SLAC Magnetic Measurements Date: 03-22-1995 Time: 13:32:52 Magnet Name (Serial #): 180 Bar Code Number: 582 Project: PEP II High Energy Ring Quadrupoles Test Stand: IR8, Q1 Measurement Coil: # 2 Operator: mkl 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: 03-22-1995 Time: 14:20:01 Magnet Name: 180 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 10.00151 +- 7.599878E-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 0.00003 0.00000 -140.00 1.04 0.2300 0.0050 2 0.01486 0.00000 45.00 0.00 100.0000 0.0000 3 0.00001 0.00000 18.44 1.61 0.0526 0.0036 4 0.00000 0.00000 -3.56 26.50 0.0025 0.0016 5 0.00000 0.00000 17.35 0.78 0.0190 0.0004 6 0.00003 0.00000 15.13 0.09 0.2208 0.0008 7 0.00000 0.00000 15.57 2.43 0.0070 0.0011 8 0.00000 0.00000 9.78 18.35 0.0024 0.0011 9 0.00000 0.00000 -3.47 2.20 0.0057 0.0010 10 0.00004 0.00000 -8.98 0.02 0.2983 0.0023 11 0.00000 0.00000 -12.49 2.76 0.0024 0.0013 12 0.00000 0.00000 0.39 12.33 0.0039 0.0020 13 0.00000 0.00000 -3.84 1.26 0.0091 0.0031 14 0.00004 0.00000 -6.43 0.03 0.2575 0.0021 15 0.00000 0.00000 -5.89 4.09 0.0039 0.0036 16 0.00000 0.00000 8.85 2.34 0.0094 0.0022 The magnetic center is at X = 66.0 +- 2.0 microns Y = 78.7 +- 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: 03-22-1995 Time: 14:26:07 Magnet Name: 180 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 25.10229 +- 4.697589E-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 0.00006 0.00000 178.55 0.79 0.1857 0.0085 2 0.03495 0.00000 45.00 0.00 100.0000 0.0000 3 0.00002 0.00000 27.13 1.76 0.0598 0.0030 4 0.00000 0.00000 -36.20 3.88 0.0057 0.0023 5 0.00001 0.00000 15.33 0.52 0.0204 0.0023 6 0.00008 0.00000 15.04 0.03 0.2245 0.0020 7 0.00000 0.00000 14.08 3.65 0.0051 0.0018 8 0.00000 0.00000 0.30 21.98 0.0117 0.0013 9 0.00000 0.00000 -2.97 0.77 0.0081 0.0044 10 0.00010 0.00000 -9.00 0.02 0.2986 0.0021 11 0.00000 0.00000 -2.28 2.54 0.0031 0.0009 12 0.00000 0.00000 -1.23 2.42 0.0053 0.0030 13 0.00000 0.00000 -0.27 1.05 0.0090 0.0050 14 0.00009 0.00000 -6.41 0.04 0.2562 0.0007 15 0.00000 0.00000 -2.97 3.43 0.0063 0.0024 16 0.00000 0.00000 -1.36 5.98 0.0049 0.0020 The magnetic center is at X = -2.1 +- 1.1 microns Y = 82.9 +- 3.8 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: 03-22-1995 Time: 14:32:19 Magnet Name: 180 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 50.0659 +- 1.381434E-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 0.00015 0.00000 165.85 1.67 0.2128 0.0037 2 0.06883 0.00001 45.00 0.00 100.0000 0.0000 3 0.00004 0.00000 28.17 1.36 0.0602 0.0045 4 0.00000 0.00000 -22.57 5.01 0.0060 0.0021 5 0.00001 0.00000 15.77 1.20 0.0202 0.0004 6 0.00015 0.00000 15.06 0.05 0.2237 0.0005 7 0.00000 0.00000 15.36 0.99 0.0049 0.0016 8 0.00000 0.00000 -19.05 2.50 0.0040 0.0009 9 0.00000 0.00000 -6.32 7.37 0.0055 0.0026 10 0.00021 0.00000 -8.99 0.02 0.3006 0.0014 11 0.00000 0.00000 -6.25 10.96 0.0022 0.0010 12 0.00000 0.00000 -3.29 10.04 0.0052 0.0021 13 0.00000 0.00000 -0.49 1.11 0.0066 0.0047 14 0.00017 0.00000 -6.40 0.02 0.2536 0.0020 15 0.00000 0.00000 -6.70 1.63 0.0064 0.0035 16 