SLAC Magnetic Measurements Date: 03-07-1995 Time: 10:06:39 Magnet Name (Serial #): 150 Bar Code Number: 481 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: 03-07-1995 Time: 10:54:04 Magnet Name: 150 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 9.998964 +- 3.521028E-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 -163.28 0.68 0.2976 0.0034 2 0.01482 0.00000 44.94 0.00 100.0000 0.0000 3 0.00002 0.00000 24.42 0.28 0.1277 0.0048 4 0.00000 0.00000 21.78 0.39 0.0269 0.0011 5 0.00000 0.00000 19.64 1.11 0.0207 0.0013 6 0.00003 0.00000 15.06 0.13 0.2120 0.0026 7 0.00000 0.00000 15.75 2.43 0.0052 0.0010 8 0.00000 0.00000 14.89 6.75 0.0019 0.0009 9 0.00000 0.00000 0.49 2.15 0.0067 0.0009 10 0.00005 0.00000 -9.06 0.03 0.3051 0.0011 11 0.00000 0.00000 5.62 4.12 0.0015 0.0009 12 0.00000 0.00000 -4.26 2.58 0.0036 0.0008 13 0.00000 0.00000 -1.26 1.80 0.0109 0.0026 14 0.00004 0.00000 -6.48 0.02 0.2602 0.0030 15 0.00000 0.00000 -6.22 3.12 0.0054 0.0048 16 0.00000 0.00000 3.95 6.20 0.0056 0.0030 The magnetic center is at X = 38.2 +- 1.6 microns Y = 127.3 +- 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: 03-07-1995 Time: 11:00:09 Magnet Name: 150 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 25.09797 +- 3.730415E-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 0.00014 0.00003 176.82 0.43 0.3409 0.0054 2 0.04070 0.01002 44.93 0.00 100.0000 0.0000 3 0.00005 0.00001 25.11 0.85 0.1265 0.0029 4 0.00001 0.00000 24.29 1.36 0.0267 0.0016 5 0.00001 0.00000 18.85 0.98 0.0211 0.0010 6 0.00009 0.00002 15.10 0.05 0.2167 0.0008 7 0.00000 0.00000 16.06 2.55 0.0082 0.0016 8 0.00000 0.00000 20.53 0.68 0.0077 0.0018 9 0.00000 0.00000 0.72 1.01 0.0076 0.0012 10 0.00012 0.00003 -9.05 0.03 0.3038 0.0027 11 0.00000 0.00000 7.38 4.08 0.0023 0.0011 12 0.00000 0.00000 0.24 1.62 0.0087 0.0019 13 0.00000 0.00000 -2.09 0.90 0.0083 0.0019 14 0.00010 0.00003 -6.48 0.05 0.2553 0.0024 15 0.00000 0.00000 -1.52 1.24 0.0105 0.0042 16 0.00000 0.00000 0.48 2.29 0.0064 0.0022 The magnetic center is at X = -8.4 +- 3.0 microns Y = 151.5 +- 51.0 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: 03-07-1995 Time: 13:05:47 Magnet Name: 150 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 50.06021 +- 1.072076E-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 0.00025 0.00000 173.03 0.23 0.3603 0.0046 2 0.06886 0.00012 44.95 0.00 100.0000 0.0000 3 0.00010 0.00000 25.52 0.38 0.1383 0.0017 4 0.00002 0.00000 23.23 0.76 0.0265 0.0017 5 0.00001 0.00000 19.43 1.21 0.0196 0.0009 6 0.00015 0.00000 15.14 0.03 0.2168 0.0008 7 0.00000 0.00000 12.90 0.96 0.0050 0.0009 8 0.00000 0.00000 3.53 3.84 0.0019 0.0007 9 0.00001 0.00000 1.77 0.83 0.0077 0.0006 10 0.00021 0.00000 -9.05 0.03 0.3040 0.0012 11 0.00000 0.00000 4.88 6.40 0.0013 0.0004 12 0.00000 0.00000 5.41 6.14 0.0019 0.0007 13 0.00001 0.00000 -1.04 0.61 0.0093 0.0009 14 0.00018 0.00000 -6.46 0.01 0.2545 0.0011 15 0.00000 0.00000 -3.06 0.83 0.0049 0.0012 16 0.00000 0.00000 0.38 9.89 0.0048 0.0008 The magnetic center is at X = -19.5 +- 0.7 