3U coil (see figure 2(b)).Although the CS3U coil is located at the top of the CS stacks, the reduction of current in this coil was effective in avoiding the axial force violation on the lowest gap (gap 0 ) located at the bottom of the CS stacks.This is mainly due to the fact that the axial forces are linked through the equation (B6 in appendix B) while the central CS coils (CS1U/L, CS2U/L) were constrained to be almost fully charged to maximize the initial poloidal magnetic flux.The poloidal magnetic flux at the CS initial magnetization (t = 0 s) in the breakdown region is reduced by ∼1.3 Wb, from 117.5 Wb to 116.2 Wb, mainly due to the reduced initial current in the CS3U coil.The poloidal magnetic fields at the breakdown time (t = ∼1.1 s), also known as magnetic null, are compared in figure 3. The redeveloped initiation phase (figure 3(b)) shows similar quality of the magnetic null compared to that in the previous study (figure 3(a)).The poloidal magnetic fields inside the designed breakdown region, shown in black dashed circle, are lower or close to 15 G in both cases, implying that there will be no additional challenges in the plasma breakdown process.
The ITER 15 MA Baseline scenario, the reference plasma operation with full CS initial magnetization, is of primary concern for operating the ITER coil systems, since it is designed to use full capacity of the systems to simultaneously achieve the challenging plasma operation goals, such as the fusion gain of Q = 10, fusion power of 500 MW, and flat-top burn duration of 300-500 s (nominally 450 s in ITER Project's requirements).Therefore, the modification of the plasma initiation in the 15 MA Baseline scenario could have an impact on the flattop burn duration, if the coil systems experience a violation of coil current, field, force criteria or a lack of necessary margins in the subsequent phases of the scenario.Therefore, the endto-end 15 MA Baseline scenario has been fully re-developed including the updated plasma start-up, and then all the CS and poloidal field (PF) coil current, field and force criteria (listed later in table 1) have been investigated for the entire scenario phases.Time traces of the plasma current and several critical parameters, CS1 coil current, and axial forces applied on gap 0 (between CS3L and lower LDP) and gap 1 (between CS2L and CS3L), are shown in figure 4. The CS axial force applied on the gap 0 (F gap 0 ) was most critical at the initiation phase as already discussed, and the CS1 coil current and CS axial force applied on the gap 1 (F gap 1 ) were approaching to their limits (−45 kA/turn and −26 MN respectively) at the end of the flat-top phase (t ∼ 598 s).The flat-top burn duration of about 498 s (from t = 100 s to t = 598 s) was achieved within all the applied coil current, field and force criteria.The poloidal Table 1.List of CS/PF coil criteria (engineering limits) applied to the identification of equilibrium operational space and validation of scenarios.This includes the CS/PF coil current limits (1-12), imbalance current limit in the vertical stabilization (VS1) circuit (13), CS/PF coil field limits (14-25), updated CS axial force limits (26)(27)(28)(29)(30)(31)(32)(33), PF vertical force limits (34-40) and CS net force limit (41) as summarized in appendix B. The colors and markers are used in the equilibrium operational space assessed by using CORSICA.magnetic flux swing until the end of the flat-top phase was reduced by ∼1.6 Wb (this is equivalent to about 34 s of burn duration), showing that there is a small additional loss of the poloidal magnetic flux apart from the major loss at the initial magnetization (∼1.3 Wb).

Assessment of plasma equilibrium operational space at burn using DINA and CORSICA
To assess the feasibility of a certain type of target plasma operation prior to the experimental research in ITER, a wide range of variant scenarios including uncertainties in the presentday physics modeling assumptions need to be considered.
Performing such assessment would be still challenging mainly due to the lack of adequate extrapolation of present-day knowledge to a future experiment where the plasma explores a new operational space in terms of physics parameters.Another challenging topic is how to provide guidance for optimization of the target plasma operation in ITER.In this regard, a pragmatic approach is to identify an equilibrium operational space of the target plasma and then compare it with the evolution of plasma discharge parameters in the reference scenario of interest.The plasma equilibrium operational space can be defined as a range of the poloidal magnetic flux (poloidal flux linkage) achievable for a given range of plasma internal inductance [7,8].Note that the dependence of the equilibrium operational space on the plasma (poloidal) beta is not investigated in this work, assuming that the plasma can access and stay close to its target flat-top performance (e.g.plasma (poloidal) beta) by means of various plasma controls and scenario recipes.The poloidal magnetic flux, produced by the CS/PF coil currents providing plasma equilibrium, needs to satisfy allowable deviations of the plasma position and shape, engineering criteria applied on the coil currents, magnetic fields and forces.The poloidal magnetic flux (poloidal flux linkage), ⟨Ψ ⟩, and plasma internal inductance, l i , are defined as: where Ψ is the magnetic flux produced by PF coil system, I p and j p are the plasma current and current density, B pol is the poloidal magnetic field produced by the plasma.The volume average of squared poloidal magnetic field is given by ⟨B 2 pol ⟩ = 1

