Frequency and time domain analysis of trapped modes in the CERN Proton Synchrotron

Frequency and time domain analysis of trapped modes in the CERN Proton Synchrotron Serena Persichelli CERN Impedance and collective effects BE-ABP-ICE

Abstract The term trapped mode refers to a resonance that can be excited by the presence of a discontinuity inside a cavity or a beam pipe. These modes cannot propagate into the beam pipe but are localized near the discontinuity, producing narrow resonances in the coupling impedance frequency spectrum. Resonances due to trapped modes can be dangerous in accelerators like PSB, PS, SPS, LHC and CLIC project: for this reason, each structure that is going to be installed in the CERN machines must be simulated in order to identify trapped modes. We will show how CERN impedance team approaches this problem, using CST both with time domain and frequency domain simulations. These results are needed to understand performance limitations of the machines like instability thresholds and beam induced heating. In particular, we will show a recent study of the impedance due to trapped modes in a new septum that will be installed in the CERN Proton Synchrotron in 2013, where our results show a good agreement between CST simulations in the two domains.

How a trapped mode looks like Time domain: Wakefield solver

How a trapped mode looks like Frequency domain: Eigenmode solver

Agenda A general method for study the impedance of an accelerator component Import and simplify the CATIA mechanical drawing Eigenmode simulation (frequency domain): Hexahedral mesh: extract parameters Rs, Q Tetrahedral mesh: extract parameters Rs, Q Wakefield simulation (time domain): Longitudinal and transvers impedance Extract parameters Rs, Q Evaluate effective imaginary impedance at low frequency (time domain) Compute longitudinal instabilities rise time Dump the modes with ferrite (time domain) Evaluate heating and power loss

Importing CATIA drawings in CST From the mechanical drawing imported from CATIA to the design used in CST for simulations This dummy septum, located in section 15 of the CERN PS, will absorb particles during extraction, providing a reduction in activation in the extraction area. PS SECTION 15 --Steel --Copper --AL 2 O 3 During extraction the particles will impact on a 40 cm long, 7 cm high and 4.2 mm thick copper blade inside the dummy septum, avoiding a strong activation on the real extraction septum, located in section 16.

Importing CATIA drawings in CST Simplify the mechanical drawing imported from CATIA The RF screen can not be processed correctly by ACIS because of the holes: a screen without holes has been considered for simulations. Elliptical beam pipes have to be extended to avoid negative impedance effects RF fingers to allow continuity between the screen and the tank has been considered in simulations What should we expect from such geometry? Degeneration of the intrinsic modes of the pillbox cavity brings trapped modes

Eigenmode simulation (CST Microwave Studio) Evaluation of frequencies, Q, R/Q, shunt impedances NB. Modes with a frequency lower than 150 MHz can be source of coupled bunch instability in the PS! Freq [MHz] Q R/Q R s [Ω] 1 119 2655 0.241 640 2 295 3975 0.199 794 3 331 3947 0.020 76 4 362 4727 0.006 25 5 420 4987 0.027 132 6 441 4885 0.046 226 7 495 5777 0.005 33 8 533 7597 0.012 94 9 616 3585 0.009 33 10 656 5805 0.031 184

Eigenmode simulation (CST Microwave Studio) Trapped mode at 119 MHz

Wakefield simulation (CST Particle Studio) Longitudinal impedance Trapped modes excited on the real part of the longitudinal impedance by a bunch of 26 cm length circulating at 5 mm from the blade σ=26 cm f MAX =0.7 GHz Wakelength=100 m Method: Direct

Wakefield simulation (CST Particle Studio) Evaluation of frequencies, Q, R/Q, shunt impedances Considering only one trapped mode: Lorentzian fit of the mode @118 MHz Q=2655 from CST MWS Q=f/Δf WL max =c/δf 6.7 km WL max is the wake length to use to get convergence the of peak s amplitude The parameters of the resonances are obtained with a Lorentzian fit of the longitudinal impedance peak evaluated for WL max Freq [MHz] Q R @27 [Ω] R @0 [Ω] R @-55 [Ω] CST MWS 118 2655 62 640 36176 CST PS 119 2616 40 510 36386

Effective imaginary impedance (time domain) Contribution to the impedance budget Longitudinal impedance before extraction --Re --Im The contribution of the dummy septum to the total imaginary part of longitudinal impedance of the PS is predicted to be less then 1% M. Migliorati, S. Persichelli et al., Beam-wall interaction in the CERN Proton Synchrotron for the LHC upgrade, Phys. Rev. ST Accel. 16, 031001 (2013)

Coupled bunch instability growth rate Compute the instability growth rate for the 118 MHz mode PS parameters (25 ns) 13 GeV 26 GeV V RF [kv] 165 100 h 21 84 Displacement from the centre [mm] Rs [Ω] R s [Ω] α [1/s] @13 Gev α [1/s] @26 Gev 0 640 10 0.15 0.08 10 1484 23 0.35 0.18 # of bunches 18 72 charge 1.28 e-07 3.2 e-08 Slippage factor 0.0163 0.0215 20 3385 53 0.82 0.43 30 7301 114 1.77 0.95 Gaussian shape of the beam 40 14762 231 3.59 1.87 50 27397 428 6.65 3.47 60 49215 770 11.97 6.25

Ferrite proposal for trapped modes damping 119 MHz mode electric field (frequency domain)

Ferrite proposal for trapped modes damping 119 MHz mode magnetic field (time domain)

Ferrite proposal for trapped modes damping Damping effect on longitudinal impedance (time domain) f=0.103 GHz Q=11 K=2.6 e-12 V/pC Rs=50 Ω TT2-11R Ferrite 24x7x395 mm

Ferrite proposal for trapped modes damping Ferrite effect on the growth rate d[mm] R s [Ω] α [1/s] @13 Gev α [1/s] @26 Gev -55 1.3 0.017 0.009 f=0.103 GHz Q=11 K=2.6 e-12 V/pC Rs=50 Ω

Procedure A general method for study the impedance of an accelerator component Import and simplify the CATIA mechanical drawing Eigenmode simulation (frequency domain): Hexahedral mesh: extract parameters Rs, Q Tetrahedral mesh: extract parameters Rs, Q Wakefield simulation (time domain): Longitudinal and transvers impedance Extract parameters Rs, Q Evaluate effective imaginary impedance at low frequency (time domain) Compute longitudinal instabilities rise time Dump the modes with ferrite (time domain) Evaluate heating and power loss

Heating and power loss Estimation of the power loss considering the heating from ferrite At extraction energy the first mode is inside the beam spectrum and the power at 118 MHz is about -20 db P db (118 MHz)= -20 db P loss =1.8 W P loss =0.71 W

Conclusions The proposed method uses CST not only for characterizing the impedance of the device, but also to understand performance limitations of the machines like instability thresholds and beam induced heating that can be dangerous in accelerators like PSB, PS, SPS, LHC and CLIC project Each structure that is going to be installed in the CERN machines must be simulated in order to identify trapped modes that are the main source of instabilities. CST is used for impedance studies at CERN for many types of devices: Kicker magnets Experimental detectors Instrumentation Cavities Septa Collimators