SLAC Magnetic Measurements Date: 03-13-1995 Time: 11:45:39 Magnet Name (Serial #): 125 Bar Code Number: 470 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: 03-13-1995 Time: 12:32:54 Magnet Name: 125 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 10.00096 +- 4.482335E-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 0.00002 0.00000 -78.27 0.65 0.1456 0.0029 2 0.01489 0.00001 44.95 0.00 100.0000 0.0000 3 0.00001 0.00000 -44.31 2.11 0.0747 0.0094 4 0.00001 0.00000 21.66 1.24 0.0783 0.0117 5 0.00000 0.00000 2.60 1.53 0.0169 0.0062 6 0.00003 0.00000 14.82 0.25 0.2076 0.0064 7 0.00000 0.00000 14.18 2.19 0.0056 0.0024 8 0.00000 0.00000 9.50 17.05 0.0049 0.0017 9 0.00000 0.00000 -7.36 0.92 0.0089 0.0008 10 0.00005 0.00000 -9.12 0.10 0.3044 0.0024 11 0.00000 0.00000 -12.78 0.63 0.0051 0.0007 12 0.00000 0.00000 7.84 0.74 0.0061 0.0014 13 0.00000 0.00000 -4.31 0.28 0.0110 0.0013 14 0.00004 0.00000 -6.52 0.04 0.2560 0.0011 15 0.00000 0.00000 -7.14 1.58 0.0048 0.0022 16 0.00000 0.00000 -1.17 7.87 0.0027 0.0012 The magnetic center is at X = 63.7 +- 1.3 microns Y = -13.2 +- 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: 03-13-1995 Time: 12:39:04 Magnet Name: 125 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 25.10088 +- 7.771439E-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 142.45 0.27 0.1624 0.0012 2 0.03494 0.00001 44.95 0.00 100.0000 0.0000 3 0.00001 0.00000 30.33 1.69 0.0286 0.0049 4 0.00003 0.00000 23.87 1.06 0.0749 0.0020 5 0.00001 0.00000 7.16 2.04 0.0150 0.0025 6 0.00007 0.00000 14.60 0.16 0.2110 0.0043 7 0.00000 0.00000 -22.22 1.92 0.0044 0.0003 8 0.00000 0.00000 11.62 4.16 0.0024 0.0005 9 0.00000 0.00000 -8.18 0.93 0.0104 0.0007 10 0.00011 0.00000 -9.02 0.09 0.3047 0.0054 11 0.00000 0.00000 -13.49 1.24 0.0036 0.0007 12 0.00000 0.00000 5.36 1.74 0.0070 0.0006 13 0.00000 0.00000 -4.45 0.25 0.0129 0.0015 14 0.00009 0.00000 -6.51 0.10 0.2528 0.0043 15 0.00000 0.00000 -2.59 5.42 0.0039 0.0019 16 0.00000 0.00000 5.01 7.83 0.0060 0.0015 The magnetic center is at X = -44.2 +- 0.4 microns Y = 57.5 +- 0.5 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: 03-13-1995 Time: 12:45:18 Magnet Name: 125 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 50.06356 +- 1.792197E-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 0.00015 0.00000 138.40 0.46 0.2245 0.0008 2 0.06881 0.00004 44.95 0.00 100.0000 0.0000 3 0.00002 0.00000 27.23 1.35 0.0317 0.0033 4 0.00005 0.00000 22.01 0.47 0.0783 0.0023 5 0.00001 0.00000 7.25 1.48 0.0165 0.0022 6 0.00015 0.00000 14.80 0.08 0.2131 0.0014 7 0.00000 0.00000 -10.27 20.82 0.0042 0.0012 8 0.00000 0.00000 17.64 0.59 0.0048 0.0013 9 0.00001 0.00000 -7.20 0.13 0.0111 0.0010 10 0.00021 0.00000 -9.08 0.02 0.3039 0.0025 11 0.00000 0.00000 -11.80 1.02 0.0043 0.0006 12 0.00000 0.00000 6.35 0.81 0.0048 0.0008 13 0.00001 0.00000 -3.84 0.23 0.0120 0.0013 14 0.00018 0.00000 -6.49 0.01 0.2565 0.0012 15 0.00000 0.00000 -6.24 1.79 0.0047 0.0028 16 0.00000 0.00000 -4.53 7.62 0.0031 0.0013 The magnetic center is at X = -66.6 +- 0.6 