microns Y = 159.7 +- 1.8 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: 03-07-1995 Time: 13:12:02 Magnet Name: 150 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 100.0551 +- 1.109802E-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 0.00052 0.00000 169.58 0.27 0.3770 0.0006 2 0.13736 0.00003 44.95 0.00 100.0000 0.0000 3 0.00019 0.00000 25.62 0.09 0.1381 0.0010 4 0.00004 0.00000 24.10 1.18 0.0256 0.0020 5 0.00003 0.00000 19.67 0.74 0.0188 0.0012 6 0.00030 0.00000 15.15 0.03 0.2173 0.0010 7 0.00001 0.00000 12.12 1.12 0.0043 0.0008 8 0.00000 0.00000 2.69 7.94 0.0015 0.0009 9 0.00001 0.00000 1.36 0.82 0.0084 0.0009 10 0.00042 0.00000 -9.06 0.04 0.3066 0.0015 11 0.00000 0.00000 6.43 3.37 0.0025 0.0013 12 0.00000 0.00000 -3.23 8.48 0.0027 0.0012 13 0.00001 0.00000 0.33 0.78 0.0088 0.0016 14 0.00035 0.00000 -6.46 0.01 0.2554 0.0011 15 0.00001 0.00000 -3.94 0.74 0.0074 0.0011 16 0.00001 0.00000 0.02 10.29 0.0042 0.0009 The magnetic center is at X = -30.4 +- 0.8 microns Y = 165.6 +- 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: 03-07-1995 Time: 13:18:15 Magnet Name: 150 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 150.065 +- 7.330971E-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 0.00080 0.00001 170.29 0.24 0.3869 0.0024 2 0.20564 0.00004 44.92 0.00 100.0000 0.0000 3 0.00026 0.00000 24.26 0.24 0.1262 0.0015 4 0.00005 0.00000 23.03 1.30 0.0249 0.0017 5 0.00004 0.00000 20.44 0.44 0.0195 0.0018 6 0.00043 0.00000 15.11 0.02 0.2095 0.0009 7 0.00001 0.00000 11.54 2.98 0.0035 0.0018 8 0.00000 0.00000 5.35 7.75 0.0019 0.0010 9 0.00002 0.00000 1.40 1.22 0.0090 0.0013 10 0.00064 0.00000 -9.09 0.03 0.3115 0.0022 11 0.00000 0.00000 3.79 6.24 0.0024 0.0007 12 0.00001 0.00000 -12.29 2.56 0.0072 0.0023 13 0.00002 0.00000 -0.55 0.41 0.0082 0.0024 14 0.00052 0.00000 -6.45 0.04 0.2549 0.0010 15 0.00001 0.00000 0.19 5.98 0.0046 0.0013 16 0.00002 0.00001 5.25 5.15 0.0079 0.0044 The magnetic center is at X = -29.1 +- 0.7 microns Y = 170.3 +- 1.1 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: 03-07-1995 Time: 13:24:29 Magnet Name: 150 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 200.3078 +- 6.196271E-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 0.00107 0.00000 169.09 0.17 0.3916 0.0011 2 0.27340 0.00005 44.92 0.00 100.0000 0.0000 3 0.00035 0.00000 24.67 0.15 0.1291 0.0009 4 0.00008 0.00000 31.27 1.49 0.0293 0.0017 5 0.00006 0.00000 20.33 1.58 0.0211 0.0008 6 0.00055 0.00000 15.11 0.04 0.2006 0.0007 7 0.00001 0.00000 12.44 3.28 0.0041 0.0015 8 0.00002 0.00001 -1.34 0.91 0.0076 0.0029 9 0.00002 0.00000 1.01 1.26 0.0073 0.0006 10 0.00086 0.00001 -9.08 0.08 0.3130 0.0019 11 0.00000 0.00000 -7.74 10.29 0.0017 0.0008 12 0.00001 0.00001 -9.05 4.14 0.0054 0.0033 13 0.00003 0.00001 -1.03 0.50 0.0099 0.0022 14 0.00070 0.00000 -6.44 0.03 0.2543 0.0005 15 0.00002 0.00001 -3.62 3.03 0.0064 0.0030 16 0.00002 0.00001 -8.76 2.31 0.0067 0.0022 The magnetic center is at X = -33.1 +- 0.5 microns Y = 171.7 +- 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: 