SLAC Magnetic Measurements Date: 03-21-1995 Time: 07:56:06 Magnet Name (Serial #): 109 Bar Code Number: 417 Project: PEP II High Energy Ring Quadrupoles Test Stand: IR8, Q1 Measurement Coil: # 2 Operator: bmd Run Number: 1 Comment: 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: 03-21-1995 Time: 08:43:28 Magnet Name: 109 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 9.999525 +- 2.821651E-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 0.00005 0.00000 -126.77 0.78 0.3529 0.0050 2 0.01495 0.00000 44.96 0.00 100.0000 0.0000 3 0.00001 0.00000 17.57 1.38 0.0872 0.0026 4 0.00000 0.00000 -24.62 1.68 0.0278 0.0015 5 0.00000 0.00000 12.46 3.62 0.0082 0.0025 6 0.00003 0.00000 15.16 0.06 0.2124 0.0006 7 0.00000 0.00000 -1.73 22.24 0.0042 0.0014 8 0.00000 0.00000 -6.68 2.89 0.0038 0.0016 9 0.00000 0.00000 5.27 1.32 0.0062 0.0015 10 0.00004 0.00000 -9.04 0.03 0.2993 0.0003 11 0.00000 0.00000 -8.73 6.95 0.0017 0.0011 12 0.00000 0.00000 -4.40 2.86 0.0040 0.0021 13 0.00000 0.00000 1.89 0.85 0.0097 0.0033 14 0.00004 0.00000 -6.44 0.05 0.2580 0.0020 15 0.00000 0.00000 0.18 6.28 0.0051 0.0021 16 0.00000 0.00000 -8.25 2.43 0.0056 0.0015 The magnetic center is at X = 126.3 +- 2.2 microns Y = 94.4 +- 2.2 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: 03-21-1995 Time: 08:49:34 Magnet Name: 109 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 25.09981 +- 3.102389E-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 0.00011 0.00000 -139.98 0.88 0.3188 0.0053 2 0.03501 0.00000 44.96 0.00 100.0000 0.0000 3 0.00002 0.00000 19.24 1.53 0.0682 0.0055 4 0.00001 0.00000 -28.93 0.97 0.0324 0.0016 5 0.00000 0.00000 11.69 3.41 0.0100 0.0023 6 0.00008 0.00000 15.11 0.05 0.2207 0.0008 7 0.00000 0.00000 11.26 18.68 0.0046 0.0019 8 0.00000 0.00000 -19.64 1.38 0.0076 0.0004 9 0.00000 0.00000 5.06 1.34 0.0064 0.0010 10 0.00011 0.00000 -9.03 0.02 0.3002 0.0015 11 0.00000 0.00000 -2.74 9.36 0.0020 0.0005 12 0.00000 0.00000 -2.38 0.95 0.0073 0.0014 13 0.00000 0.00000 1.46 1.68 0.0088 0.0030 14 0.00009 0.00000 -6.43 0.01 0.2580 0.0017 15 0.00000 0.00000 0.66 1.80 0.0053 0.0031 16 0.00000 0.00000 4.44 8.86 0.0066 0.0016 The magnetic center is at X = 91.6 +- 2.3 microns Y = 109.1 +- 2.3 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: 03-21-1995 Time: 08:55:45 Magnet Name: 109 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 50.06284 +- 4.383998E-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 0.00022 0.00000 -145.65 0.86 0.3121 0.0048 2 0.06890 0.00001 44.96 0.00 100.0000 0.0000 3 0.00004 0.00000 19.82 1.49 0.0604 0.0050 4 0.00002 0.00000 -26.73 0.40 0.0313 0.0019 5 0.00001 0.00000 10.50 2.54 0.0090 0.0009 6 0.00015 0.00000 15.14 0.10 0.2211 0.0011 7 0.00000 0.00000 21.45 4.00 0.0030 0.0013 8 0.00000 0.00000 -7.75 0.95 0.0037 0.0018 9 0.00000 0.00000 5.25 1.70 0.0055 0.0003 10 0.00021 0.00000 -9.05 0.01 0.3038 0.0018 11 0.00000 0.00000 2.53 7.48 0.0023 0.0006 12 0.00000 0.00000 -5.68 2.80 0.0044 0.0014 13 0.00001 0.00000 0.26 3.47 0.0091 0.0055 14 0.00018 0.00000 -6.47 0.02 0.2541 0.0020 15 0.00000 0.00000 -4.07 4.22 