´B2
pol dV p , V p and S p are the plasma volume and poloidal cross section area, and R = (R max + R min ) /2 is the plasma major radius defined by using maximum and minimum values of major radius (R max , R min ) measured from the poloidal cross-section of the plasma boundary.
The poloidal flux linkage is a parameter representing the distribution of the CS/PF coil currents and the plasma internal inductance represents the distribution of the plasma current density.Therefore, the equilibrium operational space indicates the achievable range of the coil system operation within the applied engineering criteria and for a given plasma equilibrium configuration (e.g.plasma shape, total current and beta).It is worth noting that the equilibrium operational space does not significantly depend on the detailed choice of the plasma equilibrium during the stationary current flat-top phase.This is because the global plasma parameters, such as the plasma current, shape and beta, are stationary, whereas the less stationary global parameters, the poloidal flux and internal inductance, are varied in the parameter scan.The internal inductance is varied in an ad-hoc manner, mainly by modifying the pedestal pressure and bootstrap current profiles while maintaining the plasma current and beta.The poloidal magnetic flux is varied by evolving PF/CS coil currents while constraining the plasma boundary to stay near the target plasma shape.The PF/CS coil currents are evolved by applying a certain rule of automation (e.g.minimizing the sum of the squared current variations from the 'reference coil currents' chosen at a specific time-slice for the plasma equilibrium) and, thus, the resulting equilibrium operating space can be misleadingly restricted if the chosen 'reference coil currents' are already too close to certain coil limits.For example, if the plasma equilibrium and 'reference coil currents' are chosen near the end of the plasma burn (EOB), the poloidal magnetic flux ⟨Ψ ⟩ is located near the lower boundary of the operational space (note that ⟨Ψ ⟩ is reduced when more poloidal flux is consumed and the lower boundary can be identified by performing downward ⟨Ψ ⟩ scans).In this case, the CS1 coil current, which is already close to its lower limit in the chosen 'reference coil currents', can easily violate its limit if it is pushed to provide more voltseconds.Then, the lower boundary is likely to be identified as a set of violations in the CS1 coil current, as expected.However, the situation can be different for the upward ⟨Ψ ⟩ scan for identifying the upper boundary if the scan starts near the lower boundary, far from the upper one.In this case, as the PF1 and PF6 coil currents in the chosen 'reference coil currents' can have little margins to their upper limits and the upward ⟨Ψ ⟩ scan can push the PF1 and PF6 coils to save volt-second (charging currents), resulting in violations of the upper current limits, earlier than accessing the upper boundary feasible for the other 'reference coil currents' sets.A slight manual adjustment of PF1 and PF6 'reference coil currents' (reduction of coil current in this case), to make neighboring coils to save more voltseconds, can quickly mitigate this issue.It should be noted that further improvement in the modeling procedures and scans would be required to make the presented methodology to be more automated and reliable, even including the expected perturbations (e.g.poloidal beta) and feedback control margins (e.g. 1 kA/turn of the CS1 coil current reserved to handle the shape evolution during H-L transition) [14].

