SLAC Magnetic Measurements Date: 04-13-1995 Time: 08:53:50 Magnet Name (Serial #): 106 Bar Code Number: 446 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: 04-13-1995 Time: 09:41:05 Magnet Name: 106 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 10.00118 +- 5.212844E-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 -161.86 0.40 0.3488 0.0025 2 0.01483 0.00000 44.99 0.00 100.0000 0.0000 3 0.00001 0.00000 20.59 0.49 0.0719 0.0016 4 0.00000 0.00000 -22.27 2.09 0.0222 0.0012 5 0.00000 0.00000 14.86 1.29 0.0203 0.0020 6 0.00003 0.00000 15.20 0.09 0.2179 0.0017 7 0.00000 0.00000 13.09 0.59 0.0064 0.0013 8 0.00000 0.00000 1.43 17.57 0.0025 0.0002 9 0.00000 0.00000 -0.16 0.75 0.0075 0.0010 10 0.00004 0.00000 -9.04 0.01 0.3003 0.0018 11 0.00000 0.00000 -5.33 8.81 0.0011 0.0008 12 0.00000 0.00000 -11.61 1.44 0.0045 0.0017 13 0.00000 0.00000 -0.83 1.53 0.0123 0.0023 14 0.00004 0.00000 -6.42 0.03 0.2558 0.0008 15 0.00000 0.00000 -4.69 3.33 0.0085 0.0033 16 0.00000 0.00000 3.10 5.07 0.0037 0.0020 The magnetic center is at X = 48.5 +- 1.1 microns Y = 148.0 +- 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: 04-13-1995 Time: 09:47:11 Magnet Name: 106 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 25.10255 +- 5.247376E-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 0.00014 0.00000 -178.12 0.43 0.3938 0.0024 2 0.03499 0.00000 44.99 0.00 100.0000 0.0000 3 0.00002 0.00000 19.22 0.70 0.0705 0.0022 4 0.00001 0.00000 -26.15 1.14 0.0242 0.0020 5 0.00001 0.00000 15.37 0.61 0.0188 0.0010 6 0.00008 0.00000 15.12 0.07 0.2246 0.0016 7 0.00000 0.00000 13.11 2.70 0.0060 0.0016 8 0.00000 0.00000 -21.93 0.23 0.0101 0.0008 9 0.00000 0.00000 1.26 1.89 0.0071 0.0017 10 0.00011 0.00000 -9.05 0.03 0.3023 0.0017 11 0.00000 0.00000 5.09 3.80 0.0015 0.0006 12 0.00000 0.00000 -5.79 3.25 0.0048 0.0022 13 0.00000 0.00000 0.39 0.72 0.0104 0.0029 14 0.00009 0.00000 -6.44 0.01 0.2550 0.0021 15 0.00000 0.00000 -4.45 2.14 0.0083 0.0013 16 0.00000 0.00000 0.06 4.17 0.0068 0.0021 The magnetic center is at X = 5.8 +- 1.3 microns Y = 175.8 +- 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: 04-13-1995 Time: 09:53:22 Magnet Name: 106 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 50.06749 +- 5.122572E-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 0.00029 0.00000 176.42 0.13 0.4190 0.0027 2 0.06897 0.00001 44.99 0.00 100.0000 0.0000 3 0.00005 0.00000 18.82 0.76 0.0726 0.0019 4 0.00002 0.00000 -23.38 0.94 0.0240 0.0018 5 0.00001 0.00000 15.23 0.75 0.0206 0.0022 6 0.00015 0.00000 15.12 0.04 0.2237 0.0012 7 0.00000 0.00000 13.80 1.03 0.0058 0.0013 8 0.00000 0.00000 1.83 18.20 0.0025 0.0006 9 0.00001 0.00000 0.77 1.30 0.0082 0.0017 10 0.00021 0.00000 -9.07 0.01 0.3036 0.0016 11 0.00000 0.00000 6.91 5.12 0.0014 0.0007 12 0.00000 0.00000 -5.92 11.00 0.0048 0.0014 13 0.00001 0.00000 0.30 0.40 0.0106 0.0034 14 0.00017 0.00000 -6.45 0.02 0.2535 0.0017 15 0.00001 0.00000 -5.78 2.20 0.0089 0.0053 16 0.00000 0.00000 6.28 2.97 0.0056 0.0026 The magnetic center is at X = -11.7 +- 0.4 microns Y = 186.8 +- 1.2 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: 04-13-1995 Time: 09:59:38 Magnet Name: 106 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 100.064 +- 2.83291E-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 0.00059 0.00000 173.61 0.30 0.4290 0.0021 2 0.13761 0.00001 44.99 0.00 100.0000 0.0000 3 0.00010 0.00000 19.61 0.35 0.0738 0.0013 4 0.00003 0.00000 -23.00 0.87 0.0242 0.0024 5 0.00003 0.00000 14.99 1.03 0.0194 0.0026 6 0.00031 0.00000 15.13 0.05 0.2244 0.0014 7 0.00001 0.00000 15.07 2.19 0.0063 0.0008 8 0.00000 0.00000 -12.97 6.25 0.0014 0.0006 9 0.00001 0.00000 0.17 0.95 0.0089 0.0013 10 0.00042 0.00000 -9.05 0.02 0.3049 0.0010 11 0.00000 0.00000 -2.23 3.77 0.0018 0.0007 12 0.00000 0.00000 -11.23 0.44 0.0031 0.0009 13 0.00002 0.00000 -0.26 0.85 0.0142 0.0019 14 0.00035 0.00000 -6.46 0.02 0.2544 0.0013 15 0.00001 0.00001 -4.83 1.91 0.0070 0.0040 16 0.00001 0.00000 4.42 3.10 0.0058 0.0030 The magnetic center is at X = -21.3 +- 1.0 microns Y = 190.4 +- 1.0 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 Date: 04-13-1995 Time: 10:05:52 Magnet Name: 106 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 150.0815 +- 8.325134E-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 0.00087 0.00000 172.65 0.21 0.4230 0.0022 2 0.20599 0.00003 44.97 0.00 100.0000 0.0000 3 0.00015 0.00001 18.96 0.62 0.0732 0.0032 4 0.00005 0.00000 -22.05 1.41 0.0243 0.0020 5 0.00004 0.00001 13.90 1.97 0.0182 0.0026 6 0.00044 0.00000 15.09 0.06 0.2160 0.0011 7 0.00001 0.00000 13.21 1.90 0.0054 0.0009 8 0.00000 0.00000 -7.93 14.47 0.0017 0.0006 9 0.00002 0.00000 0.43 1.03 0.0085 0.0019 10 0.00063 0.00000 -9.07 0.04 0.3068 0.0015 11 0.00000 0.00000 11.11 4.46 0.0017 0.0008 12 0.00001 0.00000 -5.54 11.80 0.0052 0.0021 13 0.00003 0.00000 -0.26 0.35 0.0149 0.0015 14 0.00052 0.00000 -6.46 0.02 0.2528 0.0004 15 0.00002 0.00000 -7.42 1.97 0.0080 0.0012 16 0.00001 0.00000 4.70 8.52 0.0068 0.0009 The magnetic center is at X = -24.2 +- 0.7 microns Y = 187.4 +- 1.0 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 Date: 04-13-1995 Time: 10:12:08 Magnet Name: 106 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 200.3293 +- 2.889114E-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 0.00114 0.00001 172.80 0.32 0.4176 0.0025 2 0.27385 0.00005 44.97 0.00 100.0000 0.0000 3 0.00019 0.00001 19.16 0.43 0.0708 0.0032 4 0.00007 0.00001 -30.86 1.18 0.0269 0.0025 5 0.00005 0.00001 14.04 1.72 0.0200 0.0032 6 0.00057 0.00000 15.07 0.05 0.2063 0.0011 7 0.00002 0.00000 13.38 1.10 0.0056 0.0007 8 0.00002 0.00000 -1.66 2.18 0.0060 0.0005 9 0.00002 0.00000 0.57 1.15 0.0088 0.0010 10 0.00084 0.00000 -9.06 0.03 0.3084 0.0016 11 0.00001 0.00000 -5.04 6.97 0.0023 0.0008 12 0.00001 0.00000 -0.23 8.54 0.0040 0.0013 13 0.00003 0.00001 -0.54 0.17 0.0120 0.0022 14 0.00070 0.00000 -6.50 0.02 0.2539 0.0004 15 0.00002 0.00001 -5.98 2.56 0.0059 0.0030 16 0.00002 0.00001 7.36 0.64 0.0080 0.0029 The magnetic center is at X = -23.4 +- 1.0 microns Y = 185.1 +- 