Fitting to the Linear Region of I’/q Does fitting to only the linear region stabilise the calibration constant with charge? And does it improve the resolution? (5 Parameter fit for resolution: I/q, Q/q and constant in Y.)

Changes to calibration constant Reference Sample: 51, IQ Samples: 55-60 Calibration File: IPByCal17_0dB Shift: 151119 IPBPM: B Chi Squared Fitting to all mover steps Chi Squared Fitting to mover steps 3:7 Calibration Constant 0.3978 Calibration Constant 0.4554 Fitting to only the linear range has an effect of between 5-15% on the calibration constant.

Stability of Calibration Constant Reference Sample: 51, IQ Samples: 55-60 Calibration File: IPByCal{10:19}_0dB Shift: 151119 IPBPM: B Considering just the linear region does not appear to stabilise the calibration constant with charge (see appendix). Sometimes difficult to identify linear region. Some files already approximately linear so little difference in calibration constant for these files.

Finding the linear region Reference Sample: 50, IQ Samples: 55-60 Calibration File: IPAyCal1_0dB Shift: 150612 This file has an obvious linear region, not always present. Reference Sample: 51, IQ Samples: 55-60 Calibration File: IPByCal15_0dB Shift: 151119

Improvements to resolution Reference Sample: 51, IQ Samples: 54-60 Calibration File: IP{A:C}yCal1_0dB Jitter Run: jitRun1_0dB Shift: 150612 IPBPM: A,B,C IPBPM: A Fit to mover steps 3:6 Resolution: 60.8nm Fit to all mover steps Resolution: 68.6nm Jitter file taken within linear region. Improvements to resolution from fitting just the linear region. IPBPM: B Fit to all mover steps Resolution: 65.9nm All steps within linear range IPBPM: C Fit to mover steps 2:5 Resolution: 69.6nm Fit to all mover steps Resolution 71.1nm

Resolution for Different Mover Ranges BPM A BPM B BPM C Mover Settings (1:7) 68.6 65.9 71.1 1:7 67.8 66.5 69.6 * 2:5 60.3 * 65.2 * 72.4 3:5 65.4 66.6 73.0 2:6 60.8 66.0 76.8 3:6 ---------------------------------------------- Reference Sample: 51, IQ Samples: 54-60 Calibration File: IP{B:C}yCal1_0dB Jitter Run: jitRun1_0dB Shift: 150612 BPM A BPM B BPM C Mover Settings (1:7) 155 114 74.1 1:7 131 * 111 * 88 2:5 137 75 3:5 159 113 80.5 2:6 168 71 * 3:6 Reference Sample: 51, IQ Samples: 54-60 Calibration File: IPByCal3_0dB IPCyCal8_0dB Jitter Run: jitRun7_0dB Shift: 150612 ---------------------------------------------- BPM A BPM B BPM C Mover Settings (1:7) 16.7 * 28.2 * 104.5 * 1:7 (C)/ 1:9 (AB) 16.8 28.4 111.6 2:5 (C)/ 2:8 (AB) 28.5 110.7 3:5 (C)/ 3:7 (AB) 112.5 2:6 (C)/ 2:7 (AB) 28.7 3:6 (C)/ 3:8 (AB) Reference Sample: 50, IQ Samples: 57-62 Calibration File: IPAyCal5_10dB IPCyCal14_10dB Jitter Run: jitRun10_10dB Shift: 150612 ----------------------------------------------

Next Steps: Polynomial fit How does polynomial fitting (mover setting to I’/q) affect the resolution? 𝑚𝑜𝑣𝑒𝑟 𝜇𝑚 =𝑎+𝑏 𝐼 ′ 𝑞 +𝑐 𝐼 ′ 𝑞 2 +𝑑 𝐼 ′ 𝑞 3 +… 186.5016 186.5581 186.5892 186.6285 186.6694 -1.6457 -1.7160 -1.5952 -1.7919 -1.7523 0 -0.1204 -0.2531 -0.5373 -1.0238 0 0 -0.1692 0.1832 -0.1316 0 0 0 0.3316 0.9499 0 0 0 0 0.4296 Order 1 2 3 4 5 Fitting Parameters a b c d e f

Conclusion Fitting to just linear region appears to improve resolution. Doesn’t necessarily lead to a more stable calibration constant with charge. Future steps: polynomial fitting and improvement to resolution?

Calibration constant with charge Legend???