0.00001 0.00000 0.01 10.04 0.0079 0.0033 The magnetic center is at X = -23.2 +- 2.7 microns Y = 92.2 +- 1.7 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: 03-22-1995 Time: 14:38:35 Magnet Name: 180 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 100.0597 +- 2.490208E-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 0.00031 0.00001 161.07 1.24 0.2283 0.0046 2 0.13730 0.00001 45.00 0.00 100.0000 0.0000 3 0.00008 0.00001 29.47 1.87 0.0589 0.0041 4 0.00001 0.00000 -21.42 3.50 0.0063 0.0026 5 0.00003 0.00000 16.91 0.64 0.0191 0.0011 6 0.00031 0.00000 15.08 0.04 0.2227 0.0009 7 0.00001 0.00000 14.67 0.88 0.0052 0.0009 8 0.00000 0.00000 -9.82 17.05 0.0033 0.0017 9 0.00001 0.00000 -4.68 2.85 0.0061 0.0021 10 0.00041 0.00000 -9.01 0.04 0.3017 0.0019 11 0.00000 0.00000 -3.45 3.68 0.0018 0.0005 12 0.00000 0.00000 -8.13 4.16 0.0032 0.0016 13 0.00001 0.00000 -1.62 1.14 0.0094 0.0014 14 0.00035 0.00000 -6.44 0.03 0.2547 0.0006 15 0.00001 0.00000 -1.03 7.41 0.0046 0.0030 16 0.00001 0.00001 7.83 2.22 0.0053 0.0037 The magnetic center is at X = -33.1 +- 2.2 microns Y = 96.4 +- 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: 03-22-1995 Time: 14:44:50 Magnet Name: 180 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 150.0729 +- 8.2894E-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 0.00045 0.00001 160.39 0.91 0.2209 0.0059 2 0.20549 0.00006 44.97 0.00 100.0000 0.0000 3 0.00013 0.00001 29.77 1.78 0.0638 0.0035 4 0.00002 0.00000 -22.56 6.59 0.0081 0.0012 5 0.00004 0.00000 17.58 1.09 0.0193 0.0007 6 0.00044 0.00000 15.02 0.06 0.2137 0.0011 7 0.00001 0.00000 15.17 2.11 0.0044 0.0005 8 0.00001 0.00000 -18.37 2.17 0.0041 0.0012 9 0.00001 0.00000 -4.09 1.37 0.0072 0.0016 10 0.00063 0.00000 -9.03 0.04 0.3054 0.0013 11 0.00001 0.00000 -10.54 3.79 0.0026 0.0016 12 0.00001 0.00001 -9.54 5.21 0.0058 0.0031 13 0.00002 0.00000 -3.87 1.78 0.0100 0.0022 14 0.00053 0.00000 -6.43 0.04 0.2556 0.0017 15 0.00001 0.00001 -4.00 4.19 0.0054 0.0027 16 0.00002 0.00001 3.53 8.47 0.0090 0.0031 The magnetic center is at X = -33.1 +- 1.7 microns Y = 92.9 +- 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: 03-22-1995 Time: 14:51:06 Magnet Name: 180 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 200.315 +- 1.43457E-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 0.00060 0.00002 157.41 1.14 0.2210 0.0060 2 0.27312 0.00009 44.97 0.00 100.0000 0.0000 3 0.00018 0.00001 30.31 1.16 0.0663 0.0050 4 0.00005 0.00000 -37.96 2.06 0.0172 0.0016 5 0.00005 0.00000 18.00 0.76 0.0182 0.0014 6 0.00056 0.00000 15.04 0.08 0.2052 0.0016 7 0.00001 0.00000 18.34 1.71 0.0035 0.0012 8 0.00002 0.00000 -2.96 1.71 0.0057 0.0008 9 0.00001 0.00000 -6.11 3.08 0.0039 0.0013 10 0.00084 0.00000 -9.01 0.03 0.3083 0.0008 11 0.00001 0.00000 -1.44 5.43 0.0021 0.0007 12 0.00001 0.00001 -7.36 2.99 0.0039 0.0025 13 0.00002 0.00001 -1.99 4.54 0.0058 0.0018 14 0.00070 0.00000 -6.42 0.03 0.2557 0.0015 15 0.00002 0.00001 -0.92 4.96 0.0071 0.0040 16 0.00002 0.00001 4.22 8.98 0.0074 0.0026 The magnetic center is at X = -37.9 +- 2.1 microns Y = 91.1 +- 