SLAC Magnetic Measurements Date: 02-28-1995 Time: 14:13:26 Magnet Name (Serial #): 169 Bar Code Number: 262 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: 02-28-1995 Time: 15:00:36 Magnet Name: 169 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 10.00272 +- 6.552445E-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 -100.98 0.13 1.0216 0.0008 2 0.01494 0.00000 46.94 0.00 100.0000 0.0000 3 0.00001 0.00000 43.65 1.10 0.0428 0.0020 4 0.00000 0.00000 31.07 3.22 0.0115 0.0019 5 0.00000 0.00000 19.26 1.67 0.0104 0.0015 6 0.00003 0.00000 17.06 0.01 0.2165 0.0031 7 0.00000 0.00000 12.07 4.80 0.0058 0.0020 8 0.00000 0.00000 0.18 10.66 0.0044 0.0014 9 0.00000 0.00000 7.99 0.37 0.0211 0.0015 10 0.00004 0.00000 -7.03 0.04 0.3008 0.0009 11 0.00000 0.00000 8.64 1.40 0.0040 0.0013 12 0.00000 0.00000 -4.05 3.81 0.0033 0.0010 13 0.00000 0.00000 6.50 0.44 0.0304 0.0007 14 0.00004 0.00000 -4.50 0.07 0.2541 0.0020 15 0.00000 0.00000 -0.60 8.45 0.0034 0.0008 16 0.00000 0.00000 -1.98 5.16 0.0059 0.0017 The magnetic center is at X = 447.9 +- 0.4 microns Y = 86.9 +- 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: 02-28-1995 Time: 15:06:39 Magnet Name: 169 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 25.10505 +- 2.734236E-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 0.00032 0.00000 -110.53 0.08 0.9082 0.0012 2 0.03502 0.00001 46.94 0.00 100.0000 0.0000 3 0.00002 0.00000 31.21 0.53 0.0666 0.0014 4 0.00000 0.00000 42.30 0.78 0.0057 0.0021 5 0.00001 0.00000 20.40 1.40 0.0147 0.0013 6 0.00008 0.00000 17.03 0.06 0.2195 0.0018 7 0.00000 0.00000 7.96 8.63 0.0023 0.0005 8 0.00000 0.00000 -9.61 17.64 0.0046 0.0016 9 0.00001 0.00000 7.92 0.53 0.0213 0.0008 10 0.00011 0.00000 -7.07 0.03 0.3050 0.0016 11 0.00000 0.00000 7.76 3.70 0.0039 0.0012 12 0.00000 0.00000 0.54 1.56 0.0074 0.0033 13 0.00001 0.00000 6.81 0.34 0.0314 0.0051 14 0.00009 0.00000 -4.55 0.07 0.2549 0.0027 15 0.00000 0.00000 -1.32 9.11 0.0033 0.0016 16 0.00000 0.00000 -3.11 5.53 0.0037 0.0019 The magnetic center is at X = 379.9 +- 0.5 microns Y = 142.3 +- 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: 02-28-1995 Time: 15:12:50 Magnet Name: 169 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 50.06503 +- 5.060408E-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 0.00060 0.00000 -114.56 0.11 0.8776 0.0008 2 0.06891 0.00001 46.94 0.00 100.0000 0.0000 3 0.00005 0.00000 28.24 0.39 0.0741 0.0011 4 0.00000 0.00000 -16.46 32.19 0.0023 0.0013 5 0.00001 0.00000 21.46 0.69 0.0148 0.0008 6 0.00015 0.00000 17.03 0.05 0.2225 0.0018 7 0.00000 0.00000 5.66 13.96 0.0025 0.0011 8 0.00000 0.00000 -16.76 1.95 0.0036 0.0002 9 0.00001 0.00000 7.71 0.15 0.0209 0.0007 10 0.00021 0.00000 -7.06 0.02 0.3066 0.0008 11 0.00000 0.00000 10.88 2.15 0.0055 0.0018 12 0.00000 0.00000 -8.46 1.15 0.0057 0.0028 13 0.00002 0.00000 6.58 0.20 0.0327 0.0023 14 0.00018 0.00000 -4.47 0.07 0.2544 0.0019 15 0.00000 0.00000 5.70 9.01 0.0034 0.0005 16 0.00000 0.00000 -1.79 8.31 0.0047 0.0020 The magnetic center is at X = 356.5 +- 0.4 microns Y = 162.9 +- 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: 02-28-1995 Time: 15:19:04 Magnet Name: 169 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 100.0546 +- 7.810075E-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 0.00119 0.00000 -116.18 0.08 0.8635 0.0016 2 0.13748 0.00001 46.94 0.00 100.0000 0.0000 3 0.00010 0.00000 28.24 0.75 0.0762 0.0010 4 0.00001 0.00000 -8.40 29.37 0.0051 0.0031 5 0.00002 0.00000 19.48 1.54 0.0143 0.0012 6 0.00031 0.00000 17.01 0.09 0.2222 0.0016 7 0.00000 0.00000 17.14 2.69 0.0014 0.0010 8 0.00000 0.00000 5.38 10.58 0.0025 0.0013 9 0.00003 0.00000 7.98 0.13 0.0206 0.0010 10 0.00042 0.00000 -7.06 0.02 0.3050 0.0012 11 0.00000 0.00000 6.02 2.11 0.0030 0.0013 12 0.00001 0.00000 -8.16 3.00 0.0041 0.0007 13 0.00004 0.00000 6.54 0.23 0.0323 0.0007 14 0.00035 0.00000 -4.49 0.03 0.2544 0.0027 15 0.00000 0.00000 -3.86 8.87 0.0021 0.0011 16 0.00001 0.00000 -1.03 7.12 0.0037 0.0025 The magnetic center is at X = 346.1 +- 0.7 microns Y = 170.2 +- 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: 02-28-1995 Time: 15:25:18 Magnet Name: 169 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 150.0642 +- 9.734283E-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 0.00000 -116.64 0.04 0.8557 0.0019 2 0.20577 0.00002 46.92 0.00 100.0000 0.0000 3 0.00016 0.00000 28.29 0.16 0.0758 0.0011 4 0.00001 0.00001 -29.75 3.94 0.0045 0.0027 5 0.00003 0.00000 20.61 1.55 0.0135 0.0016 6 0.00044 0.00000 16.94 0.05 0.2145 0.0012 7 0.00000 0.00000 -4.79 7.52 0.0015 0.0004 8 0.00001 0.00000 6.63 6.13 0.0043 0.0014 9 0.00004 0.00000 8.23 0.27 0.0207 0.0010 10 0.00063 0.00000 -7.07 0.05 0.3052 0.0022 11 0.00000 0.00000 7.24 9.63 0.0023 0.0020 12 0.00001 0.00000 -7.23 2.42 0.0050 0.0012 13 0.00006 0.00000 6.57 0.37 0.0296 0.0012 14 0.00052 0.00000 -4.55 0.03 0.2514 0.0021 15 0.00000 0.00000 6.60 7.12 0.0020 0.0004 16 0.00001 0.00000 -7.90 2.36 0.0049 0.0022 The magnetic center is at X = 341.6 +- 0.8 microns Y = 171.4 +- 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: 02-28-1995 Time: 15:31:32 Magnet Name: 169 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 200.3088 +- 2.560114E-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 0.00234 0.00000 -116.62 0.16 0.8565 0.0011 2 0.27351 0.00005 46.92 0.00 100.0000 0.0000 3 0.00020 0.00000 27.74 0.57 0.0743 0.0012 4 0.00005 0.00000 -37.75 1.97 0.0182 0.0016 5 0.00004 0.00001 20.89 1.47 0.0141 0.0025 6 0.00057 0.00000 17.03 0.05 0.2067 0.0010 7 0.00001 0.00000 -1.12 3.67 0.0022 0.0009 8 0.00002 0.00000 1.76 1.97 0.0068 0.0005 9 0.00006 0.00000 7.73 0.33 0.0209 0.0015 10 0.00084 0.00001 -7.08 0.02 0.3085 0.0021 11 0.00001 0.00000 11.11 2.39 0.0034 0.0018 12 0.00001 0.00001 -8.03 3.29 0.0043 0.0021 13 0.00008 0.00000 6.52 0.24 0.0277 0.0010 14 0.00071 0.00001 -4.47 0.04 0.2579 0.0021 15 0.00001 0.00000 -4.69 9.57 0.0020 0.0006 16 0.00002 0.00000 -3.48 7.83 0.0072 0.0011 The magnetic center is at X = 342.0 +- 0.7 microns Y = 171.4 +- 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: 