Identification of the plasma equilibrium operational space
The plasma equilibrium operational space, ⟨Ψ ⟩ versus l i , is foreseen to be continuously updated in ITER along with the identification of as-built properties of the tokamak components.Therefore, in this work, the CORSICA constrained equilibrium package (CEQ) [9] and the DINA [10] equilibrium analysis workflow are chosen as main tools for the ITER Organization's in-house analysis capability for continuous analysis of as-built component impact on ITER operation.A set of seven plasma profiles obtained by varying the pedestal height in an ad-hoc manner, as previously used in [8], has been re-used to generate equilibria and to scan the plasma internal inductance.This also facilitates the comparison between the previous and updated equilibrium operational spaces, by removing the potential discrepancy caused by the use of different input profiles.The plasma current density profiles, representing different internal inductances, are shown in figure 5.For a given value of l i , a range of free-boundary plasma equilibria has been evaluated using the corresponding profiles and parameters.Since the set of coil currents associated with each free-boundary equilibrium produce a particular value of ⟨Ψ ⟩, {⟨Ψ ⟩, l i } operational space has been constructed.As previously mentioned, the lower boundary of {⟨Ψ ⟩, l i } operational space represents the end of plasma burn phase in scenarios and therefore determines the burn duration.It is also worth noting that several minor design changes have occurred in ITER since the previous analysis of this topic [8].The updated target separatrix shape, radial shift of the inboard wall location (∼6 cm outwards in the direction of the major radius) to improve neutron shielding of the toroidal field coils by thicker blanket shield modules, and well as minor changes in the poloidal coil geometry and turns (see appendix B) have been included to represent the present ITER configuration in this analysis.
The main procedure to evaluate the equilibrium operational space can be summarized as follows.Firstly, a set of plasma pressure (through density and temperature profiles) and current density profiles representing the chosen plasma state (e.g. at flat-top burn) is chosen.Secondly, the plasma current density and pressure profiles are varied to produce a range of plasma internal inductances to scan.Thirdly, for a chosen plasma internal inductance, the poloidal flux linkage is scanned by varying the coil currents and constraining the target plasma shape.The poloidal flux linkage (determined by a set of coil currents) is varied by minimizing the sum of squared deviation of coil current from the reference values, Please note that the 'reference coil currents' hereinafter means a set of coil currents selected at a specific time together with the plasma equilibrium which are manually adjusted prior to the scan of the operational space, as necessary to avoid the spurious violations described above.
The plasma shape is constrained by using about 6-8 plasma boundary control points which usually include the two strike points during single null configuration (e.g.figure 8(a)).The use of the boundary control points allows the plasma shape to slightly deviate from the target plasma shape and, therefore, guarantee the existence of free-boundary equilibria during the scan.It is well-known that imposing too strong constraints on the plasma shape by adding many control points frequently makes the scan impossible since free-boundary equilibrium solutions may not exist that fit such constraints.In this regard, some posterior verification of the overall plasma shape and manual adjustment of the control point locations are applied to ensure a reasonable result of the procedure.A few other posterior verifications, such as that of the safety factor near the pedestal ('q 95 ') and the distance between the inner and outer separatrices at the mid-plane ('dRsep'), have been also included to make the computed equilibria to stay near the chosen plasma operation condition.In this work, 'q 95 'and'dRsep' were respectively constrained to be larger than 2.8 and 4 cm, respectively.The plasma boundary is allowed to have some deviation from the target separatrix shape if the gap between the plasma and wall is maintained large enough (as shown in figure 8(b)).
The full list of CS/PF coil criteria (engineering limits), including the updated CS axial force criteria, applied to the analysis of equilibrium operational space using DINA and CORSICA is shown in table 1.The first column represents criteria of the CS/PF coil currents and imbalance current in the vertical stabilization (VS1) circuit.The second column represents criteria for the poloidal magnetic field applied on the CS/PF coils.The third column represents the updated CS axial The CORSICA plasma equilibrium operational space (Case3) at burn in 15 MA DT operation.The operational space updated with new CS force criteria (black curves) is compared with those in the previously reported TSC case (dashed color curves) in [8].
force criteria.The last column represents criteria for the PF coil vertical forces and the net CS force.The markers and colors used in the CORSICA analysis of the equilibrium operational space are also indicated.
The plasma equilibrium operational space of the 15 MA Baseline scenario, obtained at the state of plasma burn using the CORSICA constrained equilibrium analysis described above, is shown in figure 6.To provide more clear information on the identified violations, those identified during a large step variation of the poloidal flux linkage (∼10 Wb) are additionally summarized in table 2. All the violated criteria are shown in figure 6, using the markers and colors listed in the table 1. Markers obtained from a small step variation of the poloidal flux linkage (∼1 Wb), performed to identify the boundary with a higher resolution, are also shown in the figure.Note that if there are multiple violations with same marker type (e.g.all the coil current limits), only the last violation is shown due to the difficulty of showing many violations at a single point.However, there was usually a single violation for each type of markers near/at the boundary, as shown in table 2, except for the CS1U and CS1L coil criteria because they are connected in a circuit.In addition, necessary keywords are added on the figures to improve the readability.Note that the area with higher l i (>0.85) is not fully explored as the expected value of l i during the flat-top is rather low.Therefore the area with higher l i is left open in our analysis similarly to [8].Besides, an extended analysis previously done with 2008 ITER configuration [14] showed that the area with higher l i did not impose significant issues at least until l i = 1.0-1.1.
In figure 6, the updated plasma equilibrium operational space is compared with the previous TSC analysis results reported in [8] using the same colors (dashed lines).Names of the coils violating the criteria at different locations of the equilibrium operational space boundary in the TSC analysis are also indicated.Note that figure 6 shows an optimized equilibrium operational space, in which the upper left corner of the boundary is expanded by slightly shifting the PF6 'reference coil current' from 43.3 kA/turn to 41 kA/turn (the PF6 coil current limit is 48 kA/turn at ⩽6.4 T).Large part of the boundaries were determined by the coil current criteria (large circle markers).The updated CS axial force criteria (cross markers) were violated at lower poloidal flux state, usually below −150 Wb, determining only one boundary point (l i ∼ 0.85, poloidal flux linkage ∼−145 Wb).At this boundary point, the CS axial force criterion (no.33 in table 1) was violated.The obtained operational space qualitatively well reproduced the previously reported TSC equilibrium operational space, in the presence of the updated CS axial force criteria.

