EMMA bpm’s

1. EMMA bpm’s Jim Crisp Fermilab October 2007

2. approach • Digitizing 60psec bunch directly is not practical • Diode detector requires matched diodes and careful temperature compensation • Switches require accurate, stable timing • Down converters would limit dynamic range and would have to be carefully matched • Simple RC filter susceptible to offset or baseline error • Consider RLC to produce a decaying sinewave from bunch transient

3. details • measure single bunch each turn for 15 turns • 55.3nsec rotation period • bunch charge 20pC min 80pC max • bunch length 60psec sigma • 84 bpms in ring with 4 buttons each • bpm 48mm ID with 20mm buttons • 3.7GHz microwave cutoff for 48mm round pipe • 25um desired alignment error • 50um desired bpm resolution • Install Feb – May 2009 • Beam July 2009

4. estimate button current • difference of two gaussian 20pC 60psec sigma bunches displaced in time by 20mm/c=133psec • 1.04pC in each half of the doublet

5. estimate frequency response • bpm peak when button is ¼ wavelength long • 3.75GHz • bpm zero when button is ½ wavelength long • 7.5GHz • bunch 60psec sigma t (gaussian) corresponds to 2.65GHz sigma f (gaussian) • peak bpm signal is 1.13 at 2.2GHz • 0.33 at 400MHz • Microwave cutoff in 48” round pipe • 3.7GHz

6. cable dispersion • 100ft of 3/8” heliax (Andrews LDF2-50) • green at bpm • red out of cable

7. ringing filter • signal must decay to 1% in 55nsec (1 turn) • Insures signal from 1 turn does not corrupt the next • 12nsec 1/e time constant • A 400MHz signal sampled at 500MHz looks like 100MHz

8. parallel RLC (time) • Consider parallel RLC on bpm button • Choose R = 25ohms • 50ohms in parallel with 50ohm cable • (for terminating the cable) • Choose time constant • 1/α =12nsec • (1% after 55nsec) • Choose frequency ω • 400MHz • Signal increases with ω • timing errors also increase with ω • C=1/(2Rα) • L=1/(ω^2C) • Q=ωRC

9. compare 3 configurations • 400MHz, 25ohms, 12nsec • 0.6628nH, 238.9pf Q=15 • 1000MHz, 25ohms, 12nsec • 0.106nH, 238.9pf Q=37.5 • 400MHz, 62.5ohms, 12nsec • 1.657nH, 95.54pf Q=15

10. 400MHz 25ohms • The 1.04pC in half of the doublet charges the 239pf cap to 4.35mV. • The second half of the doublet discharges the cap. • The remaining charge rings in the RLC circuit. • 1.66mVpk of 400MHz

11. 1000MHz 25ohms • 1000MHz = 2.5x400MHz • 1.04pC in 239pf = 4.35mV • 3.95mVpk of 1000MHz

12. 400MHz 62.5ohms • 62.5ohms = 2.5x25ohms • 1.04pC in 95.5pf = 10.9mV • 4.14mVpk of 400MHz

13. RLC conclusions • The doublet pulse from the bpm button first charges the capacitor and then discharges it leaving a small amount of energy to excite the resonant circuit. • For 400MHz and 25ohms the amplitude is only 1.67mV for 20pC 60pSec bunch. • Thermal noise would produce 100um rms of error with a 25MHz bandwidth • Inversely proportional signal amplitude and square root of impedance • bpm signal amplitude is proportional to frequency and impedance. • 2.5x larger for 62.5ohms or 1000MHz • The amplitude could be increased substantially by putting the resonant circuit on the bpm and using larger impedance. • Maximum impedance is limited by the button capacitance • Button is about 3pf • for α=12nsec, 1/(2Cα) = 1980ohms (80x larger) • need to measure a bpm to insure coupling between buttons is not a problem • Frequency limits • More than 600MHz would require a faster adc for direct digitization • Would have fewer bits • A down converter could be used to detect the peak at 2.2GHz • About 3x larger • Down converters must be carefully matched and stabilized • may limit dynamic range (good mixer ~45db) • direct adc solution has better stability, dynamic range, and adaptability • SINAD 64.3db • consider an active resonator

14. estimating position error • The radius is a reasonable estimate of the bpm sensitivity • SINAD – ‘signal to noise and distortion’ The ratio of the rms signal amplitude (set 1db below full scale) to the rms value of the sum of all other spectral components, including harmonics, but excluding dc. • The errors from two separate adc’s are not correlated and thus will be added by the square root of the sum of the squares.