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: 03-22-1995 Time: 14:57:22 Magnet Name: 180 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 250.4143 +- 1.151735E-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 0.00072 0.00001 154.85 0.99 0.2126 0.0036 2 0.33807 0.00003 44.97 0.00 100.0000 0.0000 3 0.00021 0.00001 32.00 1.25 0.0630 0.0024 4 0.00004 0.00001 -32.03 1.40 0.0130 0.0026 5 0.00006 0.00001 17.17 1.66 0.0175 0.0026 6 0.00062 0.00000 15.03 0.09 0.1823 0.0015 7 0.00001 0.00000 17.86 2.80 0.0028 0.0014 8 0.00002 0.00000 -20.13 1.15 0.0073 0.0006 9 0.00002 0.00000 -3.78 1.83 0.0067 0.0013 10 0.00105 0.00000 -9.01 0.02 0.3113 0.0009 11 0.00001 0.00000 -1.26 12.82 0.0017 0.0008 12 0.00003 0.00000 -2.13 1.87 0.0085 0.0014 13 0.00003 0.00001 -3.62 2.21 0.0090 0.0042 14 0.00086 0.00001 -6.44 0.03 0.2555 0.0020 15 0.00002 0.00001 -1.50 2.73 0.0063 0.0024 16 0.00002 0.00001 2.62 7.54 0.0050 0.0029 The magnetic center is at X = -40.4 +- 1.6 microns Y = 86.0 +- 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: 03-22-1995 Time: 15:03:38 Magnet Name: 180 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 300.4005 +- 6.534611E-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 0.00089 0.00001 158.80 1.18 0.2272 0.0038 2 0.38998 0.00008 44.97 0.00 100.0000 0.0000 3 0.00023 0.00002 28.34 2.17 0.0599 0.0039 4 0.00004 0.00001 -26.15 2.35 0.0097 0.0015 5 0.00006 0.00001 17.36 1.62 0.0162 0.0016 6 0.00051 0.00000 15.02 0.10 0.1301 0.0008 7 0.00001 0.00001 15.32 3.93 0.0038 0.0017 8 0.00004 0.00000 -20.76 0.56 0.0094 0.0008 9 0.00003 0.00001 -4.02 0.67 0.0076 0.0013 10 0.00125 0.00001 -9.01 0.01 0.3214 0.0022 11 0.00001 0.00000 -9.77 4.22 0.0034 0.0006 12 0.00002 0.00001 -4.01 3.55 0.0057 0.0017 13 0.00003 0.00002 -1.10 2.48 0.0067 0.0044 14 0.00100 0.00001 -6.42 0.03 0.2565 0.0017 15 0.00003 0.00001 -1.05 2.89 0.0065 0.0022 16 0.00004 0.00002 2.50 2.74 0.0099 0.0043 The magnetic center is at X = -36.7 +- 2.0 microns Y = 94.6 +- 1.8 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: 03-22-1995 Time: 15:09:54 Magnet Name: 180 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 350.4051 +- 4.531629E-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 0.00101 0.00003 162.84 0.82 0.2359 0.0062 2 0.42637 0.00008 44.97 0.00 100.0000 0.0000 3 0.00024 0.00002 25.72 1.30 0.0559 0.0036 4 0.00004 0.00001 -23.92 3.62 0.0103 0.0013 5 0.00007 0.00001 17.89 1.27 0.0156 0.0019 6 0.00031 0.00001 15.11 0.15 0.0722 0.0014 7 0.00002 0.00000 16.86 2.06 0.0041 0.0008 8 0.00003 0.00000 -19.13 0.84 0.0073 0.0008 9 0.00003 0.00000 -4.05 1.04 0.0078 0.0007 10 0.00141 0.00000 -9.03 0.01 0.3297 0.0010 11 0.00001 0.00001 0.30 8.51 0.0016 0.0013 12 0.00001 0.00001 5.11 7.59 0.0030 0.0025 13 0.00002 0.00000 -4.86 1.25 0.0038 0.0009 14 0.00108 0.00001 -6.47 0.02 0.2526 0.0026 15 0.00002 0.00000 -5.11 3.06 0.0051 0.0009 16 0.00004 0.00002 0.48 3.69 0.0084 0.0043 The magnetic center is at X = -31.1 +- 1.7 microns Y = 100.7 +- 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 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)