Comparison of CORSICA and DINA operational space lower boundaries
The CORSICA plasma equilibrium operational space obtained in section 3.1 is, of course, not a unique solution since the applied constraints, such as the reference coil currents and the plasma boundary control points (to be discussed in this section), can be further modified as far as the posterior validation conditions ('dRsep' and 'q 95 ′ in section 3.1) are satisfied.Therefore, not only to benchmark the CORSICA equilibrium operational space achieved in section 3.1, but also to further investigate the relationship with the posterior validation conditions, DINA constrained plasma equilibrium analysis on the lower boundary of the operational space, which represents the EOB, has been additionally performed and compared with the CORSICA results.
The lower boundaries of the plasma equilibrium operational space obtained from the DINA and CORSICA analyses are compared in figure 7. The poloidal flux linkage at the lower boundary is shown in figure 7(a) and the distances between the inner and outer separatrices on the outboard side midplane ('dRsep') are shown in figure 7(b).The plasma state at the EOB, obtained from the newly developed DINA 15 MA Baseline scenario (15 MA DT-DINA2020-04), is shown as green (+) markers.The 15 MA DINA plasma at the EOB is well within the operational space boundary (above the both DINA and CORSICA lower boundaries) and the 'dRsep' criterion (>4 cm) [15].The DINA and CORSICA lower boundaries show a good overall agreement, although the DINA lower boundary is located at lower poloidal flux linkage, implying that it can provide a longer flat-top burn duration.This difference is due to the larger separatrix deformation allowed in the DINA analysis leading to smaller 'dRsep' values (lower margin over the minimum 4 cm criterion).The plasmas separatrices obtained at the lower boundary around l i ∼ 0.7 are compared in figure 8.In DINA plasma equilibrium analysis the separatrix was allowed to be deformed relatively to the target separatrix if the minimum distances between the plasma and the wall can be maintained (i.e.focused mainly on the engineering aspects of operating the plasma inside the tokamak),  whereas the overall plasma cross section is better maintained in CORSICA equilibrium analysis (i.e.focused more on the overall plasma performance).The larger shape deformation with reduced 'dRsep' (DINA case in figures 8 and 7(b)) can increase the freedom in coil current distribution, and therefore, gives better chance to achieve an extended operational space (by having a lower poloidal flux linkage as shown in figure 7(a)) as demonstrated in the DINA analysis.However, a large plasma shape deformation may need to be avoided as it can affect the target plasma performance and stability.

Evolution of plasma discharge parameters within the equilibrium operational spaces
The ITER operation scenarios developed using CORSICA have focused on studying the feasibility of the plasma operation, especially the plasma performance and the evolution of the kinetic profiles, whereas the DINA operation scenarios have focused on investigating engineering feasibility of the ITER operation, such as the operation of the PF coil and power supply systems.These two different types of simulations are in fact complementary to each other and therefore an improved iterative process of integrating the two simulation results is required.In ITER Organization, there is an on-going activity of integrating the free-boundary equilibrium evolution and core-edge-SOL transport/source modeling capabilities, to deliver a high fidelity plasma simulator (HFPS) for ITER scenario development and physics studies [16].While this activity is foreseen to be productive in near future for improving all the required scenarios, activities of developing scenarios and performing various analyses so far have been rather unevenly distributed to comply with urgent ITER research and development needs.The 15 MA Baseline DT scenario has been continuously updated by using both the DINA and CORISCA, whereas the 12.5 MA Hybrid and 10 MA Steady-State DT scenarios have been studied by using CORSICA, mainly focused on the plasma operational and performance aspects.In this section, the evolution of plasma and CS & PF coil parameters in the physics-oriented 15 MA Baseline CORSICA scenario will be first investigated as a complementary effort to the validation of the engineering-oriented 15 MA Baseline DINA scenario (in section 3).Then, 12.5 MA Hybrid and 10 MA Steady-State CORSICA scenarios will be analyzed following the identification of their equilibrium operational spaces.Note that the CORSICA scenarios have no plasma breakdown models for plasma initiation phase and therefore assumed to start after the DINA plasma initiation phase.The studies in this section will focus only on the feasibility of the flat-top operation, i.e. to see if the CORSICA scenarios have enough margins during the flat-top phase and to investigate alternative ways of having adequate trajectories within the operational space.

