SLAC Magnetic Measurements Date: 04-18-1995 Time: 11:28:55 Magnet Name (Serial #): 186 Bar Code Number: 561 Project: PEP II High Energy Ring Quadrupoles Test Stand: IR8, Q1 Measurement Coil: # 2 Operator: mkl Run Number: 2 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: 04-18-1995 Time: 12:16:03 Magnet Name: 186 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 10.00152 +- 2.981426E-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 0.00009 0.00000 -128.88 0.53 0.5997 0.0042 2 0.01485 0.00000 45.01 0.00 100.0000 0.0000 3 0.00001 0.00000 -2.10 1.08 0.0573 0.0034 4 0.00000 0.00000 27.60 1.65 0.0125 0.0012 5 0.00000 0.00000 9.57 3.24 0.0085 0.0022 6 0.00003 0.00000 15.13 0.05 0.2200 0.0014 7 0.00000 0.00000 13.57 0.35 0.0127 0.0008 8 0.00000 0.00000 -9.41 17.84 0.0031 0.0016 9 0.00000 0.00000 5.55 2.17 0.0142 0.0058 10 0.00004 0.00000 -9.06 0.01 0.2979 0.0018 11 0.00000 0.00000 -7.68 2.80 0.0115 0.0028 12 0.00000 0.00000 -0.97 12.43 0.0043 0.0018 13 0.00000 0.00000 -2.50 1.84 0.0149 0.0052 14 0.00004 0.00000 -6.46 0.06 0.2623 0.0015 15 0.00000 0.00000 -4.13 8.66 0.0061 0.0021 16 0.00000 0.00000 0.50 5.76 0.0045 0.0028 The magnetic center is at X = 208.5 +- 2.2 microns Y = 168.1 +- 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: 04-18-1995 Time: 12:22:10 Magnet Name: 186 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 25.10337 +- 2.076603E-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 0.00016 0.00000 -151.25 0.64 0.4536 0.0068 2 0.03490 0.00000 45.01 0.00 100.0000 0.0000 3 0.00003 0.00000 22.23 1.40 0.0838 0.0040 4 0.00000 0.00000 36.40 3.46 0.0104 0.0025 5 0.00000 0.00000 11.31 3.35 0.0128 0.0039 6 0.00008 0.00000 15.13 0.05 0.2250 0.0011 7 0.00000 0.00000 12.89 1.23 0.0077 0.0009 8 0.00000 0.00000 -0.14 21.97 0.0104 0.0006 9 0.00001 0.00000 2.40 2.18 0.0144 0.0046 10 0.00010 0.00000 -9.01 0.03 0.2973 0.0016 11 0.00000 0.00000 -8.14 0.46 0.0090 0.0024 12 0.00000 0.00000 -1.03 1.72 0.0073 0.0035 13 0.00001 0.00000 -1.66 2.07 0.0144 0.0036 14 0.00009 0.00000 -6.47 0.03 0.2577 0.0009 15 0.00000 0.00000 -5.91 3.52 0.0038 0.0018 16 0.00000 0.00000 4.08 3.68 0.0048 0.0030 The magnetic center is at X = 97.4 +- 2.5 microns Y = 177.6 +- 2.9 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: 04-18-1995 Time: 12:28:21 Magnet Name: 186 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 50.06828 +- 3.834577E-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 -160.51 0.32 0.4284 0.0035 2 0.06874 0.00001 45.01 0.00 100.0000 0.0000 3 0.00007 0.00000 25.49 0.86 0.1008 0.0034 4 0.00000 0.00000 30.45 6.75 0.0050 0.0017 5 0.00001 0.00000 13.09 1.91 0.0175 0.0020 6 0.00015 0.00000 15.07 0.06 0.2236 0.0023 7 0.00000 0.00000 12.28 1.66 0.0052 0.0006 8 0.00000 0.00000 -17.57 3.52 0.0024 0.0005 9 0.00001 0.00000 1.64 2.36 0.0144 0.0043 10 0.00021 0.00000 -9.03 0.03 0.3005 0.0015 11 0.00001 0.00000 -7.08 1.88 0.0113 0.0017 12 0.00000 0.00000 -7.94 2.44 0.0042 0.0002 13 0.00001 0.00000 -3.78 0.77 0.0160 0.0063 14 0.00017 0.00000 -6.47 0.04 0.2519 0.0008 15 0.00000 0.00000 -8.41 2.52 0.0034 0.0005 