SLAC Magnetic Measurements Date: 09-26-1995 Time: 12:41:10 Magnet Name (Serial #): 181 Bar Code Number: 606 Project: PEP II High Energy Ring Quadrupoles Test Stand: IR8, Q1 Measurement Coil: # 2 Operator: dan Run Number: 1 Comment: none Standardization Currents (A): 500.0 10.0 350.0 10.0 350.0 10.0 350.0 10.0 Test Currents (A): 10.0 25.0 50.0 100.0 150.0 200.0 250.0 300.0 350.0 300.0 250.0 200.0 150.0 100.0 50.0 25.0 10.0 Harmonics Measurements Date: 09-26-1995 Time: 13:28:23 Magnet Name: 181 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 10.01085 +- 2.101408E-04 A Coil Radius, Rcoil = .0446657 m Coil # Turns, Nturns = 20 Average, # Rotations/Measurement = 10 , # Measurements = 4 N BLn sigBLn THspole sigTH BLn/BL2 sBLn/BL2 (Tm) (Tm) (deg) (deg) (%) (%) --- --------+-------- --------+-------- --------+-------- 1 0.00004 0.00000 -67.13 1.26 0.2923 0.0019 2 0.01491 0.00000 44.97 0.00 100.0000 0.0000 3 0.00001 0.00000 -25.14 5.48 0.0368 0.0015 4 0.00000 0.00000 -22.80 3.60 0.0220 0.0036 5 0.00000 0.00000 5.78 1.63 0.0251 0.0044 6 0.00003 0.00000 14.96 0.40 0.2099 0.0022 7 0.00000 0.00000 8.61 8.40 0.0103 0.0037 8 0.00000 0.00000 -9.47 12.61 0.0074 0.0025 9 0.00000 0.00000 6.61 4.04 0.0076 0.0007 10 0.00004 0.00000 -9.05 0.08 0.2965 0.0090 11 0.00000 0.00000 -1.57 9.08 0.0079 0.0030 12 0.00000 0.00000 0.27 10.16 0.0104 0.0053 13 0.00000 0.00000 6.80 5.67 0.0094 0.0041 14 0.00004 0.00000 -6.45 0.08 0.2569 0.0076 15 0.00000 0.00000 -8.18 1.43 0.0160 0.0048 16 0.00000 0.00000 3.21 6.10 0.0080 0.0037 The magnetic center is at X = 120.3 +- 1.4 microns Y = -50.8 +- 2.7 microns The magnetic center is measured relative to the coil axis effectively at the longitudinal center of the magnet. Pitch and yaw are not seen by the coil. View from the non-lead end of the magnet: y ^ | N S --> x S N Date: 09-26-1995 Time: 13:34:28 Magnet Name: 181 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 25.12678 +- 2.115407E-03 A Coil Radius, Rcoil = .0446657 m Coil # Turns, Nturns = 20 Average, # Rotations/Measurement = 10 , # Measurements = 4 N BLn sigBLn THspole sigTH BLn/BL2 sBLn/BL2 (Tm) (Tm) (deg) (deg) (%) (%) --- --------+-------- --------+-------- --------+-------- 1 0.00003 0.00000 -77.94 0.64 0.0965 0.0015 2 0.03494 0.00001 44.97 0.00 100.0000 0.0000 3 0.00001 0.00000 8.77 1.28 0.0374 0.0035 4 0.00001 0.00000 -27.00 1.54 0.0252 0.0025 5 0.00001 0.00000 6.99 1.06 0.0260 0.0022 6 0.00008 0.00000 14.94 0.07 0.2159 0.0019 7 0.00000 0.00000 2.48 15.14 0.0061 0.0023 8 0.00000 0.00000 -0.18 20.43 0.0077 0.0024 9 0.00000 0.00000 12.71 2.60 0.0054 0.0022 10 0.00010 0.00000 -9.08 0.04 0.2973 0.0030 11 0.00000 0.00000 -6.81 4.46 0.0043 0.0011 12 0.00000 0.00000 -3.44 2.30 0.0053 0.0029 13 0.00000 0.00000 9.30 1.57 0.0050 0.0030 14 0.00009 0.00000 -6.59 0.05 0.2550 0.0022 