ICAP 2002 Abstracts and Posters

A Magnetization Model for Superconducting Strands in a Rotating Electromagnetic Field

Abstract

The Large-Hadron-Collider (LHC), will consist of about 8400 superconducting magnet units of different types. Magnetic field changes in the multi-filamentary (NbTi) wires of these superconducting magnets induce shielding currents in the filaments which persist due to the lack of resistivity (neglecting flux creep). This behavior of hard superconductors is phenomenologically described by Bean's critical state model. The authors have previously presented the extension of the model to varying critical current densities within the superconducting filament and the combination of the model with numerical methods for the field calculation in the entire magnet, including the ferro-magnetic iron yoke.

This paper presents a semi-analytical 2-dimensional model of the filament magnetization (including hysteresis effects) due to field changes both in amplitude and direction. The model is based on layers of nested intersecting ellipses carrying shielding currents of field dependent critical current density, generating a uniform field inside. Field changes result in the creation of such current layers and/or in the annihilation of previously induced layers. The semi-analytical model is derived from the differential equation for the magnetic shielding of one infinitesimally thin layer and from the continuity conditions of the magnetic induction inside the filament and on its surface. The filament magnetization is then calculated from the resulting current-distribution in the filament cross-section.

The magnetization model has again been combined with the numerical field computation methods. The coupling method between boundary-elements and finite-elements (BEM-FEM) has been applied for this purpose. The BEM-FEM formulation has the major advantage that the coil does not have to be meshed in finite elements since it is positioned in the BEM domain. The field errors in the magnets can therefore be calculated with the required accuracy. The magnetization model has been applied to the calculation of field-errors in combined function magnets with nested octupole and decapole coils (MCDO) and the MCBX orbit corrector magnet with nested normal and skew dipole coils. Due to the individual powering of the circuits any arbitrary field change can be generated.

Ref: Calculation of Persistent Currents in Superconducting Magnets; Vollinger, C ; Aleksa, M ; Russenschuck, S ; Phys. Rev. Spec. Top. Accel. Beams : 3 (2000) No.12

M. Aleksa, B. Auchmann, S. Russenschuck, C. Vollinger

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