Transient Finite-Element Simulation of the Eddy-Current Losses in the Beam Tube of the SIS-100 Magnet During Ramping

The field quality of the GSI SIS-100 magnet is influenced by the eddy currents generated in the conductive beam tube during ramping. The eddy-current losses are computed on the basis of a transient 2D finite-element model. A sufficient accuracy is guaranteed by adaptively refining the mesh and by the use of error-controlled adaptive time integrators. The 2D model is accomplished by an analytical model dealing with the closing of the currents at the end parts of the beam tube and thus incorporating the most significant 3D effect. The time dependence of the field quality reveals significant differences at low aperture fields, especially for the sextupole component at the beginning of the ramping. Also without conductive beam tube and for low field values, the relative sextupole and decapole components depend on the magnitude of the field, which indicates the presence of a nonlinear effect. When the magnet operates at an injection field, the magnetic flux density in the bridge of the iron yoke is already saturated. Hence, the saturation pattern in and around this bridge changes immediately at the start of the ramping, resulting in a changing field quality.