15 0.00001 0.00000 -8.23 0.92 0.0145 0.0029 16 0.00000 0.00000 0.37 3.67 0.0078 0.0036 The magnetic center is at X = 42.1 +- 0.7 microns Y = -9.0 +- 0.5 microns The magnetic center is measured relative to the coil axis effectively at the longitudinal center of the magnet. Pitch and yaw are not seen by the coil. View from the non-lead end of the magnet: y ^ | N S --> x S N Date: 09-26-1995 Time: 13:40:40 Magnet Name: 181 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 50.1005 +- 1.538948E-03 A Coil Radius, Rcoil = .0446657 m Coil # Turns, Nturns = 20 Average, # Rotations/Measurement = 10 , # Measurements = 4 N BLn sigBLn THspole sigTH BLn/BL2 sBLn/BL2 (Tm) (Tm) (deg) (deg) (%) (%) --- --------+-------- --------+-------- --------+-------- 1 0.00002 0.00000 -105.69 3.17 0.0360 0.0014 2 0.06883 0.00001 44.97 0.00 100.0000 0.0000 3 0.00003 0.00000 13.81 0.83 0.0508 0.0022 4 0.00002 0.00000 -25.04 1.34 0.0238 0.0014 5 0.00002 0.00000 8.53 1.49 0.0237 0.0018 6 0.00015 0.00000 15.03 0.05 0.2171 0.0015 7 0.00000 0.00000 6.63 2.18 0.0066 0.0014 8 0.00000 0.00000 -1.45 2.10 0.0027 0.0014 9 0.00001 0.00000 12.54 1.91 0.0077 0.0010 10 0.00021 0.00000 -9.02 0.03 0.3000 0.0017 11 0.00000 0.00000 -1.21 12.77 0.0033 0.0010 12 0.00000 0.00000 -2.93 6.44 0.0036 0.0011 13 0.00000 0.00000 6.11 1.67 0.0055 0.0013 14 0.00017 0.00000 -6.48 0.04 0.2541 0.0031 15 0.00001 0.00000 -8.19 0.84 0.0142 0.0034 16 0.00000 0.00000 -4.92 2.80 0.0028 0.0012 The magnetic center is at X = 15.5 +- 0.7 microns Y = 4.3 +- 0.9 microns The magnetic center is measured relative to the coil axis effectively at the longitudinal center of the magnet. Pitch and yaw are not seen by the coil. View from the non-lead end of the magnet: y ^ | N S --> x S N Date: 09-26-1995 Time: 13:46:57 Magnet Name: 181 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 100.1171 +- 1.388393E-03 A Coil Radius, Rcoil = .0446657 m Coil # Turns, Nturns = 20 Average, # Rotations/Measurement = 10 , # Measurements = 4 N BLn sigBLn THspole sigTH BLn/BL2 sBLn/BL2 (Tm) (Tm) (deg) (deg) (%) (%) --- --------+-------- --------+-------- --------+-------- 1 0.00003 0.00000 -149.82 3.95 0.0235 0.0018 2 0.13731 0.00003 44.97 0.00 100.0000 0.0000 3 0.00007 0.00000 14.89 0.93 0.0525 0.0025 4 0.00004 0.00000 -24.32 0.82 0.0281 0.0021 5 0.00003 0.00000 8.29 1.13 0.0252 0.0020 6 0.00030 0.00000 15.00 0.02 0.2186 0.0014 7 0.00001 0.00000 6.72 3.12 0.0050 0.0006 8 0.00000 0.00000 -1.39 5.90 0.0035 0.0005 9 0.00001 0.00000 14.08 2.05 0.0055 0.0021 10 0.00041 0.00000 -9.06 0.05 0.2981 0.0027 11 0.00000 0.00000 -5.37 11.37 0.0021 0.0015 12 0.00001 0.00000 5.20 10.60 0.0042 0.0020 13 0.00001 0.00000 8.98 1.36 0.0042 0.0024 14 0.00035 0.00000 -6.48 0.04 0.2543 0.0010 15 0.00002 0.00001 -8.32 0.90 0.0136 0.0047 16 0.00000 0.00000 -1.17 2.60 