Finemet cavity impedance studies Serena Persichelli PS-LIU meeting 30-04-2013 Acknowledgements Simone Gilardoni Mauro Migliorati Mauro Paoluzzi Benoit Salvant

Aim of the study The aim of the study is to evaluate the impedance excited in the Finemet cavity by a bunch with the same length of the PS bunches (26 cm - 12m) Time domain simulations with CST Particle Studio have been performed in order to get the longitudinal impedance of the cavity and make a comparison with the measured longitudinal impedance The study has been performed on simplified 3D geometries imported from a mechanical CATIA drawing, assuming small impact on the final results. The Finemet cavity has been simulated starting with the one cell model (the one that has also been measured) but also the cavity complete model with six cells has been studied The dispersive material has been defined in CST with a dispersion model starting from the measurements of the μ’ and μ’’ parameters performed for Finemet by Mauro Paoluzzi .

Agenda Finemet cavity: one-cell model Finemet cavity: six-cells model Design for simulation 1-cell cavity without Finemet CST Finemet fitting (1st order): version 2012 CST Finemet fitting (nth order): version 2013 Wakefield CST Particle Studio analysis Longitudinal wake potential Comparison between measurements and simulations Finemet cavity: six-cells model Design for simulations

Agenda Finemet cavity: one-cell model Finemet cavity: six-cells model Design for simulation 1-cell cavity without Finemet CST Finemet fitting (1st order): version 2012 CST Finemet fitting (nth order): version 2013 Wakefield CST Particle Studio analysis Longitudinal wake potential Comparison between measurements and simulations Finemet cavity: six-cells model Design for simulations

Finemet 1-cell cavity design for CST simulations Perfectly conducting walls Finemet Copper Alumina NB. The design considered for CST simulations has been simplify from the original mechanical model!

Agenda Finemet cavity: one-cell model Finemet cavity: six-cells model Design for simulation 1-cell cavity without Finemet CST Finemet fitting (1st order): version 2012 CST Finemet fitting (nth order): version 2013 Wakefield CST Particle Studio analysis Longitudinal wake potential Comparison between measurements and simulations Finemet cavity: six-cells model Design for simulations

1-cell cavity without Finemet Longitudinal impedance Bunch length 260 mm Wake length 800 m fMAX 700 MHz # of mesh 356,000 Method Indirect test beam In the longitudinal and transverse impedance one can identify a mode trapped around 208 MHz. This mode will be dump by the insertion of the Finemet rings!

Agenda Finemet cavity: one-cell model Finemet cavity: six-cells model Design for simulation 1-cell cavity without Finemet CST Finemet fitting (1st order): version 2012 CST Finemet fitting (nth order): version 2013 Wakefield CST Particle Studio analysis Longitudinal wake potential Comparison between measurements and simulations Finemet cavity: six-cells model Design for simulations

CST Finemet fitting (1st order): version 2012 Fitting of μ’ used for simulations

CST Finemet fitting (1st order): version 2012 Fitting of μ’' used for simulations

Comparison between measurement and simulation Longitudinal impedance Bunch length 90 cm Wake length 600 m fMAX 200 MHz # of mesh 112.860 Method Direct Because of the imprecise fitting of the dispersion parameters in CST 2012, the impedance obtained few month ago was not in perfect agreement with measurements The differences between the two curves are due to the poor resolution at low frequencies and to the Direct integration method that has been used

Agenda Finemet cavity: one-cell model Finemet cavity: six-cells model Design for simulation 1-cell cavity without Finemet CST Finemet fitting (1st order): version 2012 CST Finemet fitting (nth order): version 2013 Wakefield CST Particle Studio analysis Longitudinal wake potential Comparison between measurements and simulations Finemet cavity: six-cells model Design for simulations

CST Finemet fitting (nth order): version 2013 Fitting of μ’ used for simulations

CST Finemet fitting (nth order): version 2013 Fitting of μ’' used for simulations εr=25

Agenda Finemet cavity: one-cell model Finemet cavity: six-cells model Design for simulation 1-cell cavity without Finemet CST Finemet fitting (1st order): version 2012 CST Finemet fitting (nth order): version 2013 Wakefield CST Particle Studio analysis Longitudinal wake potential Comparison between measurements and simulations Finemet cavity: six-cells model Design for simulations

