# Operation Margin of the ITER Central Solenoid During the Plasma Scenario
## 6 Conclusions  
The analysis of the ITER central solenoid during the 15 MA scenario was completed with a multi-physics model developed in the framework of the _SuperMagnet_ suite of codes. This model reproduces the performance during the plasma scenario of the CS modules, namely six modules for a total of 240 pancakes, and of the cryogenic system, including about 4 km of pipes with about 30 valves, the circulator and the heat exchanger. The main sources of losses that involve the CS and its cryogenic system during the scenario are accounted for in the model. A total amount of 12.1 MJ enters the system, and 75% of this total is attributed to AC losses and coupling and hysteresis losses, induced by the rapidly time-varying magnetic flux density and currents in the conductor. The static heat load in the feeders, arising from radiation heating from the thermal shields and conduction from the mechanical support, constitutes approximately 20% of the total losses. The losses in the joints are less than 1% of the total. The nuclear heating in the CS is almost negligible due the shielding effect of the components positioned between the plasma and the CS, such as the blanket, the vacuum vessel, the in-wall shielding, the thermal shield and the TF coils. The model allows us to estimate the performance of the conductors during the plasma scenario. The temperature in the conductor exhibits a peak of 7.4 K in pancake #39 of module CS1U at \(t\) = 600 s. In the other modules, the peak temperature is below 7.0 K.  
The larger amount of losses deposited at the inner turns of the CS determines a temperature increase, which is still limited to below 6.0 K, at the inlet of the pancakes. These higher losses also affect the flow circulation: a helium reverse flow is observed in particular in modules CS3L, CS1L and CS1U. After a transient time of about 10 s, the cryogenic pump is able to re-establish nominal flow operation, and fresh helium--with a temperature below 5 K--enters the pancakes without back flow during the remaining phases of the plasma scenario. Analysing the results of the main cryogenic loop, a higher peak temperature is found at the manifold collecting the outlets of the upper modules (CS3U/2U/1U) than at the  
Figure 18: Energy balance of the CS and the cryogenic circuit during the plasma scenario. corresponding manifold of the lower modules (CS3L/2L/1L). This difference, still limited to about 0.4 K, is mainly due to the different loss profiles between the modules. The main outcome of the model is the temperature margin of the coils during the plasma scenario, computed as the difference between the current-sharing temperature and the temperature in the conductor. A minimum value of 1.8 K is observed at the end of the plasma scenario in turn #1 of the central pancakes of modules CS3L, CS1L and CS1U, all assembled with Nb\({}_{3}\)Sn Jastec strands. This value is, in any case, above the prescribed threshold of 0.7 K for the CS conductor set by the design as the minimum margin. Conceptualization, L.C., M.B., J.L. and C.H. ; methodology, L.C., M.B., J.L. and C.H. ; software, L.C. ; validation, L.C., M.B., J.L. and C.H. ; formal analysis, L.C., M.B., J.L. and C.H. ; investigation, L.C., M.B., J.L. and C.H. ; resources, L.C., M.B., J.L. and C.H. ; data curation, L.C., M.B., J.L. and C.H. ; writing--original draft preparation, L.C. ; writing--review and editing, L.C., M.B., J.L. and C.H. ; visualization, L.C. ; supervision, M.B. and C.H. ; project administration, M.B. and C.H. ; funding acquisition, M.B. and C.H. All authors have read and agreed to the published version of the manuscript. The work at Universita di Bologna was supported by the ITER Organization under contract # IO/20/CT/4300002342. The views and opinions expressed herein do not necessarily reflect those of the ITER Organization. Not applicable. The data presented in this study are available on request from the corresponding author. The data are not publicly available. This paper is based on the work of many people.