Ackermann, W.

Klopfer, K.

Weiland, T.

Klopfer, Klaus

Ackermann, Wolfgang

Weiland, Thomas

TUbiblio

Eigenmode Computation for the GSI SIS 18 Ferrite Cavity

GSI Repository

Eigenmode computation for the GSI SIS 18 ferrite cavity∗K. Klopfer†1, W. Ackermann1, and T. Weiland11Technische Universita¨t Darmstadt, Institut fu¨r Theorie Elektromagnetischer Felder (TEMF), Schlossgartenstraße 8,64289 Darmstadt, GermanyIntroductionIn the heavy-ion synchrotron SIS 18 two identical cav-ities are operated, which are loaded with the Ferroxcube8C12m ferrite material. The permeability of the ferritesexhibits a characteristic dependence both on frequency andbias magnetic field strength. The latter is of particular im-portance for the tuning of the resonance frequency of theresonator system. Due to the extension of the existing fa-cility to the FAIR, new interest in a better understanding offerrite cavities of the SIS 18 type has aroused. As the aim ofthe presented study, a tool for the numerical simulation ofthe lowest eigenmodes of such resonators was developed.Clearly, its application to the SIS 18 cavity requires accu-rate material data. Hence, designated measurements werecarried out at GSI.Permeability measurementThe dependence of the permeability of the Ferroxcube8C12m material on frequency and bias magnetic was de-termined using a reflection as well as a transmission mea-surement approach. The obtained values for low RF levelsare fully compatible with each other within their estimatederror margins up to moderate frequencies. A detailed dis-cussion of the measurement results can be found in [1].Computational approachA dedicated solver was developed, implemented andsuccessfully verified. It is able to efficiently handle non-linear complex eigenvalue problems even on distributedmemory machines, which arise in the context of the ten-sor material modeling. Furthermore, the distribution of themagnetic field excited by the bias current is precisely takeninto account. For more details on the employed numericalmethods we refer to [2, 3].Analysis of the fundamental modeThe computational model used in the numerical simula-tion of the GSI SIS 18 cavity is depicted in Fig. 1. Thesimulation results for the resonance frequency of the fun-damental mode are shown in Fig. 2. Also, additional resultsobtained with an alternative equivalent circuit model takinginto account the radial dependence of the bias field are in-cluded. The simulation results are discussed in more detailin [3].∗Work supported by GSI.† klopfer@temf.tu-darmstadt.deFigure 1: CAD model used for the numerical simulationof the GSI SIS 18 cavity. It consists of ferrite ring coresas well as copper discs. The coupling windings are repre-sented by thin wires.Figure 2: Resonance frequency as a function of the biascurrent for the prototype cavity with 29 cores on each sideof the gap for small RF levels.SummaryThe computation of the fundamental mode of the GSISIS 18 ferrite cavity has successfully been demonstrated.References[1] Klaus Klopfer, Uwe Niedermayer, Harald Klingbeil, Wolf-gang Ackermann, Hans Gu¨nther Ko¨nig, and Thomas Wei-land, “Measurement of the magnetic material properties andsimulation and modeling of ferrite-loaded cavities”, Phys.Rev. ST Accel. Beams, vol. 18, issue 1, 2015.[2] Klaus Klopfer, Wolfgang Ackermann, and Thomas Weiland,“Computation of Complex Eigenmodes for Resonators FilledWith Gyrotropic Materials”, IEEE Trans. Magn., vol. 51, no.1, 2015.[3] Klaus Klopfer, “Computation of Complex Eigenmodes forResonators Filled With Gyrotropic Materials”, PhD thesis,TU Darmstadt, tuprints: 4210, 2014.[4] Uta Hartel, “Modellierung des Regelungs- undSteuerungssystems einer Beschleunigungseinheit fu¨rSynchrotrons”, Diploma thesis, TU Darmstadt, 2011.FG-SIS18-04 GSI SCIENTIFIC REPORT 2014490 DOI:10.15120/GR-2015-1-FG-SIS18-04

Eigenmode computation for the GSI SIS 18 ferrite cavity

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Eigenmode computation for the GSI SIS 18 ferrite cavity

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