Minutes of 111^th Impedance Working Group meeting

Work package in ABT working for FCC kickers and septa

• The equipment is needed for beam separation: deflect the beam going out the RF system and do not deflect the beam which is going in to avoid SR.
• Current concept considers two devices: electro-static separator under vacuum and a dipole magnet outside vacuum.
• The main challenges are HV breakdown, field quality, machine/equipment protection, sub-system integration, and beam coupling impedance
  • Beam coupling impedance:
    • preliminary simulations studies:  WF simulations and FD simulations to reproduce the wire measurements results
    • Wire measurements

Carlo comments that the impedance validation has to be conducted by checking different aspects such as, beam induced heating and stability and see how this is integrated in the full FCC-ee model which is ongoing. And the studies done now are just a starting point to look into the device and see how it looks like.

Christine asks more details about the reproduction in simulations of the wire technique, if it was what he showed before in FD simulations. Izan explained better that it was the case.

Hermann asks more details on how the results of EM and FD compare, and Izan highlight that there is some discrepancy.

Chiara asks if the EM results are already divided by the factor 2 due to the different convention of EM and indeed Izan answers that it is not yet included

Metamaterial absorbers for beam-coupling impedance mitigation

Speaker: Leonardo Sito (CERN)

• Introduction to the problem: we want to reduce beam coupling impedance.
  • Effect of a geometric wake field: trapped modes are created and following bunches can be affected.
  • Wake potential described like energy loss or gain of trailing particle wrt leading particle (damped oscillator behaviour).
  • Impedance calculated as an FFT of the wake potential, useful for frequency domain representation.
  • Longitudinal impedance modelled as resonator impedance with shunt impedance, Q factor and resonance frequency.
• Reduction of induce EM fields can be done with:
  1. Geometrical design optimization (not always possible), to change R/Q
  2. Damping of unwanted EM fields (ex. Use of ferrites in the SPS wire scanners)
• Metamaterials as possible damping solution:
  • Homogenization procedure à electric permittivity for dielectric material, represented with Lorentz model for example.
  • Create artificial crystal à standard PCB technology with metallization which will resonate at a specific frequency. Way smaller than the wavelength so homogeneity is preserved.
  • Split ring resonator. Average response of magnetic permeability follows Lorentz model with frequency of oscillation same of resonant frequency of the resonator.
  • Parameter retrieval with NRW method in simulation in CST and same was applied in measurements with a WR90 waveguide. Limitations and tolerances of not ideal setup were accounted when comparing with simulations.
• Proof of principle:

1. 1. Test cavity, pillbox, was produced with TM010 fundamental mode at about 2 GHz.
   2. Excellent agreement was found between Wakefield, Eigenmode and Measurements for the first longitudinal mode and the dipolar mode for empty cavity.
   3. Design of metamaterial for damping the fundamental mode. Damping was obtained with a reduction from 540 kOhm to 40 kOhm. In addition, a mode splitting, expected.
   4. Addition of losses with a SMD resistor over the ring gap. Impedance reduced even more, reaching a max of 1.7 kOhm (three order of magnitude reduction).

• Damping of the transverse impedance was tried with a redesign of the MTM for having a resonance frequency at the dipolar mode frequency, 3 GHz.  Positioning and size of the slabs was the same as in the longitudinal case in order to obtain the maximum coupling with H field.
  • Damping of more than 1 order of magnitude of transverse shunt impedance with less than 20 % reduction on the longitudinal mode, which we would like to keep untouched.
• Power handling capabilities were also studied.
  • Bulk MTM developed. Two options investigated with good and bad contact of metallization on the bulk.
  • Proven reduction wrt empty cavity of longitudinal mode, from 540 kOhm to 7.9 kOhm, with greater mode splitting.
  • Thermal study with thermal map with 1 W power.
    • PCB based (good contact) gave a distributed power dissipation in metal and substrate.
    • Bulk solution (bad contact) shows most of the power dissipated on the metallization (copper in simulation) which would be able to handle such power.
  • Example of SPS wire scanner. Model used was a simplified version of the original design.
    • Most of the heating on the wire coming from mode at 600 MHz.
    • Bulk MTM designed with AlN substrate, metal rings for magnetic coupling and graphite in the gap of the rings for allowing dielectric losses.
    • Designed MTM allowed a reduction of the power loss on the wire from 15.3 W to 6.6 W. Thermal load was diverted into metamaterials.
• Outlook:
  • Power handling capabilities in an experimental scenario
  • Vacuum compliance
  • Implementation in an operating device