16 0.00000 0.00000 4.40 2.60 0.0034 0.0021 The magnetic center is at X = 63.8 +- 1.1 microns Y = 180.4 +- 1.5 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: 04-18-1995 Time: 12:34:37 Magnet Name: 186 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 100.0658 +- 6.78909E-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 0.00058 0.00001 -164.93 0.48 0.4223 0.0049 2 0.13715 0.00002 45.01 0.00 100.0000 0.0000 3 0.00015 0.00001 26.45 0.76 0.1062 0.0051 4 0.00001 0.00000 -8.40 32.57 0.0040 0.0014 5 0.00002 0.00000 11.70 1.61 0.0157 0.0018 6 0.00031 0.00000 15.09 0.06 0.2237 0.0017 7 0.00001 0.00000 10.19 0.89 0.0046 0.0006 8 0.00000 0.00000 11.49 10.07 0.0011 0.0007 9 0.00001 0.00001 1.91 2.18 0.0097 0.0048 10 0.00041 0.00000 -9.03 0.02 0.3014 0.0001 11 0.00001 0.00000 -6.81 1.30 0.0091 0.0035 12 0.00001 0.00000 5.04 10.56 0.0044 0.0014 13 0.00002 0.00001 -4.00 2.36 0.0164 0.0039 14 0.00036 0.00000 -6.46 0.03 0.2588 0.0011 15 0.00001 0.00000 -4.99 7.13 0.0049 0.0013 16 0.00001 0.00000 5.47 3.29 0.0039 0.0017 The magnetic center is at X = 49.1 +- 1.6 microns Y = 182.1 +- 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: 04-18-1995 Time: 12:40:53 Magnet Name: 186 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 150.0827 +- 6.241666E-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 0.00084 0.00001 -165.29 0.58 0.4113 0.0037 2 0.20528 0.00002 44.99 0.00 100.0000 0.0000 3 0.00022 0.00001 26.49 0.81 0.1069 0.0040 4 0.00001 0.00000 9.68 24.16 0.0030 0.0007 5 0.00003 0.00001 13.79 1.60 0.0154 0.0026 6 0.00044 0.00000 15.05 0.05 0.2154 0.0018 7 0.00001 0.00000 9.39 2.61 0.0037 0.0005 8 0.00000 0.00000 -8.76 10.17 0.0020 0.0004 9 0.00002 0.00001 3.99 0.70 0.0109 0.0042 10 0.00062 0.00000 -9.04 0.04 0.3019 0.0018 11 0.00003 0.00000 -7.80 0.78 0.0128 0.0019 12 0.00002 0.00000 0.21 13.64 0.0081 0.0023 13 0.00003 0.00001 -5.17 1.49 0.0137 0.0039 14 0.00053 0.00001 -6.43 0.03 0.2578 0.0027 15 0.00002 0.00000 -7.99 1.44 0.0089 0.0017 16 0.00001 0.00001 8.64 1.72 0.0058 0.0036 The magnetic center is at X = 46.6 +- 1.8 microns Y = 177.7 +- 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: 04-18-1995 Time: 12:47:08 Magnet Name: 186 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 200.3309 +- 8.782092E-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 0.00112 0.00001 -165.76 0.56 0.4094 0.0046 2 0.27293 0.00003 44.99 0.00 100.0000 0.0000 3 0.00030 0.00001 26.69 0.82 0.1081 0.0033 4 0.00005 0.00000 0.23 43.58 0.0166 0.0008 5 0.00005 0.00000 12.56 1.62 0.0170 0.0014 6 0.00056 0.00000 15.05 0.09 0.2062 0.0008 7 0.00001 0.00000 8.54 1.67 0.0035 0.0005 8 0.00002 0.00000 -0.23 0.95 0.0072 0.0007 9 0.00003 0.00001 0.99 0.86 0.0106 0.0023 10 0.00083 0.00000 -9.01 0.04 0.3059 0.0004 11 0.00002 0.00001 -7.38 1.77 0.0071 0.0038 12 0.00001 0.00000 7.36 6.40 0.0045 0.0011 13 0.00004 0.00002 -3.95 1.84 0.0143 0.0062 14 0.00070 0.00001 -6.47 0.02 0.2573 0.0020 15 0.00002 0.00001 -6.60 2.40 0.0061 0.0023 16 0.00001 0.00000 3.61 7.99 0.0047 0.0012 The magnetic center is at X = 45.0 +- 1.8 microns Y = 177.3 +- 