1. Cockcroft Institute P. Goudket Cockcroft All Hands Meeting - March 2007 ILC Crab Cavity Collaboration Amplitude and Phase Control Development Cockcroft Institute : –Philippe Goudket (ASTeC) –Lili Ma (ASTeC) –Alex Kalinin (ASTeC) –Carl Beard (ASTeC) –Peter McIntosh (ASTeC) –Richard Carter (Lancaster University) –Amos Dexter (Lancaster University) –Graeme Burt (Lancaster University) –Imran Tahir (Lancaster University) –Roger Jones (Manchester University) FNAL –Leo Bellantoni –Mike Church –Tim Koeth –Timergali Khabiboulline –Nikolay Solyak SLAC –Chris Adolphson –Kwok Ko –Zenghai Li –Cho Ng

2. Cockcroft Institute P. Goudket Modes in the crab cavity frequency TM010 accelerating mode TM110h crabbing mode TM110v TE111h TM011 Need to extract the fundamental mode Higher order modes Extraction of the lower order mode and the higher order modes is essential to minimise disruption of the beam. v-vertical h-horizontal TE111v

3. Cockcroft Institute P. Goudket Monopole and dipole modes impedances MAFIA simulations carried out on the cavity have identified modes which may have a high coupling impedance with the beam. Apart from the fundamental monopole mode, dipole modes are the main concern. Dipole modes from MAFIA Monopole modes from MAFIA Fundamental mode Operating mode

4. Cockcroft Institute P. Goudket Aluminium crab cavity model An aluminium model of the crab cavity is currently being tested, both on a bead-pulling set-up and a stretched-wire set-up. The modular nature of the model makes it easy to change cavity configurations.

5. Cockcroft Institute P. Goudket Bead-pull theory A perturbing object inserted in the cavity will perturb the fields locally and may change the resonant conditions of the cavity. A change in frequency is proportional to the change in stored energy. The frequency shift is therefore proportional to the unperturbed electric and magnetic field strengths in the cavity. e : dielectric constant of the perturbing object m : permittivity of perturbing object : shape factor of perturbing object v: volume of perturbing object

6. Cockcroft Institute P. Goudket Bead-pull layout Bead-pulling allows the measurement of the electric and magnetic field strengths at the position of the bead. Non-spherical beads can distinguish between longitudinal and transverse field components. Dielectric beads allow the perturbation to only affect the electric field and not the magnetic field. Coupler Bead VNA offset

7. Cockcroft Institute P. Goudket Bead-pull results The fundamental and operating mode pass- bands have been studied so far. Analysis of the results shows good agreement with the theory. More measurements will be taken once potentially troublesome modes have been identified using the stretched-wire.

8. Cockcroft Institute P. Goudket Stretched-wire A pulse passing down the wire generates a TEM field pattern that simulates a bunch passing through the cavity. The wake-fields generated by the pulse feeds back onto the wire and can be measured in terms of S-parameters. Wire VNA Port 1 Port 2 Launch cone

9. Cockcroft Institute P. Goudket Stretched-wire system design

10. Cockcroft Institute P. Goudket S21 measurements The transmission of the signal through the device should be reflection-free except where there is a resonance. Moving the wire off-axis allows the study of dipole modes. The area under the curve is proportional to the loss factor of a given resonance. 3.9GHz dipole mode pass-band 2-8.5GHz frequency scan

11. Cockcroft Institute P. Goudket Impedance from stretched-wire results The S 21 data from the measurement can be converted to impedance using various formulae. Z (Ohm) F (Hz) A formally exact formula can be used to derive the impedance from the wire measurements. Formally exact method:

12. Cockcroft Institute P. Goudket Coupler model A coupler model is being designed to fit to the aluminium crab cavity model. It will allow the study of coupling factors, as well as being usable on the bead-pull and stretched-wire benches to evaluate the effect of the coupler on cavity fields.

13. Cockcroft Institute P. Goudket Future work Improve and increase understanding of measurement accuracy. Fully characterise all modes of interest in all possible crab cavity configurations. Test the coupler design and compare to simulations. Act upon the information received to improve the design in order to minimise the most troublesome modes.