1. Cockcroft Institute LC-ABD plenary April 2007 ILC Crab Cavity Collaboration Cockcroft Institute : –Richard Carter (Lancaster University) –Amos Dexter (Lancaster University) –Graeme Burt (Lancaster University) –Imran Tahir (Lancaster University) –Philippe Goudket (ASTeC) –Peter McIntosh (ASTeC) –Alex Kalinin (ASTeC) –Carl Beard (ASTeC) –Lili Ma (ASTeC) –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 Crab Cavity Function The crab cavity is a deflection cavity operated with a 90 o phase shift. A particle at the centre of the bunch gets no transverse momentum kick and hence no deflection at the IP. A particle at the front gets a transverse momentum that is equal and opposite to a particle at the back. The quadrupoles change the rate of rotation of the bunch. LC-ABD plenary April 2007

3. Cockcroft Institute RDR Crab Cavity Parameters Crossing angle 14 mrad Cavity frequency, GHz 3.9 GHz Kick required at 0.5 GeV CM 1.32 MV Anticipated operational gradient at 0.5 GeV CM 3.81 MV m -1 Max gradient achieved in 3 cell cavity MV m -1 7.5 MV m -1 RMS relative phase stability for 2% rms Luminosity drop 0.1  RMS amplitude stability for 2% rms Luminosity drop 1.2% Potential X beam jitter at crab cavity,  m 500  m Potential Y beam jitter at crab cavity,  m 35  m For 500 GeV CM we might use 1 nine cell cavity or two 5 cell cavities LC-ABD plenary April 2007

4. Cockcroft Institute Anticipated RF system ~ 14 m Cryostat Reference Phase 2 References to and from symmetrically placed crab cavities on other beam DSP Phase Control RF Amplifier Feedback loop DSP Phase Control RF Amplifier Feedback loop luminosity reference from IP BPM spent beam kick reference from spent beam IP Minimum requirement for 14 mrad crossing is 1  9 cell or 2  5 - cell cavities per linac 2  9 – cells would provide full redundancy in case of failure Need space for cryostat, input/output couplers, tuning mechanisms… Reference Phase 1 Linac timing LC-ABD plenary April 2007

5. Cockcroft Institute TM110 Dipole mode cavity View from top Magnetic field in green Electric Field in red Beam The electric and magnetic fields are 90 o out of phase. For a crab cavity the bunch centre is at the cell centre when E is max and B is zero. A particle at the centre of the bunch sees no electric or magnetic field throughout. LC-ABD plenary April 2007

6. Cockcroft Institute Beamloading Longitudinal electric field on axis is zero for dipole mode Beamloading loading is zero for on axis bunches Bunches pass cavity centre when B transverse = 0 hence of axis E = maximum Crab cavities are loaded by off axis bunches Dipole deflection cavities are not loaded by off axis bunches Power requirement for 9 cells (500 GeV CoM) ~ a few kW LC-ABD plenary April 2007

7. Cockcroft Institute Phase Control Model equivalent electrical circuit for excitation of a single cavity mode resulting differential equation conversion from circuit parameters to cavity parameters Microphonics cause  o to vary with time Beamloading causes V to jump when a bunch passes through The amplitude and phase of F depend on the controller, the amplifier, the coupler temperature we need a numerical solution LC-ABD plenary April 2007

8. Cockcroft Institute Envelope Equations Require an accurate solution over the cavity fill time plus the bunch train time At the design gradient the required energy per cell is 0.0284 J If 250 Watt per cell is available the minimum fill time ~ 0.12 ms For best possible phase performance we would want to fill slowly and let settle Allowing 4 ms for filling and operation simulation needs 20 million RF cycles Hence solve envelope equations defined by This form assumes Q o >>Q e note that Q L = Q o + Q e LC-ABD plenary April 2007

9. Cockcroft Institute Using amplifier to extract cavity energy For the crab cavity the bunches can supply or remove energy. Whilst in principle the amplifier can be used to reduce cavity energy after shifting its phase by 180 o this is undesirable when one is trying to control cavity phase. It is desirable to chose a low external Q so this never needs to happen. Bunch goes through cavity at time t =0 LC-ABD plenary April 2007

10. Cockcroft Institute Modelling of cavity amplitude with microphonics Oscillatory bunch offset of 1 mm and random arrival phase of 1 degree Drive frequency in GHz = 3.9 GHz Centre cavity frequency in GHz = 3.9 GHz Cavity Q factor = 1.0E+09 External Q factor = 3.0E+06 Cavity R over Q (2xFNAL=53 per cell) = 53 ohms Energy point ILC crab~0.0284J per cell) = 0.0284 J Amplitude set point = 301670 V Maximum Amplifier Power per cell = 300 W Maximum voltage set point (no beam) = 617740 V Maximum beam offset = 1.0 mm Maximum bunch phase error = 1.0 deg Beam offset frequency = 2kHz Bunch charge (ILC=3.2e-9) = 3.2E-09 C RF cycles between bunches = 1200 Delay for control system in cycles = 3900 Bunch length = 1 ms Cavity frequency shift from microphonics = 600 Hz Cavity vibration frequency = 230 Hz Initial vibration phase (degrees) = 20 deg PI controller with 1 ms delay c pr = 2.5e-6  Q e c ir = 1.0e-10  Q e c pi = 2.5e-6  Q e c ii = 1.0e-10  Q e LC-ABD plenary April 2007

11. Cockcroft Institute Modelling of cavity drive with microphonics follows microphonics follows beam offset LC-ABD plenary April 2007

