Calculating the 3D magnetic field of ITER for European TBM studies

The magnetic perturbation due to the ferromagnetic test blanket modules (TBMs) may deteriorate fast ion confinement in ITER. This effect must be quantified by numerical studies in 3D. We have implemented a combined finite element method (FEM) – Biot-Savart law integrator method (BSLIM) to calculate the ITER 3D magnetic field and vector potential in detail. Unavoidable geometry simplifications changed the mass of the TBMs and ferritic inserts (FIs) up to 26%. This has been compensated for by modifying the nonlinear ferromagnetic material properties accordingly. Despite the simplifications, the computation geometry and the calculated fields are highly detailed. The combination of careful FEM mesh design and using BSLIM enables the use of the fields unsmoothed for particle orbit-following simulations. The magnetic field was found to agree with earlier calculations and revealed finer details. The vector potential is intended to serve as input for plasma shielding calculations.

💡 Research Summary

The paper presents a comprehensive methodology for calculating the three‑dimensional magnetic field of ITER, explicitly accounting for the magnetization of ferromagnetic components such as the European helium‑cooled pebble‑bed (HCPB) test blanket modules (TBMs) and the ferritic inserts (FIs) that are installed to smooth the toroidal field. The authors combine a finite‑element method (FEM) simulation performed with COMSOL Multiphysics (AC/DC module) and a direct Biot‑Savart law integrator (BioSaw) to obtain a high‑resolution field that can be used without smoothing in fast‑ion orbit‑following codes.

The workflow consists of two main steps. First, a full‑geometry FEM model of the entire ITER torus—including the 18 D‑shaped toroidal field (TF) coils, the six poloidal field (PF) coils, the central solenoid (CS), and the plasma current—is built. Geometry is imported from CAD and EQDISK files; the TF coil spine curve is smoothed with a second‑order Bézier fit, and the plasma and coil current densities are assumed uniform. The ferromagnetic components are assigned nonlinear B‑H curves: SS430 stainless steel for the FIs (mean curve from reference data) and a temperature‑adjusted EUROFER curve for the TBMs.

Because the original CAD models contain many fine details (small gaps, bolt holes, thin plates) that would make a full FEM mesh intractable, the authors deliberately simplify the geometry, removing gaps smaller than 10 mm and merging thin plates. These simplifications reduce the metal volume of the TBMs and FIs by up to 26 %. To preserve the total magnetic moment of each component, they introduce a correction to the material law: the original H(B) relationship is transformed into H*(B) using a factor that depends on the volume ratio c = V_original / V_simplified (Equation 3). This ensures that, in the limit of a uniform external field, the product of magnetization and volume remains unchanged.

In the second step, the FEM solution provides the magnetization vector M throughout the ferromagnetic domains. The authors then run a “permanent‑magnet” COMSOL simulation in which all free currents are removed and the constitutive relation is set to B = μ₀(H + M). The resulting magnetic field, which represents only the contribution of the magnetized components, is superimposed on the background field computed by BioSaw from the known coil currents. The combined field yields both the magnetic flux density B and the magnetic vector potential A throughout the domain.

Boundary conditions are handled by embedding the entire model inside a 14 m radius sphere, which itself is surrounded by an “infinite shell” that maps the radial coordinate to a virtual distance of several kilometres, effectively mimicking an open‑space boundary. This approach avoids artificial reflections and ensures that the field decays correctly at large distances.

The authors validate their results against previous ITER magnetic field calculations (reference