1. 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

2. SLAC

3. 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

4. Timing Problems Stability Synchronisation
Oscillators shift period with temperature, vibration etc.
VCO shifts period with applied voltage
Atomic clock Df/f ~ ~ 1 fs per minute
Synchronisation
Two clocks with different periods at same place (PLL)
Identical delivery time to 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

5. Clock to cavity Extremely sensitive to modulator voltage
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
Every connector adds uncertainty
Waveguide
sensitive to temperature
Pulse compressor
Waveguide
Cavity

6. 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

7. 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
GHz Klystron repetition 50Hz
Vector modulation
12 GHz Oscillator
Control

8. 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

9. 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

10. 2.54 mV/mdeg 2.17 mV/mdeg 2.17 mV/mdeg
Results (from slide 7)
2.54 mV/mdeg mV/mdeg mV/mdeg
7 kHz kHz MHz
To oscilloscope
12 GHz Source
Coax line stretchers
Coax lines
Coax line
Splitter
Mixer
March 2012

11. 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.

12. 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.