ABSTRACT
The Large Hadron Collider (LHC) [6], a proton-proton superconducting accelerator, wm consist of about 8400 superconducting magnet units of different types, operating in super-fluid helium at a temperature of 1.9 K. The applied magnetic field changes induce currents in the filaments that screen the external field changes (so-called persistent currents). The filaments are made of type II hard superconducting material with the property that the magnetic field penetrates into the filaments with a gradient that is proportional to the magnitude of the persistent currents. Macroscopically, these currents (that persist due to the lack of resistivity if Hux creep effects are neglected) are the source of a magnetization M (B) of the superconducting strands. One way to calculate this magnetization would be to mesh the coil with finite elements and solve the resulting non-linear field problem numerically by making use of a measured M (B) -cwve. This approach has two main drawbacks: The numerical field computation has to be combined with a hysteresis model for hard superconductors, and the coil has to be discretized with highest accuracy also accounting for the existing gradient of the current density due to the trapezoidal shape of the cables, the conductor alignment on the winding mandrel, and the insulation layers. Hence, we aimed for computational methods that avoid the meshing of the coil by combining a semi-analytical magnetization model with the BEM-FEM coupling method [5]. In the straight section of accelerator magnets the magnetic induction is almost perpendicular to the filament axis. The effect of a magnetic induction parallel to a superconducting filament is small (see Ill)} and has therefore been neglected here. A model to calculate the magnetization of the superconducting strands is presented, considering external fields that change their magnitude and direction. For this purpose. the model introduced in [1] has been extended to account for filament magnetizations non-parallel to the outside field. As in [ 1), the model does not attempt to describe the microscopic ftux pinning, but applies the critical state model [2] which states that any external field change is shielded from the filament's core by layers of screening currents at critical density ic(B, T). The model differs from other attempts to describe a superconducting filament's response to arbitrary field changes in the transverse
With given Bold, t:,ld and B_,, the mathematical problem consists in the determination of a penetration parameter q• and the corresponding shielding vector t_ that satisfies the Eqs. (2) and (3). For the I -dimensional field change this task has been discussed in II}.