0.0028 0.0012 The magnetic center is at X = 5.3 +- 0.7 microns Y = 9.1 +- 0.8 microns The magnetic center is measured relative to the coil axis effectively at the longitudinal center of the magnet. Pitch and yaw are not seen by the coil. View from the non-lead end of the magnet: y ^ | N S --> x S N Date: 09-26-1995 Time: 13:53:11 Magnet Name: 181 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 150.1547 +- 8.670699E-04 A Coil Radius, Rcoil = .0446657 m Coil # Turns, Nturns = 20 Average, # Rotations/Measurement = 10 , # Measurements = 4 N BLn sigBLn THspole sigTH BLn/BL2 sBLn/BL2 (Tm) (Tm) (deg) (deg) (%) (%) --- --------+-------- --------+-------- --------+-------- 1 0.00002 0.00000 108.33 13.86 0.0082 0.0009 2 0.20542 0.00005 44.95 0.00 100.0000 0.0000 3 0.00010 0.00001 15.82 1.42 0.0502 0.0026 4 0.00006 0.00001 -23.49 0.82 0.0284 0.0031 5 0.00005 0.00000 9.31 1.91 0.0233 0.0012 6 0.00043 0.00000 14.94 0.09 0.2095 0.0016 7 0.00001 0.00000 6.81 2.90 0.0067 0.0005 8 0.00000 0.00000 -10.79 8.45 0.0022 0.0011 9 0.00001 0.00000 12.90 2.24 0.0059 0.0019 10 0.00062 0.00001 -9.08 0.03 0.3027 0.0030 11 0.00000 0.00000 -5.93 7.81 0.0023 0.0008 12 0.00001 0.00000 2.94 10.03 0.0036 0.0020 13 0.00001 0.00001 7.84 3.52 0.0056 0.0035 14 0.00052 0.00000 -6.53 0.03 0.2536 0.0023 15 0.00003 0.00001 -8.55 1.48 0.0142 0.0041 16 0.00001 0.00001 -1.66 5.89 0.0046 0.0027 The magnetic center is at X = -3.5 +- 0.5 microns Y = 1.2 +- 0.8 microns The magnetic center is measured relative to the coil axis effectively at the longitudinal center of the magnet. Pitch and yaw are not seen by the coil. View from the non-lead end of the magnet: y ^ | N S --> x S N Date: 09-26-1995 Time: 14:00:22 Magnet Name: 181 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 200.432 +- 1.555181E-03 A Coil Radius, Rcoil = .0446657 m Coil # Turns, Nturns = 20 Average, # Rotations/Measurement = 10 , # Measurements = 4 N BLn sigBLn THspole sigTH BLn/BL2 sBLn/BL2 (Tm) (Tm) (deg) (deg) (%) (%) --- --------+-------- --------+-------- --------+-------- 1 0.00005 0.00000 98.99 4.66 0.0180 0.0014 2 0.27310 0.00003 44.94 0.00 100.0000 0.0000 3 0.00013 0.00000 15.21 0.60 0.0490 0.0013 4 0.00009 0.00001 -30.12 0.66 0.0329 0.0020 5 0.00007 0.00001 7.93 0.98 0.0247 0.0020 6 0.00055 0.00000 15.02 0.07 0.2018 0.0009 7 0.00001 0.00000 4.07 2.66 0.0037 0.0006 8 0.00003 0.00000 -0.76 0.39 0.0104 0.0013 9 0.00002 0.00000 12.05 0.86 0.0057 0.0009 10 0.00083 0.00001 -9.08 0.03 0.3023 0.0020 11 0.00001 0.00000 -7.47 13.12 0.0035 0.0016 12 0.00001 0.00000 -9.75 3.83 0.0023 0.0015 13 0.00002 0.00000 9.12 0.90 0.0057 0.0006 14 0.00069 0.00001 -6.47 0.03 0.2543 0.0024 15 0.00004 0.00001 -8.21 0.80 0.0130 0.0029 16 0.00001 0.00000 -0.00 8.74 0.0052 0.0016 The magnetic center is at X = -7.9 +- 0.6 microns Y = 1.3 +- 0.7 