SLAC Magnetic Measurements Date: 04-06-1995 Time: 11:28:14 Magnet Name (Serial #): 129 Bar Code Number: 334 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: 04-06-1995 Time: 12:15:21 Magnet Name: 129 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 10.00208 +- 8.707305E-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 22.43 1.09 0.1182 0.0010 2 0.01493 0.00000 44.99 0.00 100.0000 0.0000 3 0.00002 0.00000 33.11 0.48 0.1028 0.0021 4 0.00000 0.00000 29.76 1.43 0.0195 0.0012 5 0.00000 0.00000 21.51 0.79 0.0217 0.0023 6 0.00003 0.00000 14.94 0.09 0.2115 0.0014 7 0.00000 0.00000 19.16 3.54 0.0049 0.0010 8 0.00000 0.00000 2.77 2.86 0.0035 0.0018 9 0.00000 0.00000 -9.28 2.29 0.0063 0.0021 10 0.00004 0.00000 -9.00 0.03 0.2965 0.0010 11 0.00000 0.00000 -4.80 11.63 0.0034 0.0023 12 0.00000 0.00000 -1.08 2.18 0.0038 0.0006 13 0.00000 0.00000 -9.25 3.24 0.0061 0.0038 14 0.00004 0.00000 -6.44 0.01 0.2568 0.0014 15 0.00000 0.00000 2.27 7.05 0.0047 0.0024 16 0.00000 0.00000 -2.55 4.96 0.0071 0.0024 The magnetic center is at X = -20.1 +- 0.9 microns Y = -48.8 +- 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: 04-06-1995 Time: 12:21:26 Magnet Name: 129 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 25.10393 +- 4.2635E-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 0.00004 0.00000 62.00 1.69 0.1064 0.0014 2 0.03499 0.00001 44.98 0.00 100.0000 0.0000 3 0.00003 0.00000 35.57 0.47 0.0784 0.0021 4 0.00000 0.00000 34.23 2.21 0.0139 0.0020 5 0.00001 0.00000 20.36 1.30 0.0168 0.0027 6 0.00007 0.00000 14.99 0.03 0.2140 0.0014 7 0.00000 0.00000 20.90 0.38 0.0048 0.0016 8 0.00000 0.00000 19.21 0.92 0.0069 0.0017 9 0.00000 0.00000 -9.92 2.08 0.0058 0.0010 10 0.00010 0.00000 -9.00 0.03 0.2966 0.0007 11 0.00000 0.00000 1.20 10.88 0.0033 0.0008 12 0.00000 0.00000 0.90 1.64 0.0071 0.0026 13 0.00000 0.00000 -4.28 4.90 0.0071 0.0034 14 0.00009 0.00000 -6.47 0.02 0.2561 0.0022 15 0.00000 0.00000 -4.33 5.57 0.0047 0.0024 16 0.00000 0.00000 -0.29 5.06 0.0073 0.0023 The magnetic center is at X = -42.0 +- 0.9 microns Y = -22.3 +- 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: 04-06-1995 Time: 12:27:37 Magnet Name: 129 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 50.0669 +- 8.008662E-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 0.00008 0.00000 77.71 1.00 0.1214 0.0027 2 0.06890 0.00001 44.98 0.00 100.0000 0.0000 3 0.00005 0.00000 35.54 0.66 0.0722 0.0011 4 0.00001 0.00000 30.86 4.08 0.0095 0.0020 5 0.00001 0.00000 21.28 2.23 0.0171 0.0018 6 0.00015 0.00000 14.97 0.05 0.2126 0.0017 7 0.00000 0.00000 18.78 2.17 0.0038 0.0013 8 0.00000 0.00000 2.99 2.73 0.0028 0.0014 9 0.00000 0.00000 -10.12 1.54 0.0047 0.0005 10 0.00021 0.00000 -9.02 0.05 0.2991 0.0014 11 0.00000 0.00000 -1.62 5.24 0.0026 0.0012 12 0.00000 0.00000 3.16 6.35 0.0039 0.0013 13 0.00001 0.00000 -7.14 2.86 0.0076 0.0025 14 0.00017 0.00000 -6.49 0.04 0.2527 0.0023 15 0.00000 0.00000 3.58 4.46 0.0046 0.0010 16 0.00001 0.00001 -1.25 6.75 0.0110 0.0076 The magnetic center is