02-28-1995 Time: 15:37:46 Magnet Name: 169 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 250.4048 +- 2.26724E-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 0.00290 0.00001 -116.72 0.16 0.8550 0.0020 2 0.33859 0.00005 46.92 0.00 100.0000 0.0000 3 0.00026 0.00001 27.71 0.51 0.0758 0.0019 4 0.00003 0.00000 -36.82 2.69 0.0100 0.0008 5 0.00004 0.00001 18.92 1.61 0.0131 0.0023 6 0.00061 0.00001 17.03 0.04 0.1801 0.0019 7 0.00001 0.00000 -0.33 4.94 0.0020 0.0010 8 0.00002 0.00000 0.96 20.89 0.0052 0.0005 9 0.00007 0.00000 8.22 0.27 0.0212 0.0008 10 0.00107 0.00000 -7.09 0.03 0.3160 0.0011 11 0.00002 0.00001 6.84 7.87 0.0046 0.0018 12 0.00002 0.00000 0.16 1.36 0.0070 0.0014 13 0.00010 0.00001 6.91 0.37 0.0301 0.0017 14 0.00086 0.00001 -4.50 0.02 0.2527 0.0032 15 0.00002 0.00000 7.83 5.91 0.0045 0.0005 16 0.00002 0.00001 -5.08 8.77 0.0053 0.0031 The magnetic center is at X = 341.1 +- 0.9 microns Y = 171.7 +- 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: 02-28-1995 Time: 15:44:01 Magnet Name: 169 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 300.3865 +- 6.962423E-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 0.00324 0.00000 -115.42 0.12 0.8290 0.0008 2 0.39055 0.00006 46.92 0.00 100.0000 0.0000 3 0.00032 0.00001 31.59 0.36 0.0824 0.0021 4 0.00003 0.00001 -27.08 2.91 0.0078 0.0017 5 0.00006 0.00000 17.13 0.78 0.0143 0.0012 6 0.00051 0.00001 17.04 0.11 0.1297 0.0014 7 0.00001 0.00000 -0.37 2.19 0.0030 0.0010 8 0.00003 0.00001 -9.30 18.14 0.0071 0.0019 9 0.00008 0.00000 8.06 0.31 0.0216 0.0010 10 0.00126 0.00001 -7.07 0.01 0.3227 0.0021 11 0.00002 0.00001 9.91 2.02 0.0051 0.0031 12 0.00002 0.00000 -7.70 1.70 0.0043 0.0005 13 0.00012 0.00001 6.58 0.52 0.0310 0.0019 14 0.00099 0.00001 -4.53 0.04 0.2543 0.0030 15 0.00001 0.00001 4.37 3.41 0.0028 0.0014 16 0.00002 0.00001 2.54 2.69 0.0056 0.0027 The magnetic center is at X = 334.4 +- 0.5 microns Y = 158.9 +- 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: 02-28-1995 Time: 15:50:15 Magnet Name: 169 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 350.3854 +- 7.218553E-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 0.00348 0.00000 -114.67 0.11 0.8140 0.0009 2 0.42705 0.00004 46.92 0.00 100.0000 0.0000 3 0.00037 0.00001 33.68 0.22 0.0872 0.0012 4 0.00004 0.00001 -29.04 2.15 0.0097 0.0014 5 0.00008 0.00001 16.85 0.95 0.0195 0.0015 6 0.00031 0.00000 17.30 0.11 0.0728 0.0007 7 0.00002 0.00001 -1.60 3.70 0.0041 0.0013 8 0.00001 0.00001 -15.77 3.84 0.0034 0.0018 9 0.00009 0.00001 8.29 0.36 0.0214 0.0014 10 0.00142 0.00001 -7.08 0.04 0.3322 0.0014 11 0.00002 0.00001 9.17 1.44 0.0044 0.0016 12 0.00003 0.00001 -8.81 2.00 0.0074 0.0018 13 0.00013 0.00001 6.61 0.28 0.0305 0.0028 14 0.00107 0.00001 -4.50 0.06 0.2499 0.0030 15 0.00001 0.00000 4.60 8.35 0.0032 0.0011 16 0.00003 0.00001 0.56 3.44 0.0070 0.0024 The magnetic center is at X = 330.4 +- 0.5 microns Y = 151.8 +- 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 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)