1. Muon-transit RF Phase Determination K Ronald, University of Strathclyde For the MICE RF group 1MICE Optics Review, 15th January 2016

2. Content 2 MICE RF system Brief summary of key features Requirement for measuring Muon RF phase Why is this measurement required Implications of performance of particle detectors to be used What sort of accuracy of RF phase is required Absolute calibration Approaches for measuring RF phase Undersampled digitisation and Fourier Domain reconstruction TDC based digitisation of RF waveform ‘zero’ crossings Timebase synchronisation Hardware Planned Digitisers, Discriminators and TDCs Summary MICE Optics Review, 15th January 2016

3. MICE High Power RF systems 3 Main features of the RF system Two cavities, bracketed by two thin LiH absorbers, sandwiching main absorber Restore part of the momentum lost in transiting the absorbers Cavity Q of ~50,000 (est. by simulation, verified by measurement by network analyser) Simulation of shunt impedance implies 8MV/m for 1MW input power Cannot be verified without passing a beam through an energised cavity with upstream and downstream diagnostics MICE Optics Review, 15th January 2016

4. MICE High Power RF cavities 4 Cavities and Couplers MICE Optics Review, 15th January 2016

5. High Power Driver System Achieved required performance Triode Output ~10dB gain 2.06MW output RF At required duty 34kV bias voltage 129A forward average current  =46% (electronic) Gain 10.8dB Input port return loss -12.5dB VSWR 1.6 Drive from Tetrode 170kW output RF 18kV bias voltage 15.5A forward average current  =61% (electronic) Gain 19dB Drive from SSPA 2.27kW Drive from oscillator 3.7dBm 5 a)HT feedline, b)Output 9 inch coaxial line, c)Input 3 inch line MICE Optics Review, 15th January 2016

6. MICE RF system 6 2MW peak output from RF drive amplifiers BUT assume LLRF ~10 % overhead to achieve regulation Estimated ~10 % reduction in operating into transmission line and reactive load Power delivered to each cavity 1.62 MW Each cavity fed from two couplers Output from each amplifier split in 90 o hybrids Line lengths balance 90 o phase shifts Anticipated gradient in each cavity ~10.3 MV/m Slight uplift in gradient from 7.2 MV/m in each ‘STEP V’ cavity Note total energy recovery 1.4 times less than ‘STEP V’ Cavity 1 RF Amp 1 LLRF Beamline HPRF RF Drive LLRF Feedback RF RF Amp 2 HPRF Cavity 2 RF Drive MICE Optics Review, 15th January 2016

7. Nature of MICE MICE is a physics experiment NOT an accelerator cooling channel Muons are produced by decay of Pions from ISIS proton beam impact on target Muons are produced in spills, duration ~ms There is no particle buncher system in place Muon arrival is completely asynchronous with the RF phase The MICE measurement approach Muon ‘beam’ is extremely tenuous Particles can be & MUST be measured individually Beam is selected ‘after the fact’ Collection of particles satisfying a range of ‘qualification’ parameters The selected ‘beam’ is representative of a REAL beam in a REAL accelerator cooling channel Ionisation cooling is a function of the particle energy Cooling effect is therefore a function of the degree of acceleration each particle experiences Need to be able to select particles for analysis by their RF transit phase Allows the ‘bundling’ of particles for coherent analysis i.e. As if we are considering the interactions of a real particle ‘bunch’ MICE Optics Review, 15th January 20167 Muon RF Phase Determination: Requirement

8. Particle transit time determined by ToF detectors- used in difference measurements ToF resolution ~50ps, absolute delay not completely defined Not an issue for difference measurements between ToF detectors Time is not currently directly referenced to external clock Closest ToF’s are ~2.5m upstream of 1 st cavity/downstream of second cavity Cavity transit time inferred by the ToF transit time and the tracker measurement of momentum Tracker resolution, p z ~ 200MeV/c is  p z ~+/-1.5MeV/c Assuming moderate transverse momentum For 2.5m gap transit delay is ~10ns +/- 33ps Combining ToF resolution and Momentum projection resolution in quadrature ~ +/- 60ps Desire to know RF phase to better than 0.3 of this ~ 20ps i.e. 10% impact on error in quadrature Key requirement is stability of measurement Absolute calibration will be done by particle measurement Providing the systematics remain stable MICE Optics Review, 15th January 20168 RF Phase precision requirement