Plasma discharge parameters within the 15 MA Baseline equilibrium operational space
The evolution of plasma discharge parameters (⟨Ψ ⟩ versus l i ) in the physics-oriented 15 MA Baseline CORSICA scenario [17] has been compared with the plasma operational space obtained in section 3.1, as shown in figure 9.The plasma current (I p ) ramp-up phase is indicated in magenta and the plasma state moves from a positive value of poloidal flux linkage at the initiation (⟨Ψ ⟩ > 100 Wb), down to ⟨Ψ ⟩ ∼−100 Wb at the end of the I p ramp-up.The plasma internal inductance at the end of I p ramp-up phase was about 0.8, within the foreseen range of vertical stability control for elongated plasmas (l i up to 1.2) using both VS1 and VS3 systems [18].During the I p flat-top phase, shown by a red curve, the plasma stayed well within the equilibrium operational space with small additional ⟨Ψ ⟩ consumption (∼−20 Wb).In this phase, the plasma internal inductance was initially reduced by about 0.1, mainly due to a transition to an H-mode, and then stayed around 0.7 until the end of the flat-top burn phase.During the I p rampdown, shown by a blue curve, ⟨Ψ ⟩ increased along with the plasma current reduction.In this phase, l i increased significantly due to the reduction in the edge bootstrap current and the associated plasma current density profile peaking, and this increase forced the plasma elongation to be reduced to maintain vertical stability.In this CORSICA scenario, the flattop duration is simply designed to have a sufficiently long flat-top length (>400 s), differently with the DINA scenario in which the maximum flat-top length is investigated within the CS1 coil current criterion (until −44 kA/turn allowed for a −45 kA/turn current limit, including 1 kA/turn as a margin for handling the shape evolution during H-L transition).Therefore, the plasma trajectory located well inside the operational space has a potential for further extending the flat-top burn operation (∼20 Wb is available for the flat-top extension).Such potential can be also found in the time traces of the coil current, field and force criteria.Figure 10 shows that even the most demanding CS1 currents in this scenario still have a sufficient margin at the end of the flat-top phase (t ∼ 500 s) and the updated CS axial forces are well within their criteria.It is worth noting that the CS axial force closest to its limit was F gap 1 in both CORSICA and DINA (see figure 4) scenarios.This indicates that both scenarios developed by applying similar operational assumptions (via a set of pulse schedule waveforms) are in a good qualitative agreement, although slightly different physics assumptions and models are applied to the whole scenario phases.Details of physics models and operational assumptions used in the physics-oriented CORSICA 15 MA Baseline scenario is given in [17].

ITER Hybrid and Steady-State plasma equilibrium operational spaces
The two Q ⩾ 5 scenarios for ITER DT plasmas, namely the 12.5 MA Hybrid and 10 MA Steady-State scenarios, are also investigated using a similar approach applied to the 15 MA Baseline scenario.The 12.5 MA Hybrid operation aims at operating the plasma longer than 1000 s with a relatively high fusion gain (Q > 5) to demonstrate the tokamak engineering capability associated with a high neutron fluence.The 10 MA Steady-State operation aims at demonstrating a fully noninductive plasma operation (>3000 s) at high fusion performance (Q ∼ 5), and therefore to address the feasibility of reactor relevant operation in future devices at ITER.Details of the 10 MA CORSICA Steady-State scenario, recently developed taking into account the removal of ITER lower hybrid current drive (LHCD) system in the heating and current drive (H&CD) upgrade options, and associated ideal MHD stability analysis can be found in [19,20].The 12.5 MA Hybrid scenario recently updated from the previous development [21] is summarized in appendix A.
In this section, these scenarios are firstly compared with the 15 MA Baseline scenario (figure 11) to highlight their distinct operational features reflected in the design of such scenarios.The 10 MA Steady-State scenario (dashed red curve) is designed to have the same initial magnetization (see table 4 for the coil currents at the start of simulations) and similar I p ramp-up process with those of the 15 MA Baseline scenario (solid blue curve), therefore the plasma state starts at the same initial point and follows a similar trajectory during the ramp-up.However, the PF coils consume less volt-seconds due to the lower flat-top plasma current, and consequently the I p ramp-up process stops at higher ⟨Ψ ⟩.For the same reason, the recovery of ⟨Ψ ⟩ during the ramp-down phase is smaller.During the flat-top burn phase, the excursion of ⟨Ψ ⟩ and l i is much smaller since the Steady-State scenario plasma is in a fully non-inductive operational state (i.e.no magnetic flux consumption).The 12.5 MA Hybrid scenario (solid green curve) is designed to have a lower initial magnetization to avoid the PF6 coil current limit as previously reported in [21].Note that the CS and PF coil currents at the start of simulation is also compared in table 4 and the ITER switching network unit (SNU) system is capable of being re-configured to have increased resistances, in order to provide necessary breakdown voltage at reduced CS coil currents.As shown in figure 11, the overall trajectory during the current ramp-up is only shifted by the difference in the initial magnetization.However, near the end of the ramp-up phase, l i is further reduced due to an early H-mode access, which is designed to maintain the central safety factor above 1.0 for a longer duration during the flat-top phase.During the flat-top phase, the excursion of ⟨Ψ ⟩ and l i are larger than that in the 15 MA Baseline scenario, due to its long inductive flat-top operation (1000 s).Note that the large initial variation of l i at the beginning of the ramp-up phase, commonly shown in all the three scenarios, is mainly due the settling of plasma profiles, started from rather arbitrary chosen initial profiles, along with the transport process and transition from a limited to a diverted configuration.
The equilibrium operational spaces of the 12.5 MA Hybrid and 10 MA Steady-State ITER scenarios are shown in figure 12, and compared with the operational space of the 15 MA Baseline scenario (green dashed lines).Theses operational spaces are developed by using the same set of plasma profile inputs used in the 15 MA operational space analysis, but after renormalizing them to match the plasma current and plasma poloidal beta to each scenario.This has been done since the operational space is mainly determined by the global plasma parameters, such as the plasma current and beta (both matched by re-normalization), and plasma internal inductance (varied for scan), rather than by detailed shapes of the plasma profiles.Note also that potential inconsistencies in the input plasma profiles caused by the simple re-normalization would be within the uncertainties assumed for the scenario development.Both operational spaces are much wider than that for the 15 MA Baseline scenario mainly at the upper part of the boundaries, even without applying any adjustment to the 'reference coil currents' (see section 3.1).The upper boundaries were mainly determined by the PF1 and PF6 coil current criteria similarly to that shown in figure 6, suggesting that there could be a common behavior when the poloidal flux linkage is high (i.e.near the start of the flat-top).The extension at the upper part of boundaries is mainly due to the lower flat-top plasma current in the selected scenarios, which increases margins in the volt-seconds of CS coils and also reduces the reference PF6 coil current (∼26.9kA/turn and ∼28.4 kA/turn) compared with that (∼43.3 kA/turn) in the 15 MA Baseline scenario.These allow the plasma to find an equilibrium at higher poloidal flux linkage without requiring additional modifications to the 'reference coil currents'.The lower boundaries were mainly determined by the CS1 coil currents at high plasma internal inductance (l i > 0.8-0.85)whereas they were determined by the updated CS axial force criterion applied between the lower LDP and the base of CS3L module (f gap 0 ) at medium/low plasma internal inductance (l i < 0.8-0.85).Note that further optimization or extension of these operational space, which would be still possible, is not attempted in this work since the obtained operational space is already sufficient to achieve the target operational goals of both scenarios.The equilibrium operational spaces (green curves in figure 13) are compared with the evolution of the plasma discharge parameters in the 12.5 MA Hybrid and 10 MA Steady-State scenarios.During the flat-top phase, the plasma trajectories were well within the operational space, although the plasma in the 12.5 MA scenario was located relatively close to the upper boundary of the operational space at the beginning of the flat-top phase (l i ∼ 0.62, poloidal flux linkage ∼−101 Wb).As we have discussed in figure 12, the entire trajectory of the 12.5 MA Hybrid scenario can be shifted down further with additional changes in the initial magnetization.Alternatively, the early H-mode access can be also adjusted to make the plasma stay at a higher plasma internal inductance as far as the operation is compatible with the Hybrid operation goals (e.g.maintaining q min > 1.0), and therefore to increase the margin (distance to the upper left corner of the boundary).The evolution of the 10 MA flat-top plasma inside its operational space showed sufficient margins, mainly due to the small excursion of the coil currents during the flat-top burn phase (steady-state with almost no flux consumption).
The time traces of the CS & PF6 coil currents and axial forces in the 12.5 MA Hybrid are shown in figure 14.The CS coil currents started at lower initial currents due to the shift in the initial magnetization (∼−40 Wb) and the CS1 current approached its lower limits (−45 kA/turn) during the flat-top phase.However, there were still significant margins at the end of a long flat-top duration (∼950 s).The time trace of the PF6 coil current shows that it approached its limit at the end of the current ramp-up.However, it did not violate its limit and then moved away from it as the plasma state moved to a lower poloidal flux linkage (i.e. as the volt-second from the PF6 coil is consumed).The CS axial forces shown in figure 14(b) were also well within their criteria with sufficient margins.The CS coil currents and axial forces in the 10 MA Steady-State scenario are shown in figure 15.Since the flat-top plasma was already in an almost fully non-inductive stationary condition, both currents and forces remain stationary and well within their criteria for the rest of the burn phase.