03-07-1995 Time: 13:30:44 Magnet Name: 150 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 250.4059 +- 2.94103E-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 0.00131 0.00001 167.04 0.08 0.3871 0.0021 2 0.33828 0.00006 44.92 0.00 100.0000 0.0000 3 0.00045 0.00000 25.26 0.18 0.1340 0.0005 4 0.00009 0.00001 28.20 0.86 0.0270 0.0024 5 0.00007 0.00001 19.81 0.63 0.0197 0.0017 6 0.00060 0.00000 15.25 0.07 0.1772 0.0007 7 0.00001 0.00000 8.69 3.22 0.0020 0.0011 8 0.00003 0.00000 11.28 18.60 0.0086 0.0010 9 0.00003 0.00000 0.10 0.08 0.0087 0.0009 10 0.00107 0.00001 -9.08 0.04 0.3149 0.0019 11 0.00001 0.00000 7.44 6.12 0.0035 0.0012 12 0.00003 0.00001 -2.06 2.31 0.0080 0.0038 13 0.00004 0.00000 -1.19 0.90 0.0113 0.0009 14 0.00086 0.00000 -6.49 0.03 0.2541 0.0007 15 0.00002 0.00001 -2.98 4.55 0.0070 0.0038 16 0.00003 0.00001 1.79 4.91 0.0080 0.0030 The magnetic center is at X = -38.8 +- 0.3 microns Y = 168.5 +- 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: 03-07-1995 Time: 13:36:58 Magnet Name: 150 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 300.3884 +- 3.674803E-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 0.00149 0.00001 166.60 0.13 0.3823 0.0016 2 0.38990 0.00009 44.92 0.00 100.0000 0.0000 3 0.00052 0.00000 25.54 0.22 0.1332 0.0008 4 0.00009 0.00000 25.53 1.36 0.0231 0.0011 5 0.00007 0.00001 19.44 1.58 0.0180 0.0014 6 0.00049 0.00000 15.34 0.09 0.1257 0.0008 7 0.00001 0.00000 6.88 7.18 0.0015 0.0008 8 0.00002 0.00000 -9.08 18.06 0.0049 0.0007 9 0.00004 0.00001 0.17 0.65 0.0099 0.0013 10 0.00128 0.00001 -9.07 0.04 0.3276 0.0034 11 0.00001 0.00000 2.81 4.25 0.0021 0.0008 12 0.00002 0.00001 -3.83 2.90 0.0058 0.0023 13 0.00004 0.00000 -1.08 1.72 0.0098 0.0005 14 0.00100 0.00001 -6.47 0.03 0.2556 0.0018 15 0.00002 0.00001 -1.29 2.40 0.0060 0.0018 16 0.00002 0.00000 -1.35 1.86 0.0064 0.0008 The magnetic center is at X = -39.6 +- 0.4 microns Y = 166.1 +- 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: 03-07-1995 Time: 13:43:13 Magnet Name: 150 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 350.391 +- 9.566908E-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 0.00161 0.00000 166.21 0.28 0.3768 0.0009 2 0.42611 0.00005 44.92 0.00 100.0000 0.0000 3 0.00056 0.00001 25.89 0.28 0.1317 0.0029 4 0.00010 0.00001 26.13 0.69 0.0228 0.0017 5 0.00008 0.00001 19.54 0.88 0.0178 0.0025 6 0.00029 0.00001 15.56 0.11 0.0688 0.0018 7 0.00001 0.00001 -8.50 16.36 0.0025 0.0015 8 0.00002 0.00000 -20.03 1.58 0.0052 0.0005 9 0.00004 0.00001 1.41 0.44 0.0083 0.0020 10 0.00144 0.00001 -9.04 0.02 0.3379 0.0024 11 0.00001 0.00000 8.93 4.92 0.0031 0.0007 12 0.00002 0.00001 -9.45 2.44 0.0053 0.0024 13 0.00004 0.00001 -0.94 1.07 0.0086 0.0016 14 0.00107 0.00001 -6.46 0.01 0.2521 0.0025 15 0.00003 0.00001 -3.17 3.09 0.0068 0.0023 16 0.00004 0.00002 -4.64 4.28 0.0092 0.0041 The magnetic center is at X = -40.1 +- 0.8 microns Y = 163.4 +- 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 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)