microns Y = 75.0 +- 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: 03-13-1995 Time: 12:51:38 Magnet Name: 125 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 100.0559 +- 4.375775E-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 0.00035 0.00000 137.81 0.29 0.2534 0.0017 2 0.13727 0.00005 44.95 0.00 100.0000 0.0000 3 0.00004 0.00000 25.06 1.41 0.0326 0.0010 4 0.00011 0.00000 22.02 0.35 0.0772 0.0015 5 0.00002 0.00000 8.51 1.57 0.0156 0.0017 6 0.00029 0.00000 14.72 0.06 0.2136 0.0015 7 0.00001 0.00000 -20.95 1.56 0.0049 0.0012 8 0.00001 0.00000 20.56 0.79 0.0054 0.0008 9 0.00001 0.00000 -7.72 0.59 0.0102 0.0009 10 0.00042 0.00000 -9.05 0.01 0.3061 0.0003 11 0.00001 0.00000 -11.76 0.91 0.0048 0.0002 12 0.00001 0.00000 8.40 0.41 0.0070 0.0011 13 0.00002 0.00000 -4.18 0.26 0.0115 0.0011 14 0.00035 0.00000 -6.47 0.02 0.2527 0.0009 15 0.00001 0.00000 -1.52 7.43 0.0052 0.0023 16 0.00000 0.00000 -6.49 0.78 0.0034 0.0023 The magnetic center is at X = -76.0 +- 0.6 microns Y = 83.9 +- 0.7 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: 03-13-1995 Time: 12:57:57 Magnet Name: 125 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 150.0694 +- 2.433047E-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 0.00056 0.00000 136.71 0.17 0.2717 0.0020 2 0.20543 0.00004 44.93 0.00 100.0000 0.0000 3 0.00008 0.00000 23.85 0.86 0.0383 0.0015 4 0.00016 0.00000 21.69 0.45 0.0766 0.0020 5 0.00003 0.00000 9.20 1.63 0.0154 0.0010 6 0.00042 0.00000 14.64 0.10 0.2067 0.0010 7 0.00001 0.00000 1.15 22.59 0.0038 0.0017 8 0.00001 0.00000 18.40 2.53 0.0049 0.0014 9 0.00002 0.00000 -7.42 0.34 0.0117 0.0007 10 0.00062 0.00000 -9.07 0.01 0.3041 0.0015 11 0.00001 0.00000 -12.34 1.97 0.0041 0.0010 12 0.00002 0.00000 10.54 1.31 0.0078 0.0007 13 0.00003 0.00000 -3.69 0.44 0.0132 0.0006 14 0.00053 0.00000 -6.48 0.05 0.2580 0.0017 15 0.00002 0.00000 -5.93 2.68 0.0084 0.0019 16 0.00002 0.00000 -0.31 1.50 0.0090 0.0018 The magnetic center is at X = -83.2 +- 0.6 microns Y = 88.3 +- 0.7 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: 03-13-1995 Time: 13:04:16 Magnet Name: 125 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 200.3117 +- 4.356779E-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 0.00077 0.00000 135.85 0.39 0.2820 0.0008 2 0.27301 0.00012 44.93 0.00 100.0000 0.0000 3 0.00013 0.00000 23.38 0.97 0.0461 0.0009 4 0.00020 0.00001 21.76 0.76 0.0731 0.0029 5 0.00004 0.00000 9.01 0.93 0.0151 0.0013 6 0.00055 0.00000 14.78 0.07 0.2010 0.0014 7 0.00001 0.00000 -20.21 1.33 0.0048 0.0010 8 0.00001 0.00000 14.95 4.43 0.0036 0.0014 9 0.00003 0.00000 -7.55 0.44 0.0121 0.0007 10 0.00084 0.00000 -9.05 0.03 0.3085 0.0008 11 0.00001 0.00000 -12.58 0.74 0.0036 0.0010 12 0.00002 0.00001 11.13 1.91 0.0062 0.0020 13 0.00003 0.00000 -4.05 0.16 0.0118 0.0017 14 0.00070 0.00001 -6.52 0.05 0.2566 0.0024 15 0.00002 0.00001 -0.80 7.59 0.0086 0.0027 16 0.00001 0.00001 -8.23 1.28 0.0044 0.0025 The magnetic center is at X = -87.7 +- 0.7 microns Y = 90.4 +- 0.7 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: 