Summary and conclusion
The CS axial force criteria have been updated taking the asbuilt ITER CS module stiffness and additional margins into account and then applied to verify and update various ITER operation scenarios.The initial verification with the previously developed 15 MA Baseline scenario, which is usually considered as most demanding one in terms of operating the ITER coil and power supply systems, has revealed that the CS axial force criteria is not satisfied for the plasma initiation phase.The plasma initiation phase has, thus, been re-developed using TRANSMAK and DINA, keeping the original goal of maximizing the poloidal magnetic flux available for the achievement of a long flat-top burn duration with Q = 10 at 15 MA.The re-developed plasma initiation phase has been integrated to produce a new 15 MA Baseline scenario.This new scenario has been investigated against the entire set of coil current, field and force criteria.Since the verification of a single scenario would not sufficient to cover a wide range of variant scenarios to be explored while performing the real experiments, the plasma equilibrium operational space has been analyzed using the CORSICA constrained equilibrium analysis capability for searching entire boundaries, as well as using the DINA equilibrium analysis workflow for benchmarking the lower boundary of the equilibrium operational space.The two analyses showed a good agreement although the applied constraints,   spaces and showed that there is enough room for operating the reference scenarios, as well as for developing variant scenarios if required.All the DINA and CORSICA scenarios developed in this work are available in the ITER IMAS scenario database [22] and summarized in table 3. It is also worth mentioning that the equilibrium operational space analyses are now available as in-house modeling capability of the ITER Organization, to allow timely update of analyses along with the identification of as-built properties of ITER tokamak components.B3.The updated force criteria on the ITER CS coils are described as follows.The compressive forces applied to the gaps between the ITER CS modules determines gap frictional forces which react to gross differential sideways movement arising from transversal loads, for example, generated   by non-concentric coil-set assembly, asymmetric plasma disruptions and seismic loads.A comprehensive analysis defines the lower bound of this compressive force in ITER to 26 MN to be adequate to ensure that all the gap frictional forces are large enough to react to the foreseen sideways movement.The schematic view of the ITER coils and forces are shown in figure 1.The seven contact surfaces between the between the load distribution plates (LDPs) and CS modules, where the compressive forces are applied, are marked as gaps.The force criteria, with forces compressing a gap treated as negative, are given as F gap j < −26 [MN] , j = 0, . . ., 6. (B1) The lowest gap between the lower LDP and the base of CS3L module (gap 0 ) forms a special case due to the unique cantilevered support of this gap.The additional criterion for the lowest gap is therefore given by f gap 0 ≡ where F ri and F ci are respectively radial and crushing forces acting on the CS modules.The radial, vertical and crushing forces are given by F ki = 2π j ϕ ˆr ϕ × B pol ds, (k = r, z) (B4) where j ϕ is toroidal current density, ϕ is a unit vector in the toroidal direction, B pol is the poloidal magnetic field, ∆z is the CS coil height, r and z are the coil radial and vertical coordinates, z is the z-coordinate of a coil geometric center, and ds represents the conducting area of the coil across which the integral forces are calculated.The pre-load at temperature of 4 K in the absence of electromagnetic force and mechanical coefficients are respectively given by F tp 4K = 190 [MW], α = −0.0019,β = [0.0389,0.1161, 0.1933, 0.2696, 0.3468, 0.4239] and γ = 0.0739.Then, the other axial forces can be computed using F gap j = F gap j +1 + F z j − mg, j = 0, . . ., 5 (B6) with the weight of a single CS module mg = 1.18 [MN].
The net vertical electromagnetic load on the CS coils is unchanged and expressed as 5 i =0 F z i < 60 MN. (B7)

