DAQ rejects all multiples of (1/integration time)

1. Patterns: pair quartet (cancels linear drifts) octet (cancels linear and quadratic drifts) modified octet (cancels linear drifts) Use of DAQ patterns to cancel types of noise • If we have short spin states the only way to reject line harmonics is with a pattern • DAQ rejects all multiples of (1/integration time) • DAQ rejects all multiples of twice the pattern (e.g. quartet, octet) frequency. For example, if we start a new spin state every (1/240)s, then a new octet would start 30 times a second, making us immune to all multiples of 60 Hz.

2. Cancelling of Drifts pairs quartets octets modified octets Linear drifts cancel over a quartet: +1-2-3+4=0 Quadratic drifts cancel over an octet: +1-4-9+16-25+36+49-64=0 The modified octet does not cancel quadratic drifts: +1-4+9-16-25+36-49+64=16

3. 240 spin states per second, toggling FFT

4. 240 spin states per second (+-+--+-+) octets 90 FFT 150 30

5. 240 spin states per second (+-+--+-+) octets 90 150 30

6. 240 spin states per second (+--+-++-) octets

7. 240 spin states per second (+-+--+-+) octets

13. 250 spin states per second, toggling

23. current helicity - + - + - + - 6 A 3.6 pA (0.6 ppm p-p) ( ppm) time Size of Qweak Signal • figure shows regular spin flip; in practice use + - - + or - + + - • for 50 kHz noise bandwidth, rms shot noise is 70 nA • on a scope the noise band would be  100,000 x the signal !

24. switching function -- 18 ms quartet 4 ms 4 ms 0.5 ms 0.5 ms 0.5 ms 0.5 ms 4 ms 4 ms

25. Switching function in time domain one 18 ms quartet. Fast Fourier Transform (FFT)

26. Switching function in time domain = ten regular 18 ms quartets. Fast Fourier Transform (FFT) Odd multiples of 55.5 Hz FFT essentially assumes waveform goes on forever

27. Simulation for finite run times • The FFT does not properly account for finite run times • For this I took a test sinusoid, multiplied by the switching function and integrated over the run time • I stepped the frequency and integrated each frequency for the run time • The simulation shows the same “acceptance” frequencies as the FFT,but shows a sensitivity to “off resonance” frequencies for finite run times. • For very long run times, only signals coherent with the switching function remain

29. switching function -- 18 ms quartet 4 ms 4 ms 0.5 ms 0.5 ms 0.5 ms 0.5 ms 4 ms 4 ms

30. switching function -- 18 ms quartet test signal -- 9 ms period sinusoid t = 9 ms f =111.1 Hz

31. (18 ms quartet) x (9 ms period test sinusoid)

32. The 18 ms quartet rejects multiples of 111.1 Hz integral any multiple ofwill integrate to zero regardlessof phase product

33. switching function test signal integral of product product

34. 100 random (+ - - +) 18 ms quartets = 1.8 s run • Exactly equal + and – rejects DC • The 4 ms spin state rejects multiples of 250 Hz • The quartet structure rejects multiples of 111.1 Hz 111.1 333.3 555.5 777.7 222.2 444.4 666.6 888.8 250 500 750 1000

35. 200 random (+ -) or(- +) 9 ms doublets = 1.8 s run • Exactly equal + and – rejects DC • The 4 ms spin state rejects multiples of 250 Hz • The doublet structure rejects multiples of 222.2 Hz 222.2 Hz 444.4 Hz 666.6 Hz 888.8 250 Hz 500 Hz 750 Hz 1000 Hz

36. 400 random (+ ) or(- ) 4.5 ms singlets = 1.8 s run • Each spin state is integrated for 4 ms • 1/4ms = 250 Hz, so multiples of 250 Hz are rejected • States are randomly chosen, so in general there will notbe exactly the same number of + and -, and there will besome sensitivity to DC. 1000 Hz 250 Hz 500 Hz 750 Hz

37. A-B (Lumi-BCM), 25 mA, LH2, 2mm square raster, normal target cooling and pump speed 60 180 240 120 300 360

38. B (BCM only), 10 mA, LH2, 2mm square raster,normal target cooling and pump speed

39. A (Lumi sum only), 10 mA, LH2, 2mm square raster, normal target cooling and pump speed

40. (A-B)/(A+B), 10 mA, LH2, 2mm square raster, normal target cooling and pump speed

42. next spin state one spin state – (1/250) second 200 s settling time (not to scale) t 1 ms NIM gate NIM gate Anticipated DAQ pattern • integrates for 4 ms • stored as four 1 ms integrals • Tsettle as short as 50 s allowed Rapid spin flip reduces noise from target boiling

43. Old “120 Hz” Qweak Integration Scheme next spin state one spin state – (1/30) second 200 s settling time (not to scale) t (1/120) • four 1/120 second integrals • multiples of 60 Hz cancel in sum • individual integrals show if 60 Hz (or odd harmonics) was present

44. Integral From Samples (rectangular rule) • sample at the center of each interval (n samples) • Q = (sum of samples) x (t) • band limit signal to small fraction of sampling frequency to eliminate the wiggles and kinks. • we impose an analog cutoff at 1/10 the sampling frequency

45. Integral From Samples (rectangular rule) 1 s 2 s = 1 ms NIM gate • sample at the center of each interval (500 samples) • first sample 1 s after gate • Q = (sum of samples) x (t) • band limit signal to small fraction of sampling frequency to eliminate the wiggles and kinks.

46. Integral From Samples (trapezoidal rule) • sample at the sides of each interval (n+1 samples) • Q = (average of first and last samples plus sum of others) x (t) • band limit signal to small fraction of sampling frequency to eliminate the wiggles and kinks. • we impose an analog cutoff at 1/10 the sampling frequency

47. Prototype TRIUMF VME integrator details Ext NIM Gate Status LEDs VME Access Ext Clock Enb Ext Gate Enb 8 inputs Ext NIM Clock VME Module Select Switches ADC FPGA Prog/ Debug Ports DC-DC Converter FPGA

48. Existing Gzero Ion Source Signals • signals derived from 20 MHz crystal clock • Qweak integrator should use this clock as well • Integration triggered by MPS (is present form OK?)

49. + helicity - helicity counts charge Q0 ADC error +s charge -s Differential Nonlinearity (DNL) Example • ADC reads S channels low below Q0 and jumps to S channels high above Q0 • This causes the measured asymmetry to depart from the real asymmetry, A0, by an amount , where  is in channels. • The DNL won’t introduce an asymmetry when none is there, it only changes an existing one.