SLAC Magnetic Measurements Date: 04-11-1995 Time: 06:55:40 Magnet Name (Serial #): 185 Bar Code Number: 530 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: 04-11-1995 Time: 07:42:56 Magnet Name: 185 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 10.00379 +- 2.105947E-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 0.00007 0.00000 -133.47 0.49 0.4806 0.0026 2 0.01486 0.00000 44.96 0.00 100.0000 0.0000 3 0.00001 0.00000 -8.12 1.24 0.0567 0.0006 4 0.00000 0.00000 4.82 23.35 0.0035 0.0009 5 0.00000 0.00000 11.38 2.53 0.0124 0.0024 6 0.00003 0.00000 15.16 0.07 0.2180 0.0015 7 0.00000 0.00000 12.36 1.22 0.0122 0.0017 8 0.00000 0.00000 17.45 5.76 0.0027 0.0014 9 0.00000 0.00000 4.39 0.62 0.0132 0.0028 10 0.00004 0.00000 -9.15 0.06 0.2980 0.0021 11 0.00000 0.00000 2.51 13.80 0.0021 0.0005 12 0.00000 0.00000 1.58 10.48 0.0029 0.0020 13 0.00000 0.00000 0.16 0.91 0.0127 0.0011 14 0.00004 0.00000 -6.50 0.04 0.2600 0.0011 15 0.00000 0.00000 -7.52 3.59 0.0059 0.0032 16 0.00000 0.00000 2.82 0.85 0.0087 0.0039 The magnetic center is at X = 155.8 +- 1.5 microns Y = 147.7 +- 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: 04-11-1995 Time: 07:49:03 Magnet Name: 185 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 25.10838 +- 2.251621E-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 0.00012 0.00000 -157.97 0.41 0.3494 0.0024 2 0.03488 0.00001 44.96 0.00 100.0000 0.0000 3 0.00002 0.00000 20.97 1.35 0.0483 0.0030 4 0.00000 0.00000 -36.06 2.64 0.0077 0.0008 5 0.00001 0.00000 11.95 0.64 0.0181 0.0018 6 0.00008 0.00000 15.08 0.11 0.2214 0.0025 7 0.00000 0.00000 10.50 0.57 0.0079 0.0017 8 0.00000 0.00000 10.90 19.27 0.0112 0.0015 9 0.00000 0.00000 4.63 0.70 0.0125 0.0007 10 0.00010 0.00000 -9.16 0.05 0.2985 0.0011 11 0.00000 0.00000 -7.21 3.38 0.0030 0.0012 12 0.00000 0.00000 -4.04 2.87 0.0037 0.0008 13 0.00001 0.00000 0.75 0.41 0.0148 0.0039 14 0.00009 0.00000 -6.46 0.02 0.2574 0.0029 15 0.00000 0.00000 -3.77 7.98 0.0065 0.0023 16 0.00000 0.00000 1.69 1.70 0.0109 0.0027 The magnetic center is at X = 58.5 +- 1.1 microns Y = 144.7 +- 1.1 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: 04-11-1995 Time: 07:55:15 Magnet Name: 185 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 50.07236 +- 2.330558E-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 0.00024 0.00000 -168.96 0.59 0.3552 0.0012 2 0.06869 0.00001 44.96 0.00 100.0000 0.0000 3 0.00004 0.00000 22.31 0.66 0.0630 0.0028 4 0.00000 0.00000 -25.59 7.26 0.0056 0.0017 5 0.00001 0.00000 12.30 1.18 0.0196 0.0027 6 0.00015 0.00000 15.11 0.07 0.2209 0.0016 7 0.00001 0.00000 10.11 0.96 0.0073 0.0008 8 0.00000 0.00000 6.89 16.61 0.0029 0.0013 9 0.00001 0.00000 4.32 0.66 0.0133 0.0012 10 0.00021 0.00000 -9.15 0.02 0.2994 0.0009 11 0.00000 0.00000 -2.24 7.47 0.0010 0.0005 12 0.00000 0.00000 -6.96 11.98 0.0043 0.0013 13 0.00001 0.00000 1.35 0.99 0.0166 0.0030 14 0.00017 0.00000 -6.52 0.02 0.2545 0.0018 15 0.00001 0.00000 -8.92 0.34 0.0093 0.0032 16 0.00001 0.00000 3.16 1.54 0.0092 0.0013 The magnetic