03-13-1995 Time: 13:10:36 Magnet Name: 125 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 250.4111 +- 1.626994E-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 0.00096 0.00000 133.84 0.16 0.2831 0.0008 2 0.33808 0.00010 44.93 0.00 100.0000 0.0000 3 0.00016 0.00000 25.49 0.47 0.0483 0.0013 4 0.00024 0.00001 24.09 0.52 0.0719 0.0028 5 0.00005 0.00000 8.72 1.86 0.0147 0.0013 6 0.00060 0.00001 14.84 0.06 0.1766 0.0016 7 0.00002 0.00000 -18.92 1.88 0.0059 0.0007 8 0.00001 0.00000 10.34 2.21 0.0026 0.0010 9 0.00003 0.00000 -8.36 0.50 0.0101 0.0007 10 0.00106 0.00000 -9.06 0.03 0.3135 0.0004 11 0.00001 0.00000 -8.71 2.39 0.0019 0.0008 12 0.00002 0.00000 6.59 1.23 0.0054 0.0009 13 0.00004 0.00000 -3.98 0.43 0.0109 0.0013 14 0.00086 0.00000 -6.51 0.03 0.2540 0.0008 15 0.00002 0.00001 -7.65 3.97 0.0069 0.0032 16 0.00002 0.00001 5.37 7.99 0.0069 0.0024 The magnetic center is at X = -91.2 +- 0.4 microns Y = 87.6 +- 0.4 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 Date: 03-13-1995 Time: 13:16:56 Magnet Name: 125 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 300.3938 +- 1.063309E-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 0.00106 0.00000 129.43 0.27 0.2709 0.0012 2 0.39009 0.00005 44.92 0.00 100.0000 0.0000 3 0.00019 0.00001 30.22 0.30 0.0496 0.0023 4 0.00027 0.00000 23.20 0.39 0.0696 0.0013 5 0.00006 0.00001 9.34 1.99 0.0153 0.0020 6 0.00052 0.00001 14.91 0.11 0.1327 0.0019 7 0.00002 0.00000 -18.83 1.94 0.0044 0.0010 8 0.00004 0.00001 20.07 0.95 0.0103 0.0016 9 0.00005 0.00000 -8.12 0.52 0.0121 0.0012 10 0.00125 0.00001 -9.07 0.02 0.3211 0.0018 11 0.00001 0.00000 -13.19 0.81 0.0038 0.0008 12 0.00003 0.00000 3.10 0.91 0.0071 0.0011 13 0.00005 0.00001 -4.10 0.27 0.0117 0.0021 14 0.00098 0.00001 -6.51 0.04 0.2525 0.0019 15 0.00003 0.00001 -3.44 2.30 0.0071 0.0022 16 0.00003 0.00001 -0.00 9.38 0.0064 0.0015 The magnetic center is at X = -93.5 +- 0.6 microns Y = 76.9 +- 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: 03-13-1995 Time: 13:23:16 Magnet Name: 125 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 350.3999 +- 2.067214E-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 0.00112 0.00001 124.84 0.35 0.2616 0.0020 2 0.42634 0.00018 44.92 0.00 100.0000 0.0000 3 0.00022 0.00001 35.33 1.04 0.0524 0.0027 4 0.00029 0.00001 22.82 0.30 0.0675 0.0027 5 0.00006 0.00001 8.35 1.12 0.0139 0.0026 6 0.00034 0.00001 14.89 0.20 0.0792 0.0021 7 0.00002 0.00000 -18.08 1.29 0.0058 0.0010 8 0.00006 0.00000 21.35 0.41 0.0130 0.0009 9 0.00005 0.00000 -8.55 0.66 0.0124 0.0004 10 0.00142 0.00001 -9.04 0.01 0.3332 0.0012 11 0.00002 0.00000 -11.84 0.70 0.0038 0.0004 12 0.00003 0.00000 3.44 0.89 0.0075 0.0012 13 0.00005 0.00000 -3.98 0.65 0.0125 0.0009 14 0.00107 0.00001 -6.51 0.05 0.2506 0.0023 15 0.00003 0.00001 -5.94 3.32 0.0071 0.0021 16 0.00003 0.00001 0.54 1.26 0.0067 0.0013 The magnetic center is at X = -95.9 +- 0.9 microns Y = 66.7 +- 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 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)