SLAC Magnetic Measurements Date: 04-07-1995 Time: 08:38:42 Magnet Name (Serial #): 110 Bar Code Number: 458 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: 04-07-1995 Time: 09:25:54 Magnet Name: 110 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 10.00119 +- 4.719346E-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 7.95 0.77 0.1330 0.0021 2 0.01491 0.00000 44.98 0.00 100.0000 0.0000 3 0.00002 0.00000 43.66 0.36 0.1416 0.0035 4 0.00000 0.00000 -20.47 2.49 0.0130 0.0019 5 0.00000 0.00000 14.05 1.58 0.0232 0.0022 6 0.00003 0.00000 15.03 0.07 0.2130 0.0017 7 0.00000 0.00000 -4.11 15.60 0.0025 0.0016 8 0.00000 0.00000 -12.80 2.41 0.0025 0.0012 9 0.00000 0.00000 -10.34 2.10 0.0053 0.0022 10 0.00004 0.00000 -9.03 0.02 0.2976 0.0015 11 0.00000 0.00000 6.53 3.24 0.0034 0.0010 12 0.00000 0.00000 -5.05 5.74 0.0016 0.0007 13 0.00000 0.00000 -1.83 1.00 0.0092 0.0025 14 0.00004 0.00000 -6.46 0.02 0.2556 0.0018 15 0.00000 0.00000 -2.66 8.65 0.0043 0.0024 16 0.00000 0.00000 -4.30 4.45 0.0052 0.0032 The magnetic center is at X = -8.2 +- 0.8 microns Y = -58.8 +- 0.9 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: 04-07-1995 Time: 09:31:59 Magnet Name: 110 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 25.10308 +- 3.107369E-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 0.00003 0.00000 133.54 2.37 0.0735 0.0022 2 0.03496 0.00001 44.97 0.00 100.0000 0.0000 3 0.00002 0.00000 36.65 0.79 0.0673 0.0031 4 0.00001 0.00000 -29.02 1.74 0.0156 0.0020 5 0.00001 0.00000 15.48 1.28 0.0184 0.0016 6 0.00008 0.00000 15.05 0.05 0.2199 0.0024 7 0.00000 0.00000 20.07 3.24 0.0039 0.0009 8 0.00000 0.00000 11.01 18.92 0.0091 0.0007 9 0.00000 0.00000 -6.50 1.59 0.0049 0.0018 10 0.00010 0.00000 -9.01 0.02 0.2987 0.0012 11 0.00000 0.00000 -7.40 8.64 0.0020 0.0013 12 0.00000 0.00000 -1.52 1.63 0.0068 0.0015 13 0.00000 0.00000 -3.53 1.00 0.0106 0.0023 14 0.00009 0.00000 -6.50 0.04 0.2559 0.0006 15 0.00000 0.00000 0.43 1.73 0.0051 0.0022 16 0.00000 0.00000 1.85 5.24 0.0055 0.0009 The magnetic center is at X = -23.8 +- 1.2 microns Y = 22.6 +- 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: 04-07-1995 Time: 09:38:11 Magnet Name: 110 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 50.06659 +- 4.654634E-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 136.05 1.13 0.1366 0.0024 2 0.06889 0.00001 44.97 0.00 100.0000 0.0000 3 0.00005 0.00000 33.02 0.91 0.0657 0.0018 4 0.00001 0.00000 -22.35 2.17 0.0145 0.0019 5 0.00001 0.00000 17.29 0.28 0.0185 0.0026 6 0.00015 0.00000 15.00 0.08 0.2190 0.0023 7 0.00000 0.00000 20.18 2.72 0.0048 0.0009 8 0.00000 0.00000 2.33 10.37 0.0018 0.0011 9 0.00000 0.00000 -7.44 1.72 0.0044 0.0005 10 0.00021 0.00000 -9.03 0.04 0.3009 0.0013 11 0.00000 0.00000 9.30 1.04 0.0034 0.0003 12 0.00000 0.00000 -9.21 1.27 0.0047 0.0026 13 0.00001 0.00000 -5.17 1.91 0.0110 0.0017 14 0.00017 0.00000 -6.49 0.04 0.2528 0.0010 15 0.00000 0.00000 0.28 1.34 0.0050 0.0031 16 0.00000 0.00000 -4.27 8.47 0.0055 0.0008 The magnetic center is