at X = -53.0 +- 1.2 microns Y = -11.5 +- 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: 04-06-1995 Time: 12:33:52 Magnet Name: 129 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 100.0631 +- 8.404896E-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 0.00018 0.00000 85.24 0.79 0.1292 0.0015 2 0.13744 0.00002 44.98 0.00 100.0000 0.0000 3 0.00009 0.00000 35.07 0.51 0.0648 0.0021 4 0.00001 0.00000 32.98 1.77 0.0086 0.0018 5 0.00002 0.00000 20.71 1.69 0.0163 0.0035 6 0.00029 0.00000 15.04 0.06 0.2131 0.0016 7 0.00001 0.00000 16.89 2.81 0.0043 0.0018 8 0.00000 0.00000 5.10 2.25 0.0036 0.0006 9 0.00001 0.00000 -10.44 1.83 0.0050 0.0009 10 0.00041 0.00000 -9.03 0.03 0.3009 0.0005 11 0.00000 0.00000 -8.40 6.47 0.0023 0.0007 12 0.00000 0.00000 1.83 8.67 0.0018 0.0014 13 0.00001 0.00000 -4.98 2.27 0.0103 0.0032 14 0.00035 0.00000 -6.44 0.02 0.2572 0.0018 15 0.00001 0.00001 1.75 7.05 0.0065 0.0044 16 0.00001 0.00001 -2.75 6.64 0.0080 0.0058 The magnetic center is at X = -57.5 +- 0.7 microns Y = -4.8 +- 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: 04-06-1995 Time: 12:40:06 Magnet Name: 129 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 150.0789 +- 6.214094E-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 0.00028 0.00000 83.23 0.30 0.1341 0.0011 2 0.20565 0.00009 44.96 0.00 100.0000 0.0000 3 0.00013 0.00000 35.34 0.87 0.0614 0.0022 4 0.00001 0.00000 29.59 3.97 0.0071 0.0024 5 0.00004 0.00000 21.92 1.81 0.0173 0.0021 6 0.00042 0.00000 14.95 0.06 0.2047 0.0023 7 0.00001 0.00000 18.03 0.79 0.0051 0.0014 8 0.00000 0.00000 6.28 6.37 0.0023 0.0016 9 0.00001 0.00000 -11.87 1.06 0.0060 0.0008 10 0.00062 0.00001 -9.05 0.02 0.3037 0.0028 11 0.00001 0.00000 8.10 10.14 0.0026 0.0015 12 0.00001 0.00000 -1.49 12.95 0.0043 0.0011 13 0.00001 0.00000 -6.29 3.26 0.0072 0.0020 14 0.00052 0.00000 -6.48 0.01 0.2542 0.0010 15 0.00002 0.00001 2.02 6.15 0.0080 0.0042 16 0.00002 0.00001 0.63 6.80 0.0075 0.0038 The magnetic center is at X = -59.5 +- 0.5 microns Y = -7.1 +- 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: 04-06-1995 Time: 12:46:22 Magnet Name: 129 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 200.326 +- 4.262231E-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 0.00036 0.00000 82.19 0.50 0.1304 0.0008 2 0.27326 0.00004 44.96 0.00 100.0000 0.0000 3 0.00016 0.00001 35.84 0.92 0.0570 0.0036 4 0.00006 0.00001 41.74 1.60 0.0210 0.0032 5 0.00004 0.00001 21.48 1.66 0.0152 0.0029 6 0.00053 0.00001 15.02 0.10 0.1953 0.0024 7 0.00001 0.00000 18.01 2.96 0.0040 0.0005 8 0.00003 0.00000 0.84 0.57 0.0118 0.0010 9 0.00001 0.00000 -11.16 1.79 0.0045 0.0014 10 0.00084 0.00000 -9.02 0.04 0.3067 0.0009 11 0.00001 0.00000 7.85 9.87 0.0023 0.0017 12 0.00001 0.00000 -1.53 5.13 0.0040 0.0016 13 0.00003 0.00001 -8.29 2.24 0.0107 0.0035 14 0.00070 0.00001 -6.48 0.02 0.2565 0.0029 15 0.00002 0.00001 3.38 3.09 0.0068 0.0033 16 0.00003 0.00002 -3.26 8.07 0.0102 0.0056 The magnetic center is at X = -57.7 +- 0.4 microns Y = -7.9 +- 