Wakefield CST Particle Studio analysis Longitudinal wake potential Bunch length 260 cm Wake length 700 m fMAX 700 MHz # of mesh 98,175 Method Indirect test beam NB. This model of longitudinal wake potential can be used for Headtail simulations

Wakefield CST Particle Studio analysis Electric field monitor All the modes of the pillbox cavity are strongly dumped by the Finemet rings: we predict to have no issues regarding trapped or parasitic modes in the cavity

Comparison between measurement and simulation Longitudinal impedance: real part Bunch length 90 cm Wake length 600 m fMAX 200 MHz # of mesh 112.860 Method Indirect test beam Results obtained with CST 2013 show a good agreement with the measured impedance! This improvement in resolution at low frequencies has been obtained thank to a better fitting of the dispersion parameters and to the use of the Indirect test beam integration method

Comparison between measurement and simulation Longitudinal impedance: imaginary part Bunch length 90 cm Wake length 600 m fMAX 200 MHz # of mesh 112.860 Method Indirect test beam Results obtained with CST 2013 show a good agreement with the measured impedance! This improvement in resolution at low frequencies has been obtained thank to a better fitting of the dispersion parameters and to the use of the Indirect test beam integration method

Agenda Finemet cavity: one-cell model Finemet cavity: six-cells model Design for simulation 1-cell cavity without Finemet CST Finemet fitting (1st order): version 2012 CST Finemet fitting (nth order): version 2013 Wakefield CST Particle Studio analysis Longitudinal wake potential Comparison between measurements and simulations Finemet cavity: six-cells model Design for simulations

Finemet 6-cell cavity design for CST simulations Few moths ago we had several problem in the model because of the errors encountered during import from CATIA. These problems were source of loss of resolution but they have been solved on the new model!

Agenda Finemet cavity: one-cell model Finemet cavity: six-cells model Design for simulation 1-cell cavity without Finemet CST Finemet fitting (1st order): version 2012 CST Finemet fitting (nth order): version 2013 Wakefield CST Particle Studio analysis Longitudinal wake potential Comparison between measurements and simulations Finemet cavity: six-cells model Design for simulations

Wakefield CST Particle Studio analysis Longitudinal wake potential Bunch length 50 cm Wake length 800 m fMAX 345 MHz # of mesh 3,000,816 Method Indirect test beam NB. This model of longitudinal wake potential can be used for Headtail simulations

Wakefield CST Particle Studio analysis Electric field monitor All the modes of the pillbox cavity are strongly dumped by the Finemet rings: we predict to have no issues regarding trapped or parasitic modes in the cavity

Comparison between measurement and simulation Longitudinal impedance: real part Bunch length 50 cm Wake length 800 m fMAX 354 MHz # of mesh 3,000,816 Method Indirect test beam Results obtained with CST 2013 show a good agreement with the measured impedance! The blue curve was obtained multiplying by a factor 6 the data from measurement of the 1-cell cavity

Comparison between measurement and simulation Longitudinal impedance: imaginary part Bunch length 50 cm Wake length 800 m fMAX 354 MHz # of mesh 3,000,816 Method Indirect test beam Results obtained with CST 2013 show a good agreement with the measured impedance! The blue curve was obtained multiplying by a factor 6 the data from measurement of the 1-cell cavity

Conclusions From simulations performed with two different versions of CST Particle Studio we can confirm that the impedance observed with measurements can be exited by bunches circulating in the PS. In the six-cell cavity, a circulating bunch can excite a longitudinal impedance that has a maximum of 2 kΩ around 4 MHz on the real part, that also correspond to the zero crossing of the imaginary part curve. The same mode seems to be produced also on the transverse plane: more investigations with the new SCT version are needed . All the eigenmodes of the cavity are strongly dumped by the Finemet rings: we predict to have no issues regarding trapped or parasitic modes in the Finemet cavity. Improvements of the quality of simulation have been obtained thanks to a better fitting of the dispersion parameters of CST version 2013 and thanks to the use of an indirect integration method that is more accurate that the direct method used few months ago. .