9. ToF Hodoscopes normally used in difference mode Fixed systematic delays unimportant Now wish to compare to fundamentally different detector Different systematic delays Need to align measurements Assume we can plot momentum change against RF phase with arbitrary offset- first measurement of cavity shunt impedance MICE Optics Review, 15th January 20169 RF Phase absolute calibration Assume the trackers have a p z resolution of about+/- 1.5 MeV/c Estimate ~ +/- 135ps uncertainty in absolute phase (+/- 2.7% of the cycle, ~ +/- 10 o ) Implies alignment at accelerator bunch significant level

10. Sub sample digitisation 10 RF cavities are high Q f 0 =201.25MHz, tuning range ~few hundred kHz LLRF will regulate frequency tightly Exploit feedback to hold cavity on resonance with tuners Q ~50,000,  f~5kHz Nyquist limit is NOT f s =3xf 0 but f s =3x  f No requirement to sample at high speed – mitigate recorded bandwidth We KNOW the resonant frequency and linewidth We KNOW the signal does not repeat for 1s We can perform enhanced Fourier transform Fourier domain resolution enhanced by knowledge of duty pattern Fourier domain width reduced by knowledge of signal spectral structure IFT back to time domain Only over ‘live’ spectral domain and only to ‘live’ temporal domain We can reconstruct the entire pulse history Using minimum data MICE Optics Review, 15th January 2016

11. Sub sample digitisation 11MICE Optics Review, 15th January 2016 Signal (blue) from FNAL cavity tests- 500  s window sampled at 5G.Sa/sec- 2.5M.Sa Subsample (red) at 12.5M.Sa/sec, reduce data by x400, and 48x < Nyquist @ 200MHz dFT to spectral domain Focus on spectrum where energy expected, i.e. 100kHz linewidth about 201.25MHz Spectral resolution enhanced (x4) exploiting knowledge of duty pattern Red is fft of whole data set and Blue is dftx400 of subsampled data f/100MHz Rel Magnitude Real Part f/100MHz Rel Magnitude Imaginary Part

12. Sub sample digitisation 12MICE Optics Review, 15th January 2016 Phase error ~10ps near flat part of pulse No apparent fixed offset Note DSP is effectively a 100kHz filter Raw data has a 1MHz Butterworth Filter Time/s Signal/V Reconstructing by DSP gives high fidelity to raw signal (Blue is Raw, Red is ift of Fourier domain reconstructed dft) over entire pulse duration In MICE will not need to perform full pulse ift ToF will indicate when we wish to know relative phase ift (computationally expensive) is efficiently applied Narrow spectral range and narrow temporal range Time/s Time Offset/s

13. TDC approach 13 Time to Digital Convertors (TDC) are presently used to timestamp particle transit through the hodoscopes, ToF ‘s 0,1,2 4 CAEN V1290A’s are used to record the hodoscopes Ideal to use similar electronics for RF Mitigates risk of ‘walk’ due to different electronics response to environment TDC’s run at 40MHz clock (25ns) with Vernier schemes to yield 25ps bin lengths Sufficient for required accuracy based on UPDF statistics Need a device to turn RF signal into edges for TDC RF signal is (over interesting range) simple, Amplitude and frequency fixed by LLRF feedback No need for CF discriminators- leading edge threshold discriminators are acceptable Set discriminator threshold above noise but in linear part of trig function Interpolate back to zero from TDC readout using prior knowledge of wave amplitude and frequency LeCroy 4415A used for the ToF readout has insufficient analogue bandwidth 9MHz as built and 30MHz with user modification- c.f. 201MHz MICE Optics Review, 15th January 2016

14. Timebase Synchronisation 14 Need to consider mechanism to align timebase of diverse measurements Provide TDC’s and Digitisers for RF measurements with aligned timebase with hodoscopes 4 CAEN V1290A TDC’s are used to record the hodoscopes Driven by LeCroy 4415A discriminators monitoring PM tube output Currently operating with asynchronous clocks Use identical TDC for RF TDC’s require a 40MHz clock for high resolution Provide 40MHz clock using LLRF technology- discussion with Daresbury LLRF group Use digitiser which can also use 40MHz clock rate Trigger signal to digitiser needs to synchronise to TRST signal to TDC’s MICE Optics Review, 15th January 2016