microns The magnetic center is measured relative to the coil axis effectively at the longitudinal center of the magnet. Pitch and yaw are not seen by the coil. View from the non-lead end of the magnet: y ^ | N S --> x S N Date: 09-26-1995 Time: 14:06:38 Magnet Name: 181 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 250.5577 +- 4.244179E-03 A Coil Radius, Rcoil = .0446657 m Coil # Turns, Nturns = 20 Average, # Rotations/Measurement = 10 , # Measurements = 4 N BLn sigBLn THspole sigTH BLn/BL2 sBLn/BL2 (Tm) (Tm) (deg) (deg) (%) (%) --- --------+-------- --------+-------- --------+-------- 1 0.00008 0.00000 91.11 3.19 0.0230 0.0008 2 0.33777 0.00007 44.94 0.00 100.0000 0.0000 3 0.00016 0.00001 16.88 1.36 0.0481 0.0022 4 0.00010 0.00000 -27.06 0.86 0.0300 0.0004 5 0.00008 0.00000 9.23 0.77 0.0231 0.0011 6 0.00060 0.00000 15.03 0.05 0.1787 0.0007 7 0.00002 0.00000 4.99 2.64 0.0052 0.0006 8 0.00002 0.00000 0.63 21.59 0.0073 0.0012 9 0.00002 0.00000 11.62 1.21 0.0051 0.0003 10 0.00104 0.00000 -9.09 0.04 0.3068 0.0006 11 0.00001 0.00001 -11.63 5.23 0.0028 0.0020 12 0.00002 0.00000 -2.08 2.77 0.0064 0.0015 13 0.00002 0.00000 8.30 1.83 0.0054 0.0013 14 0.00086 0.00001 -6.48 0.02 0.2538 0.0019 15 0.00004 0.00001 -8.49 1.67 0.0118 0.0034 16 0.00001 0.00000 -2.07 7.04 0.0033 0.0003 The magnetic center is at X = -10.3 +- 0.3 microns Y = 0.2 +- 0.6 microns The magnetic center is measured relative to the coil axis effectively at the longitudinal center of the magnet. Pitch and yaw are not seen by the coil. View from the non-lead end of the magnet: y ^ | N S --> x S N Date: 09-26-1995 Time: 14:12:54 Magnet Name: 181 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 300.5616 +- 1.645192E-03 A Coil Radius, Rcoil = .0446657 m Coil # Turns, Nturns = 20 Average, # Rotations/Measurement = 10 , # Measurements = 4 N BLn sigBLn THspole sigTH BLn/BL2 sBLn/BL2 (Tm) (Tm) (deg) (deg) (%) (%) --- --------+-------- --------+-------- --------+-------- 1 0.00006 0.00001 109.21 2.28 0.0166 0.0015 2 0.38945 0.00006 44.95 0.00 100.0000 0.0000 3 0.00018 0.00001 14.16 0.53 0.0452 0.0015 4 0.00010 0.00000 -23.43 0.70 0.0267 0.0010 5 0.00009 0.00001 8.22 1.54 0.0231 0.0019 6 0.00050 0.00000 15.10 0.04 0.1275 0.0004 7 0.00002 0.00000 3.84 1.95 0.0046 0.0011 8 0.00002 0.00000 -17.50 1.48 0.0045 0.0008 9 0.00002 0.00000 13.26 2.66 0.0062 0.0005 10 0.00124 0.00000 -9.06 0.02 0.3171 0.0004 11 0.00001 0.00001 -8.24 12.14 0.0029 0.0015 12 0.00001 0.00000 0.07 6.46 0.0026 0.0008 13 0.00002 0.00001 8.00 1.98 0.0053 0.0018 14 0.00100 0.00001 -6.52 0.02 0.2557 0.0024 15 0.00005 0.00001 -7.48 0.65 0.0128 0.0013 16 0.00002 0.00001 -0.03 1.72 0.0054 0.0029 The magnetic center is at X = -7.0 +- 0.6 microns Y = 2.4 +- 0.4 microns The magnetic center is measured relative to the coil axis effectively