Figure 1 .
Figure 1.Schematic view of the poloidal cross-section of the ITER CS/PF coil and first wall geometry.Gaps between CS coils and upper/lower Load Distribution Plate (LDP) are indicated in red.Note that detail structures of LDPs are not shown for simplicity.

Figure 2 .
Figure 2. Time traces of (a) the plasma current, (b) CS3U coil current and (c) axial force applied at gap 0 (between CS3L and lower LDP).The plasma initiation has been compared between the previous 15 MA Baseline DINA scenario (15 MA DT-DINA2016-01, shown in blue) and the one newly developed (15 MA DT-DINA2020-04, shown in green) to avoid the updated CS axial force criteria (shown in red line in (c)).

Figure 3 .
Figure 3. Lines of the constant values of poloidal magnetic field (in G) at the breakdown time (t = ∼1.1 s) (a) in the previous 15 MA Baseline DINA scenario (15 MA DT-DINA2016-01) and (b) in the re-developed initiation phase within the updated CS force criteria (15 MA DT-DINA2020-04).The figures also show axisymmetric model of the conducting structures which eddy currents affect magnetic field at the breakdown (two walls of the vacuum vessel, support of the blanket modules #18, divertor inboard rail).

Figure 4 .
Figure 4. Time traces of (a) the plasma current, (b) CS1 coil current, (c) axial force applied at gap 0 (between CS3L and lower LDP) and (d) gap 1 (between CS2L and CS3L).The reference coil current is indicated as red dashed line in (b) and the updated CS axial force limits are shown in red lines in (c) and (d).15 MA Baseline DINA scenario (15 MA DT-DINA2020-04).

Figure 5 .
Figure 5.The plasma current density profile used in the DINA analysis of plasma equilibrium operational space at burn in 15 MA DT operation.

Figure 6 .
Figure 6.The CORSICA plasma equilibrium operational space (Case3) at burn in 15 MA DT operation.The operational space updated with new CS force criteria (black curves) is compared with those in the previously reported TSC case (dashed color curves) in[8].

Figure 7 .
Figure 7.The poloidal flux linkage (a) and the distance between the inner and outer separatrices on the outboard side mid-plane (b) at the lower boundaries (EOB) of the DINA (red cross) and CORSICA (blue circle) plasma equilibrium operational spaces are compared.The plasma state at the EOB of the newly developed DINA 15 MA Baseline scenario (15 MA DT-DINA2020-04) is also shown as green plus markers.

Figure 8 .
Figure 8.The separatrices from CORSICA (a) and DINA (b) equilibrium analysis.These separatrices are obtained at the EOB boundary of {⟨Ψ ⟩, l i } operational space at l i ∼ 0.7.The separatrix control points are shown in green circles in (a).The target separatrix shape is shown either as a black dashed curve in (a) or a black solid curve in (b).The separatrices from the free-boundary equilibrium solutions are shown by red curves.

