Cockcroft Institute ILC Crab Cavity Collaboration Cockcroft Institute

Cockcroft Institute ILC Crab Cavity Collaboration • Cockcroft Institute : – – – – – Richard Carter (Lancaster University) Amos Dexter (Lancaster University) Graeme Burt (Lancaster University) Imran Tahir (Lancaster University) Philippe Goudket (ASTe. C) Peter Mc. Intosh (ASTe. C) Alex Kalinin (ASTe. C) Carl Beard (ASTe. C) Lili Ma (ASTe. C) Roger Jones (Manchester University) • FNAL – – – • Leo Bellantoni Mike Church Tim Koeth Timergali Khabiboulline Nikolay Solyak SLAC – – Chris Adolphson Kwok Ko Zenghai Li Cho Ng

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

Cockcroft Institute RDR Crab Cavity Parameters Crossing angle 14 mrad Cavity frequency, GHz 3. 9 GHz Kick required at 0. 5 Ge. V CM 1. 32 MV Anticipated operational gradient at 0. 5 Ge. V 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 Ge. V CM we might use 1 nine cell cavity or two 5 cell cavities LC-ABD plenary April 2007

Cockcroft Institute Anticipated RF system spent beam BPM Cryostat IP ~ 14 m RF Amplifier Feedback loop DSP Phase Control Feedback loop kick reference from spent beam DSP Phase Control luminosity reference from IP Linac timing Reference Phase 2 • • • Reference Phase 1 References to and from symmetrically placed crab cavities on other beam 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… LC-ABD plenary April 2007

Cockcroft Institute TM 110 Dipole mode cavity Electric Field in red View from top Beam Magnetic field in green • 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

Cockcroft Institute Beamloading • Longitudinal electric field on axis is zero for dipole mode • Beamloading 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 Ge. V Co. M) ~ a few k. W LC-ABD plenary April 2007

Cockcroft Institute Using amplifier to extract cavity energy Bunch goes through cavity at time t =0 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. LC-ABD plenary April 2007

Cockcroft Institute Modelling of cavity amplitude with microphonics Oscillatory bunch offset of 1 mm and random arrival phase of 1 degree PI controller with 1 ms delay cpr = 2. 5 e-6 Qe cir = 1. 0 e-10 Qe cpi = 2. 5 e-6 Qe cii = 1. 0 e-10 Qe Drive frequency in GHz Centre cavity frequency in GHz Cavity Q factor External Q factor Cavity R over Q (2 x. FNAL=53 per cell) Energy point ILC crab~0. 0284 J per cell) Amplitude set point Maximum Amplifier Power per cell Maximum voltage set point (no beam) Maximum beam offset Maximum bunch phase error Beam offset frequency Bunch charge (ILC=3. 2 e-9) RF cycles between bunches Delay for control system in cycles Bunch length Cavity frequency shift from microphonics Cavity vibration frequency Initial vibration phase (degrees) = 3. 9 GHz = 1. 0 E+09 = 3. 0 E+06 = 53 ohms = 0. 0284 J = 301670 V = 300 W = 617740 V = 1. 0 mm = 1. 0 deg = 2 k. Hz = 3. 2 E-09 C = 1200 = 3900 = 1 ms = 600 Hz = 230 Hz = 20 deg LC-ABD plenary April 2007

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

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

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

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

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

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

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

Cockcroft Institute Prototype Coupler 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 LC-ABD plenary April 2007

Cockcroft Institute Placet 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. LC-ABD plenary April 2007

Cockcroft Institute Phase Control Development The phase control work at is focusing on the use of a 1. 3 GHz digital phase detector with fast 16 bit ADC and DAC conversion. Digital Phase Detector Calibration Chart 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 100 k. Hz bandwidth LC-ABD plenary April 2007

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

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

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 50 k. Hz. Have yet to implement FPGAs hence slow read & write. Read time by DSP CPU~300 ns Write time to DAC ~200 ns. Steady State pk-pk phase jitter = +/- 15 mdeg Still using in built functions to get sine and cosine for vector modulator hence processing is a little slow. LC-ABD plenary April 2007

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

Cockcroft Institute Phase Synchronisation II Cavity Control vector mod. digital phase detector D/A Ü DSPÜ A/D synchronous output 3. 9 GHz master oscillator loop filter 3 d. B directional coupler interferometer line length adjustment Note that the phase detectors for each system should be as close as possible to their cavity output couplers. digital phase detector synchronous output phase shifter divide or mix to 1. 3 GHz D/A Ü DSPÜ A/D digital phase detector Load 1. 3 GHz master oscillator vector mod. divide or mix to 1. 3 GHz digital phase detector loop filter ~ 50 metre coax link 3 d. B directional coupler precision reflector • managing reflection on the interferometer is the biggest challenge LC-ABD plenary April 2007 phase shifter

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