at the longitudinal center of the magnet. Pitch and yaw are not seen by the coil. View from the non-lead end of the magnet: y ^ | N S --> x S N Date: 09-26-1995 Time: 14:19:10 Magnet Name: 181 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 350.5883 +- 2.526102E-03 A Coil Radius, Rcoil = .0446657 m Coil # Turns, Nturns = 20 Average, # Rotations/Measurement = 10 , # Measurements = 4 N BLn sigBLn THspole sigTH BLn/BL2 sBLn/BL2 (Tm) (Tm) (deg) (deg) (%) (%) --- --------+-------- --------+-------- --------+-------- 1 0.00004 0.00000 108.19 11.08 0.0098 0.0009 2 0.42569 0.00008 44.94 0.00 100.0000 0.0000 3 0.00018 0.00001 15.02 0.95 0.0424 0.0026 4 0.00012 0.00001 -25.22 0.59 0.0282 0.0013 5 0.00010 0.00001 9.21 1.16 0.0224 0.0023 6 0.00030 0.00000 15.26 0.13 0.0710 0.0005 7 0.00002 0.00000 3.72 1.05 0.0056 0.0004 8 0.00002 0.00000 -13.23 1.85 0.0035 0.0004 9 0.00003 0.00000 11.09 1.49 0.0067 0.0004 10 0.00140 0.00001 -9.09 0.03 0.3277 0.0024 11 0.00002 0.00001 -4.03 8.95 0.0039 0.0024 12 0.00002 0.00001 5.48 9.93 0.0042 0.0012 13 0.00002 0.00001 9.41 1.03 0.0052 0.0026 14 0.00108 0.00001 -6.50 0.03 0.2537 0.0012 15 0.00005 0.00003 -2.89 8.08 0.0119 0.0059 16 0.00005 0.00001 0.77 0.86 0.0107 0.0014 The magnetic center is at X = -4.2 +- 0.5 microns Y = 1.4 +- 0.8 microns The magnetic center is measured relative to the coil axis effectively at the longitudinal center of the magnet. Pitch and yaw are not seen by the coil. View from the non-lead end of the magnet: y ^ | N S --> x S N SUMMARY OF THE CALCULATIONS AND CONVENTIONS USED Calculation Of GL: V2 = Nturns * velocity * B2 * L = Nturns * Rcoil * ang_freq * GL * Rcoil = Nturns * Rcoil^2 * ang_freq * GL GL = V2 / (Nturns * Rcoil^2 * ang_freq) Calculation Of The Harmonics: Magnitude, harmonic n: Vn = Nturns * velocity * Bn * L = Nturns * Rcoil * ang_freq * (BLn) BLn = Vn / (Nturns * Rcoil * ang_freq) Rn = BLn / BL2 = Vn / V2 Phase, harmonic n: At the coil radius, the radial field as a function of angle is, BLn(th) = BLn * cos(n*(th - THspole)) The coil voltage Vn(th) = Nturns * velocity * BLn(th) Vn(th)= Nturns * Rcoil * ang_freq * BLn * cos(n*(th - THspole)) The FFT gives Vn and PhiVn in the formula Vn(i) = Vn * cos(n*2pi*i/N + PhiVn) So, Nturns * Rcoil * ang_freq * BLn = Vn -n * THspole = PhiVn Or, BLn = Vn / (Nturns * Rcoil * ang_freq) THspole = -PhiVn / n Calculation Of The Magnetic Center: In the quadrupole's frame, Bx' = G * y', By' = G * x'. In the coil's frame (unprimed frame) the magnetic center is at (x0, y0). In the coil's frame, Bx = G * (y - y0), By = G * (x - x0). This gives the magnetic center in terms of the measured dipole field. x0 = - By / G, y0 = - Bx / G In terms of the measured integrated strengths, Xcenter = - (1/GL) * BL1 * sin(THspole1) Ycenter = - (1/GL) * BL1 * cos(THspole1)