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: 04-13-1995 Time: 10:18:25 Magnet Name: 106 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 250.4318 +- 6.92512E-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 0.00135 0.00001 173.12 0.23 0.3971 0.0026 2 0.33898 0.00003 44.96 0.00 100.0000 0.0000 3 0.00021 0.00001 21.02 0.76 0.0621 0.0025 4 0.00007 0.00001 -29.28 1.98 0.0211 0.0020 5 0.00006 0.00001 13.28 0.98 0.0182 0.0023 6 0.00062 0.00000 15.16 0.07 0.1829 0.0006 7 0.00001 0.00001 11.56 1.79 0.0040 0.0015 8 0.00003 0.00000 0.18 21.35 0.0079 0.0013 9 0.00003 0.00000 1.28 0.63 0.0087 0.0008 10 0.00106 0.00000 -9.06 0.04 0.3124 0.0014 11 0.00001 0.00000 3.58 5.06 0.0024 0.0011 12 0.00002 0.00001 2.39 3.46 0.0052 0.0024 13 0.00005 0.00001 0.04 0.18 0.0150 0.0015 14 0.00086 0.00001 -6.49 0.03 0.2545 0.0022 15 0.00002 0.00001 -2.84 7.88 0.0057 0.0030 16 0.00002 0.00001 8.58 0.92 0.0068 0.0029 The magnetic center is at X = -21.3 +- 0.7 microns Y = 176.1 +- 1.2 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: 04-13-1995 Time: 10:24:42 Magnet Name: 106 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 300.4203 +- 7.831194E-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 0.00159 0.00001 174.16 0.32 0.4057 0.0017 2 0.39088 0.00012 44.96 0.00 100.0000 0.0000 3 0.00024 0.00001 18.88 1.16 0.0616 0.0029 4 0.00007 0.00001 -25.86 2.54 0.0173 0.0018 5 0.00006 0.00001 13.03 2.30 0.0166 0.0030 6 0.00051 0.00001 15.16 0.13 0.1296 0.0016 7 0.00002 0.00000 14.68 1.62 0.0047 0.0008 8 0.00003 0.00000 0.07 21.80 0.0075 0.0007 9 0.00004 0.00000 -0.03 0.44 0.0092 0.0008 10 0.00127 0.00000 -9.07 0.01 0.3238 0.0005 11 0.00001 0.00000 2.63 8.05 0.0018 0.0008 12 0.00001 0.00001 -6.06 3.96 0.0033 0.0015 13 0.00005 0.00001 0.29 1.22 0.0135 0.0033 14 0.00100 0.00001 -6.48 0.02 0.2555 0.0015 15 0.00003 0.00001 -6.08 0.76 0.0070 0.0035 16 0.00003 0.00001 4.30 3.28 0.0085 0.0019 The magnetic center is at X = -18.4 +- 1.0 microns Y = 180.3 +- 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: 04-13-1995 Time: 10:30:59 Magnet Name: 106 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 350.4277 +- 6.696505E-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 0.00176 0.00001 175.01 0.17 0.4112 0.0023 2 0.42725 0.00009 44.96 0.00 100.0000 0.0000 3 0.00026 0.00001 17.80 0.65 0.0606 0.0017 4 0.00007 0.00001 -26.93 2.05 0.0154 0.0021 5 0.00008 0.00001 12.58 1.37 0.0184 0.0014 6 0.00030 0.00001 15.43 0.29 0.0709 0.0013 7 0.00002 0.00000 14.65 2.34 0.0050 0.0010 8 0.00002 0.00000 -0.65 20.88 0.0053 0.0011 9 0.00004 0.00001 0.81 0.31 0.0098 0.0012 10 0.00143 0.00000 -9.07 0.03 0.3344 0.0007 11 0.00001 0.00000 -4.86 7.74 0.0026 0.0005 12 0.00002 0.00001 -5.03 6.40 0.0055 0.0022 13 0.00006 0.00002 -0.63 1.20 0.0138 0.0043 14 0.00108 0.00001 -6.46 0.02 0.2516 0.0016 15 0.00003 0.00001 -2.77 5.89 0.0082 0.0033 16 0.00002 0.00001 0.17 3.81 0.0049 0.0021 The magnetic center is at X = -16.0 +- 0.5 microns Y = 183.0 +- 1.0 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)