center is at X = 30.4 +- 1.6 microns Y = 155.7 +- 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: 04-11-1995 Time: 08:01:31 Magnet Name: 185 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 100.0665 +- 6.845655E-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 0.00050 0.00001 -172.42 0.51 0.3681 0.0038 2 0.13702 0.00002 44.96 0.00 100.0000 0.0000 3 0.00009 0.00001 21.92 0.50 0.0659 0.0047 4 0.00001 0.00000 -24.44 8.19 0.0053 0.0017 5 0.00003 0.00000 12.83 0.92 0.0194 0.0023 6 0.00030 0.00000 15.08 0.07 0.2215 0.0021 7 0.00001 0.00000 10.72 1.10 0.0069 0.0016 8 0.00000 0.00000 -0.44 20.14 0.0030 0.0005 9 0.00002 0.00000 4.47 0.49 0.0131 0.0011 10 0.00041 0.00000 -9.17 0.03 0.3009 0.0013 11 0.00000 0.00000 -8.04 11.04 0.0022 0.0003 12 0.00001 0.00000 -6.33 10.92 0.0045 0.0021 13 0.00002 0.00001 1.79 0.24 0.0147 0.0041 14 0.00035 0.00000 -6.48 0.02 0.2579 0.0014 15 0.00002 0.00000 -8.58 0.91 0.0110 0.0025 16 0.00001 0.00000 3.46 0.93 0.0073 0.0015 The magnetic center is at X = 21.7 +- 1.5 microns Y = 163.0 +- 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: 04-11-1995 Time: 08:07:46 Magnet Name: 185 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 150.0811 +- 3.252127E-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 0.00076 0.00000 -174.15 0.37 0.3698 0.0007 2 0.20508 0.00002 44.94 0.00 100.0000 0.0000 3 0.00014 0.00001 22.27 0.59 0.0693 0.0045 4 0.00001 0.00000 -22.39 6.49 0.0044 0.0024 5 0.00004 0.00000 13.21 1.92 0.0202 0.0022 6 0.00044 0.00000 15.06 0.07 0.2138 0.0022 7 0.00001 0.00000 11.13 1.61 0.0061 0.0009 8 0.00000 0.00000 19.69 1.67 0.0023 0.0003 9 0.00002 0.00000 4.46 0.52 0.0110 0.0016 10 0.00062 0.00000 -9.17 0.02 0.3026 0.0011 11 0.00001 0.00000 6.71 12.92 0.0036 0.0009 12 0.00002 0.00000 -13.33 0.79 0.0074 0.0024 13 0.00003 0.00000 0.92 0.44 0.0127 0.0017 14 0.00053 0.00000 -6.50 0.06 0.2587 0.0018 15 0.00002 0.00001 -8.19 0.98 0.0103 0.0041 16 0.00002 0.00001 3.76 1.46 0.0080 0.0029 The magnetic center is at X = 16.8 +- 1.1 microns Y = 164.3 +- 0.3 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: 04-11-1995 Time: 08:14:02 Magnet Name: 185 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 200.3315 +- 1.803396E-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 0.00101 0.00001 -175.31 0.45 0.3717 0.0030 2 0.27268 0.00005 44.94 0.00 100.0000 0.0000 3 0.00020 0.00001 22.60 1.05 0.0724 0.0020 4 0.00004 0.00000 -41.95 2.36 0.0164 0.0009 5 0.00006 0.00001 13.50 2.16 0.0203 0.0020 6 0.00056 0.00000 15.08 0.06 0.2054 0.0004 7 0.00002 0.00000 9.92 1.46 0.0070 0.0009 8 0.00001 0.00001 2.67 1.97 0.0054 0.0020 9 0.00004 0.00000 4.21 1.01 0.0131 0.0007 10 0.00083 0.00001 -9.14 0.02 0.3046 0.0041 11 0.00001 0.00000 -7.52 11.04 0.0027 0.0009 12 0.00001 0.00001 -4.74 9.31 0.0045 0.0020 13 0.00005 0.00000 0.57 0.79 0.0187 0.0008 14 0.00070 0.00000 -6.48 0.02 0.2556 0.0011 15 0.00003 0.00000 -4.05 8.99 0.0098 0.0016 16 0.00003 0.00001 3.69 2.13 0.0100 0.0043 The magnetic center is at X = 13.6 +- 1.3 microns Y = 165.5 +- 1.3 