at X = -42.4 +- 1.2 microns Y = 43.9 +- 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: 04-07-1995 Time: 09:44:26 Magnet Name: 110 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 100.0631 +- 6.717551E-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 0.00023 0.00001 135.46 0.39 0.1663 0.0039 2 0.13747 0.00002 44.97 0.00 100.0000 0.0000 3 0.00009 0.00000 31.37 0.75 0.0664 0.0017 4 0.00002 0.00000 -22.00 1.87 0.0150 0.0019 5 0.00003 0.00000 17.54 0.90 0.0199 0.0020 6 0.00030 0.00000 15.02 0.11 0.2192 0.0014 7 0.00001 0.00000 6.87 18.81 0.0053 0.0017 8 0.00000 0.00000 -3.23 11.52 0.0019 0.0008 9 0.00000 0.00000 -5.36 1.74 0.0035 0.0008 10 0.00042 0.00000 -9.04 0.04 0.3024 0.0017 11 0.00000 0.00000 -0.52 9.14 0.0030 0.0009 12 0.00001 0.00000 -9.54 1.84 0.0048 0.0014 13 0.00001 0.00000 -4.37 2.26 0.0098 0.0019 14 0.00035 0.00000 -6.48 0.04 0.2545 0.0009 15 0.00001 0.00000 -1.02 2.84 0.0047 0.0016 16 0.00001 0.00000 2.20 8.49 0.0065 0.0011 The magnetic center is at X = -52.1 +- 1.3 microns Y = 52.9 +- 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: 04-07-1995 Time: 09:50:41 Magnet Name: 110 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 150.0784 +- 7.858647E-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 134.15 0.15 0.1737 0.0007 2 0.20572 0.00005 44.95 0.00 100.0000 0.0000 3 0.00014 0.00001 31.38 0.33 0.0665 0.0025 4 0.00003 0.00000 -21.58 2.24 0.0153 0.0013 5 0.00004 0.00001 17.24 0.68 0.0209 0.0025 6 0.00043 0.00000 15.01 0.10 0.2111 0.0019 7 0.00001 0.00000 19.77 4.16 0.0037 0.0016 8 0.00000 0.00000 6.39 15.78 0.0014 0.0012 9 0.00001 0.00000 -8.85 2.04 0.0045 0.0020 10 0.00063 0.00000 -9.04 0.04 0.3064 0.0015 11 0.00001 0.00000 10.01 2.41 0.0049 0.0010 12 0.00001 0.00000 -12.32 2.06 0.0061 0.0018 13 0.00002 0.00001 -4.03 3.39 0.0083 0.0033 14 0.00052 0.00000 -6.50 0.05 0.2520 0.0013 15 0.00001 0.00001 -6.88 3.10 0.0057 0.0038 16 0.00001 0.00000 -2.66 7.81 0.0058 0.0024 The magnetic center is at X = -55.7 +- 0.3 microns Y = 54.1 +- 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: 04-07-1995 Time: 09:56:56 Magnet Name: 110 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 200.3246 +- 2.01507E-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 0.00048 0.00001 134.85 0.81 0.1758 0.0019 2 0.27344 0.00003 44.95 0.00 100.0000 0.0000 3 0.00018 0.00001 30.55 0.63 0.0660 0.0034 4 0.00006 0.00000 -33.66 2.03 0.0220 0.0015 5 0.00005 0.00000 16.36 0.74 0.0192 0.0018 6 0.00055 0.00000 15.07 0.03 0.2006 0.0014 7 0.00001 0.00000 6.98 18.91 0.0043 0.0009 8 0.00002 0.00000 -0.91 0.74 0.0084 0.0010 9 0.00001 0.00000 -9.22 2.21 0.0050 0.0010 10 0.00084 0.00000 -9.02 0.02 0.3080 0.0013 11 0.00001 0.00000 8.10 5.09 0.0028 0.0007 12 0.00001 0.00001 -0.69 8.97 0.0036 0.0018 13 0.00002 0.00001 -1.63 1.53 0.0091 0.0028 14 0.00070 0.00000 -6.50 0.02 0.2555 0.0013 15 0.00001 0.00001 -2.97 6.00 0.0045 0.0021 16 0.00002 0.00001 -4.22 6.05 0.0079 0.0028 The magnetic center is at X = -55.7 +- 1.0 microns Y = 55.4 +- 