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: 04-06-1995 Time: 12:52:38 Magnet Name: 129 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 250.4288 +- 7.181364E-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 0.00040 0.00001 73.78 1.37 0.1171 0.0021 2 0.33797 0.00004 44.96 0.00 100.0000 0.0000 3 0.00017 0.00001 39.51 0.52 0.0496 0.0019 4 0.00004 0.00001 19.96 36.85 0.0132 0.0031 5 0.00005 0.00001 21.55 1.22 0.0134 0.0022 6 0.00059 0.00001 14.93 0.10 0.1740 0.0028 7 0.00001 0.00001 19.47 1.36 0.0044 0.0016 8 0.00001 0.00000 -1.71 18.72 0.0034 0.0009 9 0.00002 0.00001 -10.71 1.26 0.0054 0.0023 10 0.00105 0.00000 -9.06 0.02 0.3096 0.0013 11 0.00001 0.00000 -2.92 8.59 0.0027 0.0008 12 0.00003 0.00000 -0.00 1.65 0.0086 0.0011 13 0.00003 0.00001 -5.77 3.89 0.0083 0.0034 14 0.00085 0.00000 -6.49 0.02 0.2528 0.0012 15 0.00002 0.00000 -1.67 4.09 0.0053 0.0011 16 0.00003 0.00002 -1.32 8.75 0.0095 0.0060 The magnetic center is at X = -50.2 +- 1.0 microns Y = -14.6 +- 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: 04-06-1995 Time: 12:58:55 Magnet Name: 129 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 300.4167 +- 1.277098E-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 0.00041 0.00000 61.72 2.05 0.1060 0.0013 2 0.38972 0.00007 44.96 0.00 100.0000 0.0000 3 0.00018 0.00001 44.36 0.44 0.0463 0.0021 4 0.00003 0.00001 20.13 36.38 0.0066 0.0019 5 0.00005 0.00001 19.44 2.04 0.0126 0.0015 6 0.00046 0.00001 15.10 0.08 0.1182 0.0018 7 0.00002 0.00001 12.18 3.31 0.0040 0.0022 8 0.00002 0.00001 18.20 2.32 0.0048 0.0015 9 0.00002 0.00001 -12.08 3.18 0.0058 0.0027 10 0.00124 0.00001 -9.06 0.03 0.3177 0.0016 11 0.00001 0.00000 -3.03 12.16 0.0017 0.0004 12 0.00002 0.00001 -0.00 5.08 0.0041 0.0018 13 0.00003 0.00001 -8.30 1.71 0.0082 0.0030 14 0.00099 0.00001 -6.49 0.03 0.2530 0.0020 15 0.00003 0.00001 -0.78 2.69 0.0069 0.0020 16 0.00003 0.00001 4.05 3.72 0.0077 0.0020 The magnetic center is at X = -41.7 +- 0.9 microns Y = -22.4 +- 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: 04-06-1995 Time: 13:05:11 Magnet Name: 129 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 350.4236 +- 9.281559E-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 0.00041 0.00001 53.69 1.09 0.0972 0.0015 2 0.42614 0.00006 44.95 0.00 100.0000 0.0000 3 0.00018 0.00000 48.40 0.23 0.0421 0.0008 4 0.00003 0.00001 -1.26 40.90 0.0071 0.0022 5 0.00004 0.00001 21.44 1.98 0.0105 0.0016 6 0.00026 0.00001 14.97 0.15 0.0610 0.0019 7 0.00002 0.00001 15.38 2.50 0.0046 0.0016 8 0.00001 0.00000 10.64 6.25 0.0016 0.0010 9 0.00002 0.00001 -9.68 1.32 0.0051 0.0021 10 0.00140 0.00001 -9.05 0.03 0.3293 0.0020 11 0.00001 0.00001 -5.95 11.61 0.0020 0.0013 12 0.00002 0.00001 -3.11 7.24 0.0040 0.0025 13 0.00003 0.00002 -8.95 1.96 0.0078 0.0041 14 0.00107 0.00000 -6.48 0.05 0.2513 0.0006 15 0.00003 0.00001 0.69 4.40 0.0069 0.0025 16 0.00003 0.00001 -3.77 3.80 0.0065 0.0012 The magnetic center is at X = -35.0 +- 0.7 microns Y = -25.7 +- 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)