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: 04-11-1995 Time: 08:20:19 Magnet Name: 185 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 250.4357 +- 2.944986E-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 0.00124 0.00000 -177.42 0.28 0.3660 0.0003 2 0.33753 0.00008 44.94 0.00 100.0000 0.0000 3 0.00027 0.00001 23.43 0.66 0.0796 0.0035 4 0.00003 0.00001 -37.67 2.55 0.0098 0.0017 5 0.00007 0.00001 12.72 1.25 0.0219 0.0038 6 0.00062 0.00000 15.10 0.03 0.1823 0.0011 7 0.00002 0.00000 7.03 1.37 0.0066 0.0007 8 0.00002 0.00000 10.26 18.81 0.0053 0.0008 9 0.00005 0.00001 3.73 0.87 0.0136 0.0016 10 0.00104 0.00001 -9.17 0.02 0.3082 0.0018 11 0.00001 0.00000 -6.68 7.30 0.0022 0.0005 12 0.00001 0.00000 1.23 3.84 0.0040 0.0014 13 0.00006 0.00001 0.89 0.48 0.0165 0.0023 14 0.00087 0.00001 -6.53 0.01 0.2566 0.0020 15 0.00003 0.00001 -9.10 0.69 0.0087 0.0017 16 0.00004 0.00001 3.95 1.20 0.0109 0.0026 The magnetic center is at X = 7.4 +- 0.8 microns Y = 163.3 +- 0.1 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: 04-11-1995 Time: 08:26:34 Magnet Name: 185 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 300.4207 +- 6.412324E-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 0.00139 0.00002 -177.23 0.60 0.3579 0.0044 2 0.38964 0.00005 44.93 0.00 100.0000 0.0000 3 0.00030 0.00001 24.70 0.95 0.0760 0.0031 4 0.00003 0.00001 -31.62 3.02 0.0074 0.0014 5 0.00009 0.00001 12.71 1.65 0.0226 0.0018 6 0.00052 0.00001 15.20 0.07 0.1322 0.0016 7 0.00002 0.00000 6.92 1.89 0.0059 0.0009 8 0.00004 0.00000 21.50 0.75 0.0094 0.0006 9 0.00005 0.00000 3.57 0.89 0.0140 0.0012 10 0.00124 0.00001 -9.18 0.03 0.3174 0.0016 11 0.00001 0.00000 -7.15 13.43 0.0032 0.0008 12 0.00001 0.00001 -0.93 9.15 0.0026 0.0015 13 0.00005 0.00001 0.87 0.63 0.0137 0.0025 14 0.00101 0.00001 -6.53 0.03 0.2581 0.0021 15 0.00004 0.00001 -7.88 1.91 0.0106 0.0020 16 0.00007 0.00002 2.99 1.18 0.0168 0.0041 The magnetic center is at X = 7.7 +- 1.7 microns Y = 159.7 +- 1.9 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: 04-11-1995 Time: 08:32:50 Magnet Name: 185 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 350.4278 +- 1.154537E-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 0.00156 0.00002 -177.96 0.45 0.3662 0.0045 2 0.42623 0.00006 44.93 0.00 100.0000 0.0000 3 0.00035 0.00001 24.13 0.51 0.0817 0.0031 4 0.00003 0.00001 -33.80 2.51 0.0072 0.0020 5 0.00010 0.00000 13.06 1.76 0.0241 0.0005 6 0.00032 0.00001 15.50 0.24 0.0753 0.0012 7 0.00003 0.00001 7.27 1.35 0.0066 0.0018 8 0.00003 0.00000 10.37 18.96 0.0065 0.0006 9 0.00006 0.00001 4.27 0.72 0.0143 0.0013 10 0.00140 0.00000 -9.19 0.02 0.3292 0.0007 11 0.00001 0.00000 -1.71 12.48 0.0024 0.0002 12 0.00002 0.00001 -6.54 11.41 0.0051 0.0029 13 0.00006 0.00001 0.72 1.32 0.0142 0.0032 14 0.00108 0.00000 -6.49 0.02 0.2542 0.0006 15 0.00003 0.00001 -3.92 8.00 0.0076 0.0033 16 0.00007 0.00001 1.63 0.44 0.0154 0.0027 The magnetic center is at X = 5.8 +- 1.3 microns Y = 163.5 +- 2.0 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)