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: 04-07-1995 Time: 10:03:13 Magnet Name: 110 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 250.4275 +- 3.834482E-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 0.00057 0.00001 135.34 0.51 0.1688 0.0019 2 0.33839 0.00004 44.95 0.00 100.0000 0.0000 3 0.00022 0.00001 30.88 0.86 0.0641 0.0024 4 0.00006 0.00000 -29.21 0.69 0.0177 0.0014 5 0.00006 0.00000 17.75 1.25 0.0186 0.0008 6 0.00060 0.00001 15.12 0.08 0.1768 0.0022 7 0.00001 0.00001 4.25 18.71 0.0034 0.0015 8 0.00001 0.00001 21.74 0.41 0.0042 0.0019 9 0.00002 0.00001 -9.07 1.61 0.0063 0.0021 10 0.00105 0.00000 -9.07 0.06 0.3111 0.0012 11 0.00001 0.00000 -1.14 13.17 0.0024 0.0004 12 0.00003 0.00001 -0.81 0.71 0.0079 0.0025 13 0.00003 0.00002 -4.21 1.49 0.0099 0.0046 14 0.00086 0.00000 -6.51 0.04 0.2536 0.0012 15 0.00001 0.00001 2.23 5.82 0.0029 0.0015 16 0.00003 0.00001 -0.66 8.53 0.0087 0.0042 The magnetic center is at X = -53.0 +- 0.8 microns Y = 53.6 +- 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: 04-07-1995 Time: 10:09:30 Magnet Name: 110 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 300.415 +- 7.075209E-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 0.00062 0.00001 131.28 0.68 0.1591 0.0025 2 0.39065 0.00002 44.95 0.00 100.0000 0.0000 3 0.00026 0.00000 33.26 0.25 0.0654 0.0010 4 0.00006 0.00001 -25.26 1.47 0.0156 0.0016 5 0.00007 0.00001 16.96 0.88 0.0189 0.0024 6 0.00048 0.00001 15.12 0.16 0.1223 0.0014 7 0.00002 0.00000 7.93 18.76 0.0044 0.0012 8 0.00002 0.00000 -0.50 21.18 0.0056 0.0004 9 0.00002 0.00000 -6.72 1.17 0.0053 0.0010 10 0.00125 0.00000 -9.05 0.05 0.3212 0.0010 11 0.00001 0.00000 3.07 10.49 0.0037 0.0012 12 0.00002 0.00001 -5.75 4.59 0.0043 0.0018 13 0.00004 0.00001 -4.97 0.84 0.0103 0.0031 14 0.00100 0.00000 -6.51 0.01 0.2552 0.0011 15 0.00002 0.00001 3.66 3.80 0.0062 0.0016 16 0.00003 0.00000 -1.31 0.72 0.0086 0.0011 The magnetic center is at X = -53.4 +- 1.0 microns Y = 46.9 +- 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: 04-07-1995 Time: 10:15:46 Magnet Name: 110 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 350.4217 +- 5.02151E-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 0.00065 0.00001 131.14 0.98 0.1526 0.0018 2 0.42721 0.00006 44.95 0.00 100.0000 0.0000 3 0.00028 0.00001 33.48 0.19 0.0651 0.0015 4 0.00007 0.00001 -26.24 1.57 0.0157 0.0018 5 0.00008 0.00001 16.88 0.49 0.0178 0.0023 6 0.00027 0.00001 15.36 0.22 0.0629 0.0024 7 0.00001 0.00000 10.64 14.62 0.0019 0.0006 8 0.00001 0.00000 -19.26 1.69 0.0026 0.0008 9 0.00003 0.00000 -7.68 1.83 0.0060 0.0010 10 0.00142 0.00001 -9.05 0.06 0.3328 0.0022 11 0.00001 0.00001 11.03 2.66 0.0025 0.0017 12 0.00002 0.00001 -7.93 4.10 0.0051 0.0023 13 0.00005 0.00001 -3.56 1.01 0.0112 0.0013 14 0.00108 0.00000 -6.49 0.02 0.2516 0.0006 15 0.00002 0.00001 6.35 2.95 0.0046 0.0015 16 0.00003 0.00001 -0.51 1.18 0.0076 0.0034 The magnetic center is at X = -51.3 +- 1.0 microns Y = 44.8 +- 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)