---
title: Modeling of HTS bulks surrounded by magnetic components using the H–φ formulation
description: "HTS Modelling Workgroup | Model files\nModeling of HTS bulks surrounded by magnetic components using the H–φ formulation"
---

[Model files](https://htsmodelling.com/model-files)

# [Modeling of HTS bulks surrounded by magnetic components using the H–φ formulation](https://htsmodelling.com/model-files/modeling-of-hts-surrounded)

 Written by [administrator](https://htsmodelling.com/model-files/author/administrator) | Mar 20, 2024 6:31:30 PM

#### These models were shared by Alexandre Arsenault, Polytechnique Montréal, Montréal.

These two models use the reduced H-phi formulation to efficiently simulate the magnetic field of a superconducting bulk surrounded by magnetic components. The magnetic field is separated into a source and reaction field component in order to reduce the simulated domain surrounding the superconductor. The source field is used as a source in the reaction field simulations using a modified H-formulation in the superconducting domain. The first model simulates the zero field cooled magnetization of a superconducting cube between a set of Helmholtz coils. The coils are simulated in a 2D axisymmetric component and extruded to a 3D component using a “general extrusion” operator.

The second model simulates a permanent magnet levitating over a superconducting bulk. The motion of the permanent magnet is considered with a time-dependent z-coordinate in the extrusion of the source field to the reaction field simulations with a “general extrusion” operator. Both models show very good agreement with the pure H-formulation, and are more than three times faster.

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References

1. [Alexandre Arsenault et. al., “Efficient Modeling of High-Temperature Superconductors Surrounded by Magnetic Components Using a Reduced H–φ Formulation”, IEEE Transactions on Applied Superconductivity, volume 31, no. 4, June, 2021](https://doi.org/10.1109/TASC.2021.3073274)

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