4C
The confinement of hightemperature plasmas peculiar of nuclear fusion devices requires magnetic fields of several Tesla. In several fusion experiments (e.g., Tore Supra, KSTAR, EAST) as well as in future devices (e.g., ITER, W7X, JT60SA, EU DEMO) and most likely in a fusion reactor, these high fields are produced by superconducting (SC) coils, wound relying on the cableinconduit conductor (CICC) concept and carrying currents of several tens of kA each.
Due to the complexity of the magnet system and the large variety of transients that are expected to take place during a fusion reactor lifetime, together with the strict requirements for a safe and cheap operation of the cryoplant supplying the supercritical He (SHe) for the cooling of the SC coils, thermalhydraulics (TH) has become a key issue in a fusion reactor design.
Since 2008, the Cryogenic Circuit Conductor and Coil (4C) code has been developed at the Energy Department of the Politecnico di Torino to allow the TH modeling of transients in the whole magnet system of fusion devices.
The 4C code is currently the stateoftheart tool for this kind of modelling: it is flexible and easytouse in terms of geometry definition and model implementation and it has a modular structure. Each module, suitably coupled to the others, describes a subsection of the magnet system:
 Coil winding. This is an updated version of the Multiconductor Mithrandir (M&M) code and analyzes the SC winding with its cooling paths. Each hydraulic channel is addressed as a 1D SHe flow in the conductor axial direction and is discretized with finite elements method. Mass, momentum and energy conservation equations are solved in each He region, coupled with transient conduction equations in the conductor and (separately) in the jacket.
 Coil structures cooling channels. When the coil is encapsulated in bulky envelopes, additional casing cooling channels (CCC) are required. Each hydraulic channel is addressed as a 1D SHe flow in the CCC axial direction, is discretized with finite elements method and the solution of the mass, momentum and energy conservation equation for the cooling He results in the computation of He speed, temperature and pressure. The pipe wall can also be included in the model, solving a 1D heat conduction equation, coupled with the three He equations.
 Coil structures. The thermal analysis of the bulky structures of the coil is performed computing the temperature map on a selected set of 2D azimuthal (poloidal) cross sections, approximating with finite elements the real 3D heat conduction problem.
 Cryogenic circuit. The external cryogenic circuit(s) for the SHe is modeled using the objectoriented, equation based modeling language Modelica. The models of all the main cryogenic circuit components (pipes, valves, volumes, circulators, LHe bath, controllers, heat exchangers) are contained in the newly developed Cryogenics library, which is a suitable extension of the ThermoPower opensource library to the cryogenic operating conditions.
After the development of its core structure, the 4C code entered a long, detailed, successful (and neverending) validation and benchmark campaign, exploiting experimental data from a wide range of transients and possible CICC configurations. The validation includes both the interpretative and predictive analysis of experimental data, so the tool is now ready for application to project design.
Research topics
Publications
2017
Analysis of the cooldown of the ITER central solenoid model coil and insert coil
Article
Bonifetto, Roberto; Brighenti, Alberto; Isono, Takaaki; Martovetsky, Nicolai; Kawano, Katsumi; Savoldi, Laura; Zanino, Roberto
SUPERCONDUCTOR SCIENCE & TECHNOLOGY
Institute of Physics
Vol.30 pp.17 ISSN:09532048 DOI:10.1088/09532048/30/1/015015

Development of a ThermalHydraulic Model for the European DEMO TF Coil
Article
Zanino, Roberto; Bonifetto, Roberto; Dicuonzo, Ortensia; Muzzi, Luigi; Nallo, GIUSEPPE FRANCESCO; Savoldi, Laura; TurtÃ¹, Simonetta
IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY
The IEEE Council on Superconductivity
Vol.26 pp.6 ISSN:10518223 DOI:10.1109/TASC.2016.2523241

Verification of the Predictive Capabilities of the 4C Code Cryogenic Circuit Model
Proceeding
Zanino, Roberto; Bonifetto, Roberto; Hoa, C.; Savoldi, Laura
AIP CONFERENCE PROCEEDINGS
In: Advances in Cryogenic Engineering
Cryogenic Engineering Conference (Anchorage (AK)) June 1721, 2013
Vol.1573 pp.8 (pp.15861593) ISSN:0094243X ISBN:9780735412033 DOI:10.1063/1.4860896 
Analysis of the Effects of the Nuclear Heat Load on the ITER TF Magnets Temperature Margin
Article
Savoldi, Laura; Bonifetto, Roberto; Bottero, U.; Foussat, A.; Mitchell, N.; Seo, K.; Zanino, Roberto
IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY
The IEEE Council on Superconductivity
Vol.24 pp.4 ISSN:10518223 DOI:10.1109/TASC.2013.2280720

Validation of the 4C ThermalHydraulic Code against 25 kA Safety Discharge in the ITERToroidal Field Model Coil (TFMC)
Article
Zanino, Roberto; Bonifetto, Roberto; Heller, R.; Savoldi, Laura
IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY
IEEE
Vol.21 pp.5 (pp.19481952) ISSN:10518223 DOI:10.1109/TASC.2010.2089771

The 4C Code for the Cryogenic Circuit Conductor and Coil modeling in ITER
Article
Savoldi, Laura; Casella, F; Fiori, B; Zanino, Roberto
CRYOGENICS
Vol.50 (pp.167176) ISSN:00112275

M&M: MultiConductor Mithrandir Code for the Simulation of ThermalHydraulic Transients in Superconducting Magnets
Article
Savoldi, Laura; Zanino, Roberto
CRYOGENICS
Vol.40 (pp.179189) ISSN:00112275
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