RF Synchronisation Issues Xband Linacs for FELs Lancaster University October 2014 Red linac sections are X band Off crest acceleration provides bunch compression Phase errors in linac RF cavities gives unwanted beam energy spread in undulator Average phase in linac RF cavities must be correct to within 0.02 degrees ~ 5 fs 5 fs ~ 1.5 mm at speed of light Once stability achieved must have beam measurement and active correction to remove fs level offsets

SLAC XL4 stability is a prediction. Requires a lot of effort to achieve it.

SLAC achieving 0.08o stability translate to about 0.32o at XBand LCLS Klystron SLAC achieving 0.08o stability translate to about 0.32o at XBand

Timing Problems Stability Synchronisation Oscillators shift period with temperature, vibration etc. VCO shifts period with applied voltage Atomic clock Df/f ~ 10-14 ~ 600 fs per minute Optical clock Df/f ~ 10-17 ~ 36 fs per hour Synchronisation Two clocks with different periods at same place (PLL) Identical delivery time/phase at two places (Crab Cavity Problem) Same clock at two places Resynchronisation requires constant propagation time of signal Detector with femtosecond accuracy Trigger an event at a later and a different location Needs two stable clocks which are synchronised Must be able to generate event from clock pulse with tiny jitter 10 fs looks achievable see work at DESY and MIT

Extremely sensitive to modulator voltage sensitive to temperature Clock to Cavity Optical clock signal LLRF control - feedforward to next pulse based on last pulse and environment measurements Locked microwave oscillator Solid state amplifier IQ modulator Extremely sensitive to modulator voltage Solid state amplifier TWT amplifier Waveguide Klystron Absolute timing impossible as every component and connector adds phase uncertainty Waveguide Pulse compressor Waveguide sensitive to temperature Cavity

CLIC Cavity Synchronisation CLIC bunches ~ 45 nm horizontal by 0.9 nm vertical size at IP. Cavity to Cavity Phase synchronisation requirement Target max. luminosity loss fraction S f (GHz) sx (nm) qc (rads) frms (deg) Dt (fs) Pulse Length (ms) 0.98 12.0 45 0.020 0.0188 4.4 0.156 So need RF path lengths identical to better than c Dt = 1.3 microns

RF path length measurement RF path length is continuously measured and adjusted 4kW 5ms pulsed 11.8 GHz Klystron repetition 5kHz Cavity coupler 0dB or -40dB Cavity coupler 0dB or -40dB Waveguide path length phase and amplitude measurement and control Forward power main pulse 12 MW Single moded copper plated Invar waveguide losses over 40m ~ 3dB -30 dB coupler -30 dB coupler Expansion joint Expansion joint LLRF Magic Tee LLRF Reflected power main pulse ~ 600 W Reflected power main pulse ~ 500 W Phase shifter trombone (High power joint has been tested at SLAC) Phase shifter trombone Waveguide from high power Klystron to magic tee can be over moded Phase Shifter Main beam outward pick up Main beam outward pick up From oscillator 48MW 200ns pulsed 11.994 GHz Klystron repetition 50Hz Vector modulation 12 GHz Oscillator Control

LLRF Hardware Requirements Fast phase measurements during the pulse (~20 ns). Full scale linear phase measurements to centre mixers and for calibration. High accuracy differential phase measurements of RF path length difference (5 μs, 5 kHz). DSP control of phase shifters. Linear Phase Detector Amp + LPF 10.7GHz Oscillator DBM DBM ADC Amp + LPF ADC DSP DBM DAC Wilkinson splitters -30 dB coupler -30 dB coupler To Cavity Magic Tee To Cavity Manual phase shifter for initial setup Fast piezoelectric phase shifter Prototype systems have been developed.

Digital phase detector Board Development Front end electronics to enable phase to be measure during the short pulses to an accuracy of 2 milli-degrees has been prototyped Wilkinson splitter Digital phase detector 10.7 GHz VCO PLL controller MCU Power Meter Output Input 1 DBMs Input 2 Power Meter Output

Phase measurement accuracy Accuracy depends on measurement bandwidth due to noise limitations (bandwidth determines minimum measurement time). Table below shows data for a single mixer + amplifier with 14 dBm power input: can use 4 to double accuracy and use more power. High Speed op amp Double balanced mixer Reflection from cavity 1 Variable LPF Voltage to oscilloscope /ADC Reflection from cavity 2 Pulse length Bandwidth Thermal calculation (milli-deg) RMS resolution measured (milli-deg) 0.14 ms 7 kHz 0.56 1.0 5 μs 200 kHz 3.0 4.6 33 ns 30MHz 37 57

2.54 mV/mdeg 2.17 mV/mdeg 2.17 mV/mdeg Results (from slide 7) 2.54 mV/mdeg 2.17 mV/mdeg 2.17 mV/mdeg 7 kHz 200 kHz 30MHz To oscilloscope 12 GHz Source Coax line stretchers Coax lines Coax line Splitter Mixer March 2012

Waveguide choice Waveguide type 35 meters COPPER Expansion = 17 ppm/K Mode Transmission Timing error/0.3°C Width Timing error/0.3°C length No of modes WR90(22.86x10.16mm) TE10 45.4% 210.5 fs 498.9 fs 1 Large Rectangular (25x14.5mm) 57.9% 189.3 fs 507.8 fs 2 Cylindrical r =18mm TE01 66.9% 804.9 fs 315.9 fs 7 Cylindrical r =25mm 90.4% 279.6 fs 471.4 fs 17 Copper coated extra pure INVAR 35 meters Expansion = 0.65 ppm/K Mode Transmission Timing error/0.3°C Width Timing error/0.3°C length No of modes WR90(22.86x10.16mm) TE10 45.4% 8.13 fs 19.04 fs 1 Large Rectangular (25x14.5mm) 57.9% 6.57 fs 19.69 fs 2 Cylindrical r =18mm TE01 66.9% 30.8 fs 12.1 fs 7 Cylindrical r =25mm 90.4% 10.7 fs 18.02 fs 17 Rectangular invar is the best choice as it offers much better temperature stability-> Expands 2.3 microns for 35 m of waveguide per 0.1 °C.

Laser Distribution Diagram from Florian Loehl, Cornell University

RF Interferometer Synchronisation when return pulse arrives at time when outward pulse is sent Position along cable Far location 180o adjust effective position of far location with a phase shifter 0o Near location time Interferometer line length adjustment Precision reflector synchronous output synchronous output digital phase detector digital phase detector loop filter loop filter coax link master oscillator phase shifter Phase shifter directional coupler directional coupler

Laser to RF f = f0 + KVLF lRF/2 Diagram from J.W.Kim et al. MIT p/2 Loop filter t j The pulses sit on the zero-crossings of VCO output when it is locked. F(s) f = f0 + KVLF VCO j Balanced detector t Ti:sapphire ML-laser 2GHz phase modulator 100MHz Rep rate lRF/2 Diagram from J.W.Kim et al. MIT p/2