Boine-Frankenheim, O.

Eidam, L.

Niedermayer, U.

GSI Repository

Computation and bench measurements of beam coupling impedanceU. Niedermayer ∗1, L. Eidam1, and O. Boine-Frankenheim1,21Institut fu¨r Theorie Elektromagnetischer Felder, TU-Darmstadt, Schlossgartenstr. 8 64289 Darmstadt; 2GSIHelmholtzzentrum fu¨r SchwerionenforschungIntroductionBeam coupling impedance can cause excessive heatload and coherent beam instabilities in high intensity syn-chrotrons. Therefore, a quantification of the beam couplingimpedance for the components in SIS100 is outlined. Wedescribe the development of a 2D Finite Element (FEM)frequency domain solver for longitudinal and transversebeam coupling impedances for arbitrary relativistic beamvelocity. This solver can compute space charge and resis-tive wall impedances on a triangular mesh. It is based onthe open source FEM package FEniCS [1] and mesh gen-erator GMSH [2] and it is available for download at [3].The beam coupling impedance of different componentswas also measured by the wire method. The wire method isbased on emulating the electromagnetic fields of a particlebeam by a TEM mode, i.e. it corresponds only to an ultra-relativistic beam. In the following we show a comparisonfor a ferrite ring, which is also analytically accessible.A Ferrite Ring as ExampleA ferrite ring of outer diameter 3.05cm and length2.54cm was chosen for the validation of both measurementtechnique and our simulation code. The measurement re-sults, together with a 3D reference simulation in time do-main by CST Particle Studio R©[4] for relativistic velocityβ = 1 can be seen in Fig. 1 (top). The discrepancy vis-ible in the plot originates mostly from the error in the ap-plied material data as given in the frequency domain bythe manufacturer of the ring[5], and the fit of these dataon a impulse response function, necessary to perform timedomain computations. The measurement was performedwith a Vector Network Analyzer, where the longitudinalimpedance is obtained from the measured S21-parameterby [6]Z‖(f) = 2Z0 lnSREF21 (f)SDUT21 (f), (1)with Z0 being the characteristic impedance and SREF21 be-ing the transmission in the empty measurement housing.A 2D simulation with our code, compared to 2D ana-lytic calculations is depicted in Fig. 1 (bottom). Such asimulation in frequency domain allows arbitrary relativis-tic velocity. The 2D calculations are valid for distributedimpedances, i.e. above a certain length, see [7].Details about our FEM frequency domain solver can befound in [8], and a detailed analysis of the wire measure-∗ u.niedermayer@gsi.deFigure 1: Top: impedance measurement using the wiremethod [7] vs. 3D numerical computation in the time do-main. Bottom: 2D analytical and numerical calculationwith the newly developed FEM code [8]. All computationsrely on the manufacturer’s material data [5], which is spec-ified with 20% error range.ment method is available in [7]. The wire measurementmethod was also applied to a SIS18 kicker magnet, see [9].References[1] FEniCS, www.fenicsproject.org, 2014[2] C. Geuzaine and J.-F. Remacle, GMSH,www.geuz.org/gmsh, 2014[3] https://bitbucket.org/uniederm/beamimpedance2d/src, 2015[4] CST Studio Suite 2013, www.cst.com[5] http://www.amidon.de/contents/de/d542.html, accessed 2013[6] L. S. Walling et al., NIM-A 281, 433, 1989[7] U.Niedermayer et al., NIM-A 776, 129-143, 2015[8] U.Niedermayer et al., accepted for pub. in PR-STAB, 2015[9] L. Eidam, Master Thesis, TU-Darmstadt, 2014GSI SCIENTIFIC REPORT 2014 FG-SIS100-08DOI:10.15120/GR-2015-1-FG-SIS100-08 477

Computation and bench measurements of beam coupling impedance

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Computation and bench measurements of beam coupling impedance

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