15. additional errors • AU – ‘aperture uncertainty’ The sample to sample variation in aperture delay. • AU error is proportional to the derivative of the signal • The effect of AU increases with frequency • INL – ‘integral non-linearity’ The deviation of the transfer function from a reference line measured in fractions of 1 LSB using a ‘best straight line” determined by a least-square curve fit.

16. rms of decaying sinewave • rms value of the decaying sinewave is about 0.233 of the peak. • (12nsec time constant, 55nsec window) • position error also decreases with the square root of the number of samples

17. Fermi digitizer board • Currently designing ATCA board • ATCA – ‘Advanced Telecommunications Computing Architecture’ • FPGA with enough memory to sample all 15 turns at 500MHz • 16 dac channels AD97736 • 12 bit 1200msps • 16 adc channels ADS5463 • 12 bit 500msps • SINAD 64.3dbc • AU 0.16psec • INL 1lsb • 2.2Vpp max input • Rough estimate $8k for 1 board (parts only) • 21 boards = (84bpms x 4 buttons / 16) • 21 x $8k = $168k • ATCA crates $10k each • estimate 12 boards per crate maximum • Prototype board expected 3/2008 • Would like to test with beam • Final design 6/08 • EMMA Installation 2/09 • EMMA Beam 7/09

18. signal processing • For each turn (27 samples) • Multiply samples by sin(t) and integrate (As,Bs) • Multiply samples by cos(t) and integrate (Ac,Bc) • Could use decaying sinwaves but advantage is small • t = ½ {atan(As/Ac) + atan(Bs/Bc)}/  • A = sqrt(As^2+Ac^2) for plate A • Intensity = A+B • Position = 24mm(A-B)/(A+B)

19. expected errors • for a full scale peak signal (2.2Vp-p) • rms of decaying sinewave, 27 samples, 24mm radius • 2.2Vp-p* ½ *0.233 = 0.26Vrms • SINAD • 8.5um • 0.14psec • INL • 4.0um • 0.07psec • AU • 6.8um (proportional to frequency) • 0.11psec • totals • 12um • 0.20psec • thermal noise for 25ohm 400MHz RLC (25MHz bandwidth) • 100um • 1.7psec

20. time error • The proposed system measures the phase or time of a particular frequency component. • The phase of this component wrt the ‘center of mass’ of the bunch will depend on bunch shape.

21. bpm system • Each ATCA crate would have a front end or ‘slot zero controller’ that processes and delivers data to an EPICS application. • Each ATCA crate would likely have one timing distribution card • The EPICS application is important and represents significant effort carefully coordinated with physics requirements of the machine.

22. conclusions • A simple resonant filter was explored. • Need to consider higher impedance at bpm • A down converter could provide some improvement at the expense of dynamic range • The bpm signal amplitude should match the adc input range • A/B will change by up to 10db (factor of 3) with position • bunch charge can change from 20 to 80pC (factor of 4) • 12um rms error for full scale inputs could increase to 144um rms • recommend good quality solid jacketed cable with low dispersion • Andrew LDF2-50 or equal • Need to carefully define the Accelerator Physics requirements to best serve the user • Need to get a bpm to measure

23. Recycler digital receivers • 14 bit 80MHz adc’s, 120 samples, 63mm radius • each position measured 100 times • Mean is plotted on the left and the standard deviation is on the right

24. Recycler adc linearity • Position depends on linearity of a and b adc’s • Dotted lines from 0.3bits typical for the 12 bit AD9430 • Solid lines indicate error from previous slide