0.0053 0.0028 16 0.00001 0.00000 1.17 9.73 0.0089 0.0016 The magnetic center is at X = 78.7 +- 2.1 microns Y = 115.1 +- 2.1 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: 03-21-1995 Time: 09:02:00 Magnet Name: 109 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 100.0569 +- 2.6429E-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 0.00043 0.00001 -149.53 0.38 0.3122 0.0063 2 0.13751 0.00003 44.96 0.00 100.0000 0.0000 3 0.00008 0.00000 19.79 1.98 0.0613 0.0017 4 0.00005 0.00000 -26.25 0.61 0.0328 0.0020 5 0.00001 0.00000 10.48 1.33 0.0079 0.0014 6 0.00031 0.00000 15.13 0.11 0.2218 0.0016 7 0.00000 0.00000 18.34 5.36 0.0032 0.0010 8 0.00001 0.00000 -7.93 2.18 0.0037 0.0007 9 0.00001 0.00000 5.35 4.00 0.0045 0.0011 10 0.00042 0.00000 -9.04 0.04 0.3040 0.0006 11 0.00000 0.00000 -8.89 2.88 0.0019 0.0012 12 0.00001 0.00000 -7.72 1.36 0.0038 0.0012 13 0.00001 0.00000 0.92 2.41 0.0066 0.0036 14 0.00035 0.00000 -6.45 0.01 0.2557 0.0026 15 0.00001 0.00000 -0.37 2.28 0.0053 0.0032 16 0.00001 0.00000 -1.51 8.16 0.0043 0.0020 The magnetic center is at X = 70.7 +- 1.6 microns Y = 120.2 +- 2.5 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: 03-21-1995 Time: 09:08:14 Magnet Name: 109 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 150.0708 +- 4.294882E-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 0.00063 0.00001 -150.55 0.90 0.3071 0.0030 2 0.20578 0.00003 44.94 0.00 100.0000 0.0000 3 0.00012 0.00000 20.57 1.18 0.0565 0.0019 4 0.00007 0.00001 -26.35 0.75 0.0318 0.0031 5 0.00002 0.00000 10.84 2.50 0.0090 0.0010 6 0.00044 0.00000 15.16 0.06 0.2130 0.0020 7 0.00001 0.00000 4.27 16.57 0.0032 0.0016 8 0.00001 0.00000 -8.33 4.02 0.0032 0.0008 9 0.00001 0.00000 4.67 2.87 0.0051 0.0017 10 0.00063 0.00000 -9.10 0.02 0.3075 0.0012 11 0.00000 0.00000 1.37 8.99 0.0019 0.0007 12 0.00001 0.00000 -8.78 3.00 0.0072 0.0018 13 0.00002 0.00001 2.52 0.47 0.0118 0.0063 14 0.00052 0.00000 -6.50 0.03 0.2529 0.0018 15 0.00001 0.00001 1.52 7.61 0.0057 0.0025 16 0.00002 0.00001 -0.76 9.47 0.0075 0.0025 The magnetic center is at X = 67.4 +- 2.0 microns Y = 119.4 +- 1.6 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: 03-21-1995 Time: 09:14:29 Magnet Name: 109 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 200.313 +- 7.117043E-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 0.00086 0.00002 -151.80 0.31 0.3155 0.0064 2 0.27339 0.00002 44.94 0.00 100.0000 0.0000 3 0.00016 0.00000 18.79 2.01 0.0603 0.0011 4 0.00010 0.00000 -31.76 0.35 0.0367 0.0010 5 0.00003 0.00000 10.81 1.56 0.0092 0.0007 6 0.00056 0.00001 15.08 0.07 0.2045 0.0019 7 0.00001 0.00000 -3.60 20.24 0.0042 0.0007 8 0.00003 0.00000 -2.09 0.73 0.0102 0.0013 9 0.00001 0.00000 5.39 2.03 0.0050 0.0018 10 0.00085 0.00001 -9.04 0.03 0.3097 0.0019 11 0.00000 0.00000 -0.28 8.80 0.0008 0.0004 12 0.00002 0.00001 -6.73 2.21 0.0062 0.0025 13 0.00002 0.00001 0.38 3.30 0.0071 0.0037 14 0.00070 0.00000 -6.50 0.02 0.2548 0.0010 15 0.00003 0.00001 -4.60 3.33 0.0095 0.0041 16 0.00003 0.00001 10.68 0.46 0.0103 0.0031 The magnetic center is at X = 66.6 +- 1.5 microns Y = 124.2 +- 2.6 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: 03-21-1995 Time: 09:20:46 Magnet Name: 109 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 250.4126 +- 5.681723E-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 0.00107 0.00002 -151.03 0.55 0.3167 0.0056 2 0.33836 0.00007 44.94 0.00 100.0000 0.0000 3 0.00019 0.00001 18.37 1.26 0.0571 0.0028 4 0.00011 0.00001 -29.08 1.38 0.0314 0.0022 5 0.00003 0.00001 10.48 2.44 0.0096 0.0031 6 0.00062 0.00000 15.18 0.09 0.1820 0.0013 7 0.00001 0.00000 -6.28 16.48 0.0022 0.0014 8 0.00001 0.00000 -18.48 1.31 0.0041 0.0008 9 0.00002 0.00001 3.89 1.47 0.0058 0.0020 10 0.00106 0.00000 -9.05 0.03 0.3135 0.0013 11 0.00001 0.00000 6.96 13.27 0.0016 0.0008 12 0.00003 0.00000 -3.62 1.20 0.0102 0.0005 13 0.00003 0.00001 1.13 1.41 0.0085 0.0018 14 0.00086 0.00000 -6.46 0.02 0.2534 0.0015 15 0.00001 0.00000 0.42 4.23 0.0044 0.0011 16 0.00002 0.00001 9.64 0.81 0.0064 0.0024 The magnetic center is at X = 68.5 +- 1.7 microns Y = 123.8 +- 2.3 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: 03-21-1995 Time: 09:27:02 Magnet Name: 109 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 300.3982 +- 0 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 0.00122 0.00002 -151.12 0.34 0.3112 0.0039 2 0.39055 0.00009 44.93 0.00 100.0000 0.0000 3 0.00023 0.00001 20.05 0.63 0.0578 0.0023 4 0.00011 0.00001 -25.90 1.02 0.0278 0.0022 5 0.00004 0.00001 10.22 1.38 0.0113 0.0018 6 0.00050 0.00001 15.22 0.10 0.1272 0.0017 7 0.00001 0.00000 -0.84 18.83 0.0032 0.0008 8 0.00002 0.00001 -8.56 17.52 0.0048 0.0017 9 0.00002 0.00001 2.48 1.04 0.0044 0.0014 10 0.00126 0.00001 -9.07 0.04 0.3228 0.0012 11 0.00001 0.00000 3.59 9.52 0.0014 0.0008 12 0.00003 0.00001 -5.66 1.65 0.0066 0.0033 13 0.00003 0.00000 1.30 1.83 0.0079 0.0005 14 0.00099 0.00001 -6.47 0.02 0.2547 0.0019 15 0.00001 0.00001 -6.16 4.52 0.0035 0.0020 16 0.00002 0.00001 7.29 2.06 0.0046 0.0017 The magnetic center is at X = 67.1 +- 1.1 microns Y = 121.7 +- 1.6 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: 03-21-1995 Time: 09:33:18 Magnet Name: 109 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 350.4023 +- 9.289082E-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 0.00130 0.00001 -151.35 0.60 0.3038 0.0031 2 0.42698 0.00008 44.93 0.00 100.0000 0.0000 3 0.00025 0.00002 20.74 1.06 0.0576 0.0043 4 0.00011 0.00001 -26.60 0.97 0.0261 0.0021 5 0.00005 0.00001 10.85 0.76 0.0119 0.0015 6 0.00030 0.00001 15.50 0.18 0.0693 0.0024 7 0.00001 0.00001 -0.30 20.51 0.0027 0.0013 8 0.00001 0.00001 -4.45 15.41 0.0027 0.0017 9 0.00002 0.00001 3.82 1.88 0.0048 0.0027 10 0.00142 0.00000 -9.06 0.02 0.3326 0.0006 11 0.00001 0.00000 -2.17 4.15 0.0032 0.0011 12 0.00002 0.00001 -7.70 2.93 0.0051 0.0016 13 0.00004 0.00000 1.05 1.02 0.0087 0.0011 14 0.00107 0.00000 -6.48 0.02 0.2516 0.0004 15 0.00002 0.00001 -5.81 3.63 0.0045 0.0015 16 0.00001 0.00001 4.92 4.08 0.0026 0.0014 The magnetic center is at X = 65.1 +- 1.4 microns Y = 119.1 +- 1.4 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 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)