# Operation Margin of the ITER Central Solenoid During the Plasma Scenario
## 1 Introduction  
The International Thermonuclear Experimental Reactor (ITER), under construction in Cadarche, in Southern France, aims to create a sustained deuterium/tritium plasma predominantly heated by \(\alpha\) particles, thus proving the technological and scientific feasibility of fusion power reactors [1, 2]. The reference plasma scenario for the ITER's operation is the high-confinement state (H-mode) [3], with a longer energy confinement time than in the low-confinement state (L-mode); the latter one is characterised by relatively higher turbulence, which allows the energy to escape the plasma [4]. The H-mode provides the basis for achieving a net gain of the reactor of up to 10 (Q = 10), with 500 MW of fusion power from 50 MW of input heating power [5]. The DINA code has been developed for the simulation of the plasma scenario [5], and it has been validated with experiments [6, 7]. Simulations of the plasma burn in the ITER reactor were provided for two representative scenarios of ITER operation [8]. The first scenario has a 15 MA plasma current with a full-bore plasma producing 500 MW of fusion power with Q = 10 for about 400 s. The second scenario is a steady-state case with a plasma current of 9 MA and a highly shaped plasma, producing about 300 MW of fusion power with a net gain higher than 5 (Q > 5) for about 3000 s [2]. During the plasma scenario, several loss sources arise, which involve the superconducting coils, cooled by supercritical helium (SHe), and the cryogenic system. The major contributors are as follows. 1. AC losses in the coils: The rapidly time-varying currents required by the plasma control and the corresponding time-varying magnetic flux density induce coupling currents between the cable components, thus generating coupling losses in the conductor and hysteresis losses in the superconducting material [9; 10]. 2. Eddy current losses in the structure: The surrounding metallic structure working as a mechanical support for the magnet experiences rapidly time-varying magnetic fields with resulting eddy currents and losses [11; 12]. 3. Losses in the joints: The joints between the superconducting cables include a resistive part connecting the two superconducting parts. The transport current flowing through the resistive component of the joints generates non-negligible Joule losses. Furthermore, coupling and hysteresis losses occur in the superconducting cables inside the joint [13; 14]. 4. Nuclear heat load: Heat can be generated in the coils due to the 14 MeV neutrons escaping from the vacuum vessel (the major contribution), radioactive isotopes of nitrogen (\({}^{16}\)N) from the plasma, and radioactive decay [15]. 5. Static heat load in the feeders: The feeders of the helium cooling circuit are located outside the cryostat and experience radiation heating from the thermal shields and conduction from the mechanical support. Maintaining the superconducting magnets within a controlled temperature increase is crucial for the safe operation of the reactor. An uncontrolled temperature rise can lead to the current-sharing temperature threshold being exceeded, generating Joule heating and then an irreversible quench during plasma operation [16; 17]. Adequate numerical modelling of the superconducting magnets during plasma scenarios is crucial in estimating the operational temperature margin of the coils and preventing permanent damage to the magnet [18]. The challenge of these analyses, when using numerical methods, is related to two main aspects:  
1. The model requires a multi-physics analysis, able to tackle thermal, hydraulic and electromagnetic phenomena;
2. A large number of degrees of freedom is required to discretise a large-scale magnet, wound with several kilometres of cable-in-conduit conductors (CICCs), and its cryogenic system, with several kilometres of pipes and different components, such as bypass and control valves, heat exchangers and the circulation pump.