Simulation software, supported by CERN, for the creation of
Digital twins of Superconducting Magnets

Numerical Modeling in Superconducting Magnet Design

Superconducting magnets are widely used in MRI machines, NMR equipment, mass spectrometers, magnetic separation processes, and particle accelerators. Lately, they have been used in generators of wind turbines and in transportation. SC technology allows users to produce extremely high magnetic fields without the many kilowatt, or even megawatt, power supplies needed for electromagnets. Once ‘brought to field’, SC magnets can be almost disconnected from their power source and function in persistent mode, resulting in significant savings in electricity costs.

Numerical simulation is widely used in the R&D of superconducting magnets. Their design can’t rely on simple analytical calculations because of the complex structure and harsh requirements. High-level numerical analysis technology is applied in magnet systems to decide the electromagnetic structure parameters. The use of numerical simulation is mandatory to consider the various parameters that affect the magnet design such as geometrical features, the field of application, environment, function and material properties. The cost of a magnet and the very strict allowed tolerances is such that any design iterations shall be made only within a numerical environment. This process leads to the optimization of the design which shall be verified only by few, if not only one, prototype

The high magnetic field is an exciting cutting-edge technology full of challenges and essential for many significant discoveries in science and technology.

The Knowledge Transfer group at CERN aims to engage with experts in science, technology and industry in order to create opportunities for the transfer of CERN’s technology and know-how. FEAC is proud to be one of the few companies supported by the CERN Knowledge Transfer group, in the category “Industry 4.0”. Read more here

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    • A superconducting dipole magnet used in compact hadron therapy gantries. Hadron therapy is an advanced radiotherapy technique using proton or ion beams to deliver precision treatment of tumors, sparing the surrounding healthy tissues from unwanted radiation.
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    • The FCC (Future Circular Collider) is a future Hadron Collider which will likely succeed the LHC as the most powerful particle accelerator in the world, providing scientists in the field of high energy physics with a powerful discovery tool. It will be constructed in a tunnel of ~100 km in length. The development of the powerful 16T main dipole magnet implies important engineering challenges.
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    • MKQXF is an alternative superconducting quadrupole design for the future upgrades of the CERN accelerator chain along with the future high-energy colliders, notably the FCC.
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    • 15T magnet for Future High-Energy Colliders
      Nb3Sn magnets with a nominal operation field of 15-16 T are being considered for the LHC energy upgrade (HE-LHC) and a post-LHC Future Circular Collider (FCC). To demonstrate the feasibility of 15 T accelerator quality dipole magnets, the US Magnet Development Program (MDP) is developing a single-aperture 15 T Nb3Sn dipole demonstrator

Vector & Scalar Potentials


Meshless Method


Top-class Accelerated FEM/BEM solver
Lorentz Forces


Field Harmonics


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    • PITHIA’s solver offers unprecedented capabilities to the user over the competition:

      1) Based on the accelerated Boundary Element Method, it is capable of solving complex models corresponding to more than 1million DoF (Degrees of Freedom). This reduces the need for simplifcations and modeling assumptions. Instead, it increases the confidence & accuracy of the computed results.

      2) By implementing innovative numerical techniques, it offers drastically faster solution times

      3) It minimizes the computer hardware requirements.

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    • PITHIA-EM drives innovation in Digital Twins of Electro-magnetic systems and provides unprecedented capabilities compared to the competition.
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    • The dominant competing solution is the Finite Element Method (FEM), which generally is very well implemented but has certain limitations in problems dealing with infinite/semi-infinite domains. The method has significantly higher computational requirements, making it unsuitable for e.g. acoustic, vibration wave propagation in soil and electromagnetic problems. PITHIA is based on the Boundary Element Method (BEM), the main advantage of which is the reduction of the dimensionality of the problem. This means that only the boundaries of the problem is required to be discretized in contrast with the FEM where the volume of the e.g. sea, soil or water must be discretized. Thus, the model preparation in PITHIA is significant simpler. Additionally, it well-known that the Boundary Element method offer unprecedented accuracy compared to the Finite Element Method.

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FEAC's PITHIA for EM-Brochure