15. Timing System, General Layout TDC’s and Digitisers in same rack room Ensure regulated environment Trigger for digitisers (TRST for TDC’s) from RF diagnostics Clock from LLRF technology- might be in rack room- depends on whether synchronisation with RF clocks appropriate 15MICE Optics Review, 15th January 2016 ToF 1 Cavity 1 RF Amp 1 LLRF Beamline HPRF RF Drive LLRF Feedback TDC’s (ToF) TDC’s (RF) Digitisers Datarecorders RF 40 MHz Clock Trigger/CRST Discriminators (RF) Discriminators (ToF) ToF Signals RG213 Computers RF Amp 2 HPRF Cavity 2 RF Drive Cavity 2 (RG213) Cavity 1 (RG213)

16. Hardware: TDC approach 16 TDC’s presently used to record ToF: CAEN V1290A, VME instruments Presently operate with 40MHz internal async. clocks PLL boosts clock to 320MHz, and DLL with 32 elements -> 100ps resoln. Up to 32 Ch Analogue RC Vernier -> 25ps resolution Records either leading edge or trailing edge of ‘hit’ event At 25ps resolution, main timer roll over (FSR) is after 52  s Operate in trigger matching mode with Ext. Trig. Time Tag (ETTT) enabled Use clock or similar as regular trigger signal Extends timebase FSR up to 100s with 32bit counter synced to trigger 32k events: can record every tenth zero crossing RF signal stability < 1 part in 40,000 For a drift of 25ps, require 1  s Propose to sample at every 50ns- max projection is 25ns Timebase synchronisation T=0 defined on first 40MHz clock event after CRST Use external clock- 40MHz to sync all TDC’s- discussion with DL LLRF group MICE Optics Review, 15th January 2016

17. Hardware: TDC approach 17 Require discriminator to drive TDC’s LeCroy 4415A has inadequate bandwidth for RF operation Procurement underway of Phillips Scientific 704D Quad channel NIM discriminator Non-updating variant of 300MHz leading edge discriminator CF discriminators not required- LLRF ensures signal amplitude 3.3ns double pulse resolution- does not update during output Output width adjustable from 2 to 50 ns- use as effective internal veto Selects every tenth event for TDC recording 1ns edge, pulse shape unaffected by loading, Has external common veto Each channel has independent threshold adj. -10mV to 1V MICE Optics Review, 15th January 2016

18. Hardware: Digitisation 18 Require digitiser synced to same clock as TDC, ideally also VME instrument Require Analogue bandwidth ~ 500MHz Ideally like option to record super Nyquist- e.g. for diagnostics, troubleshooting Demands > 2G.Sa/s and > 2M points/ch Principle mode is sub Nyquist sample rate recording Vertical resolution: As high as possible Procurement underway of CAEN V1761, 2 Ch, 10 bit, 4G.Sa/s, 7.2M.Sa VME digitiser Can accept external clock at 40MHz i.e. same as TDC’s Exploit this to synchronise clocks and timebases Programmable PLL- sets sample clock from main clock Select suitable sub-sample rate Record sparse, sub sampled data- probably only need to record ONE cavity LLRF defines phase relationship of the two cavities Validate with simple analogue phase detector Mitigates memory requirements Postprocess by DFT- enhance resolution with knowledge of pulse structure D IFT to determine waveform at times of interest Use spare channels to provide additional timebase alignment correlation tests MICE Optics Review, 15th January 2016

19. Summary 19 Nature of MICE requires measurement of RF phase for each particle RF phase should ideally be known to a stability of 20ps Does not compromise existing resolution limits imposed by precision and location of particle detectors Absolute calibration by measurement of momentum change in transit of cooling channel Calibration achieved by trackers Possible early calibration measurements using ToF detectors Two techniques possible TDC driven by Discriminators and Digitisation Digitisation potential enhanced by sparse radio spectrum Mitigate data by Fourier domain reconstruction methods TDC gives required resolution and FSR If it can be driven correctly by discriminators Hardware being procured to Facilitate clock synchronisation Provide fast discrimination of RF waveform & self veto’ing of output Appropriate digitisation Clock generation being discussed with LLRF team MICE Optics Review, 15th January 2016