Figure 9 .
Figure 9.The evolution of plasma discharge parameters (⟨Ψ ⟩ versus l i ) in the CORSICA simulation of 15 MA Baseline scenario (connected Ip ramp-up-magenta, Ip flat-top-red and Ip ramp-down-blue curves) is compared with the plasma equilibrium operational space at burn in15 MA DT operation (green).

Figure 10 .
Figure 10.Time traces of (a) the CS coil currents and (b) updated CS axial forces in the 15 MA Baseline scenario are compared with their limits (shown as dashed lines).

Figure 11 .
Figure 11.The evolution of plasma discharge parameters (⟨Ψ ⟩ versus l i ) in the 15 MA Baseline, 12.5 MA Hybrid and 10 MA Steady-State CORSICA simulations are compared.

Figure 12 .
Figure 12.The equilibrium operational spaces of (a) the 12.5 MA Hybrid and (b) 10 MA Steady-State ITER scenarios.The operational space of the 15 MA Baseline scenario is also shown in green dashed lines.

Figure 13 .
Figure 13.The evolution of plasma discharge parameters (poloidal flux linkage versus l i ) in the (a) 12.5 MA Hybrid and (b) 10 MA Steady-State CORSICA simulations (connected magenta, red and blue curve) are compared with the equilibrium operational spaces during the flat-top phase (green curve).

Figure 14 .
Figure 14.Time traces of (a) the CS & PF6 coil currents and (b) updated CS axial forces in the 12.5 MA Hybrid scenario are compared with their limits (shown as dashed lines).

Figure 15 .
Figure 15.Time traces of (a) the CS coil currents and (b) updated CS axial forces in the 10 MA Steady-State scenario are compared with their limits (shown as dashed lines).

Figure A1 .
Figure A1.Time traces of the plasma parameters in the 12.5 MA Hybrid scenario.The plasma current (IP), volume averaged electron density (<ne>), bootstrap current (IBS), neutral beam and electron cyclotron driven currents (INB and IEC), and effective charge number (Zeff) are shown in the top figure (a)-(a ′ ).The power crossing the separatrix (Pin-Prad), alpha particle self-heating power (Palpha), total auxiliary heating power (Paux), H-mode threshold power (Pth), electron cyclotron heating power (PEC) and neutral beam heating power (PNB) are shown in the bottom figure (b)-(b ′ ).

Figure A2 .
Figure A2.The plasma profiles of the 12.5 MA Hybrid scenario.The electron and ion temperature profile (a), and electron, ion, tritium, deuterium, alpha, neutral beam fast ion densities at the of the flat-top (b), and the evolution of the plasma, bootstrap, neutral beam and electron cyclotron driven current density profiles (c) and safety factor profile (d) are shown.

Table 2 .
List of violations of the CS/PF coil criteria (engineering limits) identified in the CORSICA constrained plasma equilibrium analysis of the 15 MA Baseline operation.

Table 3 .
List of DINA and CORSICA scenarios presented in this work.Note that IDS run number can be varied (usually increased) along with the improvement of the scenario.

Table 4 .
List of the CS/PF coil currents [kA/turn] at the start in the DINA and CORSICA scenarios presented in this work (as listed in table3).Note that the coil currents in the DINA scenario are taken at the plasma initiation while those in the CORSICA scenarios are measured at Ip = 0.1 MA (note that CORSICA has no model of the plasma breakdown).

Table A1 .
Plasma parameters obtained at t = 300 s in the 12.5 MA ITER Hybrid scenario updated using CORSICA simulation.Note that β N and l i (3) estimated without including the pressure from fast alphas.

Table B1 .
ITER poloidal filed coil geometry including radial and vertical positions of coil center, coil width and height in the poloidal cross section and numbers of turns.

ITER CS & PF coil geometry and turns, and the list of coil current, field and force limits used in this work
The ITER CS & PF coil geometry and turns are shown in table B1 and the coil current and field limits are shown in tableB2.The imbalance current in the coils, PF2-PF5 (the current flowing in the Vertical Stabilization Converter), is calculated usingI imb = I PF2 + I PF3 − I PF4 − I PF5and it should not exceed 22.5 [kA/turn].The maximum vertical forces on the PF coils are shown in table

Table B2 .
Maximum current and magnetic field in one turn of the ITER CS & PF coils.The coil current limits (Imax) is determined by the applied magnetic field (B) or the coil filed limit (Bmax) is determined by the applied coil current (I) as shown below.CoilI 1 (kA/turn) B 1 (T) I 2 (kA/turn) B 2 (T)

Table B3 .
Maximum vertical forces on the ITER PF coils.
=0 F zi is the net vertical forces applied on the CS stack and F gap 0 is the axial force applied on the lowest gap.The axial force acting across each CS gap is calculated progressively starting from the axial force applied on the gap between the upper LDP and the top of CS3U module (gap 6 ) given by F gap 6 = F tp 4K + α o = 16.82 [MN] and dF = −0.53.The 5 i