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: 04-18-1995 Time: 12:53:23 Magnet Name: 186 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 250.4356 +- 5.177881E-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 0.00136 0.00001 -167.53 0.20 0.4019 0.0040 2 0.33788 0.00006 44.99 0.00 100.0000 0.0000 3 0.00038 0.00001 26.18 0.55 0.1115 0.0020 4 0.00003 0.00001 -39.68 2.67 0.0101 0.0021 5 0.00005 0.00001 12.32 1.71 0.0152 0.0023 6 0.00062 0.00000 15.14 0.07 0.1824 0.0002 7 0.00001 0.00000 8.25 4.48 0.0034 0.0011 8 0.00002 0.00000 -20.13 2.02 0.0048 0.0006 9 0.00003 0.00001 1.84 0.64 0.0096 0.0032 10 0.00105 0.00000 -9.05 0.05 0.3095 0.0014 11 0.00003 0.00000 -7.99 1.69 0.0102 0.0002 12 0.00002 0.00001 -2.76 4.52 0.0072 0.0023 13 0.00004 0.00001 -3.88 1.21 0.0127 0.0020 14 0.00086 0.00001 -6.47 0.07 0.2549 0.0025 15 0.00003 0.00001 -6.25 2.53 0.0078 0.0032 16 0.00002 0.00001 3.47 7.64 0.0068 0.0019 The magnetic center is at X = 38.8 +- 0.7 microns Y = 175.3 +- 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: 04-18-1995 Time: 12:59:39 Magnet Name: 186 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 300.4242 +- 4.752323E-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 0.00164 0.00002 -170.01 0.33 0.4197 0.0057 2 0.38988 0.00005 44.99 0.00 100.0000 0.0000 3 0.00048 0.00001 24.60 0.64 0.1230 0.0037 4 0.00003 0.00001 -33.02 5.45 0.0078 0.0022 5 0.00007 0.00001 14.02 0.99 0.0169 0.0017 6 0.00052 0.00000 15.05 0.10 0.1321 0.0013 7 0.00001 0.00000 4.92 4.68 0.0019 0.0006 8 0.00003 0.00000 -9.28 18.18 0.0068 0.0007 9 0.00005 0.00001 1.84 0.74 0.0120 0.0019 10 0.00125 0.00000 -9.03 0.01 0.3205 0.0011 11 0.00005 0.00001 -8.21 0.87 0.0119 0.0021 12 0.00001 0.00000 2.37 2.21 0.0028 0.0013 13 0.00005 0.00002 -5.72 1.82 0.0117 0.0045 14 0.00101 0.00001 -6.51 0.02 0.2594 0.0026 15 0.00002 0.00001 -10.24 1.26 0.0054 0.0025 16 0.00003 0.00001 0.82 0.96 0.0068 0.0025 The magnetic center is at X = 32.5 +- 1.2 microns Y = 184.6 +- 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: 04-18-1995 Time: 13:05:55 Magnet Name: 186 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 350.4338 +- 4.503282E-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 0.00183 0.00002 -171.73 0.57 0.4289 0.0052 2 0.42636 0.00003 44.99 0.00 100.0000 0.0000 3 0.00055 0.00001 24.23 0.63 0.1300 0.0027 4 0.00003 0.00001 -34.28 4.30 0.0081 0.0027 5 0.00009 0.00001 12.39 0.93 0.0206 0.0022 6 0.00031 0.00000 15.27 0.12 0.0738 0.0011 7 0.00001 0.00000 7.66 9.27 0.0013 0.0010 8 0.00002 0.00000 -9.84 18.46 0.0046 0.0004 9 0.00005 0.00001 2.74 0.77 0.0126 0.0025 10 0.00141 0.00001 -9.03 0.04 0.3307 0.0017 11 0.00004 0.00001 -7.98 1.67 0.0097 0.0018 12 0.00002 0.00000 -9.34 2.83 0.0049 0.0010 13 0.00004 0.00001 -4.01 1.21 0.0086 0.0025 14 0.00108 0.00001 -6.47 0.05 0.2523 0.0030 15 0.00003 0.00001 -7.70 1.46 0.0067 0.0024 16 0.00003 0.00001 2.61 1.15 0.0072 0.0016 The magnetic center is at X = 27.6 +- 1.9 microns Y = 189.6 +- 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 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)