12. Cockcroft Institute Modelling of cavity drive power with microphonics A single klystron can’t easily do this but solid state amplifiers can. To work with a Klystron we must lower the external Q LC-ABD plenary April 2007

13. Cockcroft Institute Modelling of cavity phase with microphonics Oscillatory bunch offset of 1 mm and random arrival phase of 1 degree Modelling suggests that we might be able to control the phase of the cavity to within 6 milli-degrees of the measured phase error with respect to a local reference. LC-ABD plenary April 2007

14. Cockcroft Institute Wire Measurement Technique LC-ABD plenary April 2007 Technique employed extensively on X-band structures at SLAC. Bench measurement provides characterization of: - mode frequencies - kick factors - loss factors

15. Cockcroft Institute Wire Theory LC-ABD plenary April 2007 A wire through a uniform reference tube can be regarded as a transmission line characterised by R o, L o and C o The impedance Z ll is large close to each cavity mode. One measures the phase lag  of a wave passing along the wire for the cavity (DUT) with respect to the plain tube (Ref) then determines Z ll and hence k loss from the equations opposite. A wire through the cavity under investigation is modelled with an additional series impedance Z ll / l As  is measured as a function of frequency one obtains a loss factor at each frequency where Z ll is large i.e. for each mode.

16. Cockcroft Institute Impedance Measurements LC-ABD plenary April 2007 The coupling impedance has been calculated for a 3 cell cavity in order to investigate systematic errors in the measurements. Measurements are underway to measure the loss factors of the dominant modes in the crab cavity.

17. Cockcroft Institute Long Range Wakefields LC-ABD plenary April 2007 The long range wakes are found by summing over all modes and all bunches

18. Cockcroft Institute Prototype Coupler LC-ABD plenary April 2007 A prototype Coupler has been constructed with replaceable tips and variable cavity separation to measure the external Q for a variety of coupler configurations. A probe coupler will be matched to the ohmic Q of the cavity and calibrated using S 11, with the loaded Q being measured using the bandwidth. Then the external Q can be measured from

19. Cockcroft Institute Placet LC-ABD plenary April 2007 The crab cavity has now been inserted into PLACET and bunches have been tracked through the final focus, with and without crab cavities. The results give good agreement with the previous analytical results, and show little emittance growth.

20. Cockcroft Institute Phase Control Development The phase control work at is focusing on the use of a 1.3GHz digital phase detector with fast 16 bit ADC and DAC conversion. The digital phase detector offers an absolute measurement without calibration. They may eventually be used alongside phase quadrature measurements with double balanced mixers at an intermediate frequency for enhanced resolution. Used in quadrature double balanced mixers give both phase and amplitude. A diode detector being used for amplitude measurements at the moment. Vector modulation available to 4 GHz Degrees per Volt of a digital phase detector can be amplified to overcome ADC noise. Ultimate resolution is 5 milli-degree rms for 100kHz bandwidth Digital Phase Detector Calibration Chart LC-ABD plenary April 2007

21. Cockcroft Institute Phase Control Implementation for single Cavity LC-ABD plenary April 2007 A randomly vibrating tuning stub simulates microphonics in a warm cavity

22. Cockcroft Institute 16 bit ADC Sample Rate = 105MSPS, Latency = 130ns 16 bit DAC Sample Rate = 40MSPS, Settling time = 10ns Have potential to react to a phase error of 5 mdeg in 2-3  s. Development of 16 bit DAC & ADC Boards LC-ABD plenary April 2007

23. Cockcroft Institute Status of measurement precision Precision of the measurement is determined by looking at the jitter on a DAC output using digital amplification inside DSP, when a controller in the DSP is used to phase lock a low Q cavity. Programmed basic control software in DSP and have demonstrated phase locking of warm cavity to better than 0.01 degrees rms within bandwidth of 50kHz. Have yet to implement FPGAs hence slow read & write. Read time by DSP CPU~300 ns Write time to DAC ~200 ns. Still using in built functions to get sine and cosine for vector modulator hence processing is a little slow. Steady State pk-pk phase jitter = +/- 15 mdeg LC-ABD plenary April 2007

24. Cockcroft Institute Phase synchronisation I If cavities are stabilized with respect to local references to ± 0.01 degrees we then seek synchronisation between local references to 0.06 degrees at 3.9 GHz = 43 fs Optical systems have been developed elsewhere that achieve this. Initial plans are to see what can be achieved with coax and s.o.a. RF components. simple synchronisation scheme LC-ABD plenary April 2007

25. Cockcroft Institute Phase Synchronisation II synchronous output synchronous output 1.3 GHz master oscillator phase shifter loop filter 3 dB directional coupler phase shifter loop filter 3dB directional coupler digital phase detector digital phase detector ~ 50 metre coax link interferometer line length adjustment precision reflector D/A  DSP  A/D vector mod. vector mod. D/A  DSP  A/D digital phase detector digital phase detector Cavity Control 3.9 GHz master oscillator Load phase shifte r managing reflection on the interferometer is the biggest challenge divide or mix to 1.3 GHz divide or mix to 1.3 GHz Note that the phase detectors for each system should be as close as possible to their cavity output couplers. LC-ABD plenary April 2007

26. Cockcroft Institute Vertical Cryostat Phase Control Tests Local reference and controller Phase measurement Line to synchronise the local references must have its length continuously measured to with an accuracy of a few microns LC-ABD plenary April 2007