SLAC Magnetic Measurements Date: 03-28-1995 Time: 10:34:02 Magnet Name (Serial #): 147 Bar Code Number: 326 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: 03-28-1995 Time: 11:21:11 Magnet Name: 147 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 10.00167 +- 3.459781E-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 10.93 0.44 0.5593 0.0065 2 0.01485 0.00000 44.95 0.00 100.0000 0.0000 3 0.00001 0.00000 55.19 0.81 0.0806 0.0046 4 0.00001 0.00000 17.59 0.16 0.0447 0.0016 5 0.00000 0.00000 2.10 0.80 0.0272 0.0029 6 0.00003 0.00000 15.00 0.10 0.2173 0.0018 7 0.00000 0.00000 5.77 1.68 0.0083 0.0010 8 0.00000 0.00000 19.12 1.12 0.0071 0.0007 9 0.00000 0.00000 -14.95 1.35 0.0105 0.0010 10 0.00005 0.00000 -9.13 0.08 0.3051 0.0013 11 0.00000 0.00000 -7.00 13.31 0.0027 0.0002 12 0.00000 0.00000 10.73 5.26 0.0097 0.0020 13 0.00000 0.00000 -9.29 0.90 0.0121 0.0028 14 0.00004 0.00000 -6.44 0.07 0.2645 0.0040 15 0.00000 0.00000 -4.47 7.95 0.0065 0.0017 16 0.00000 0.00000 3.45 1.99 0.0051 0.0017 The magnetic center is at X = -47.4 +- 1.9 microns Y = -245.3 +- 2.8 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: 03-28-1995 Time: 11:27:18 Magnet Name: 147 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 25.10479 +- 1.860252E-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 36.92 0.52 0.4261 0.0068 2 0.03493 0.00000 44.95 0.00 100.0000 0.0000 3 0.00002 0.00000 31.06 1.81 0.0510 0.0022 4 0.00001 0.00000 19.52 1.21 0.0387 0.0009 5 0.00001 0.00000 4.65 1.33 0.0211 0.0024 6 0.00008 0.00000 14.95 0.05 0.2210 0.0016 7 0.00000 0.00000 11.21 3.13 0.0045 0.0023 8 0.00000 0.00000 21.28 0.63 0.0136 0.0010 9 0.00000 0.00000 -14.53 1.49 0.0100 0.0019 10 0.00011 0.00000 -9.12 0.02 0.3058 0.0024 11 0.00000 0.00000 7.55 13.41 0.0040 0.0009 12 0.00000 0.00000 2.84 6.08 0.0072 0.0032 13 0.00000 0.00000 -10.03 0.71 0.0139 0.0011 14 0.00009 0.00000 -6.42 0.03 0.2661 0.0026 15 0.00000 0.00000 -9.15 1.50 0.0079 0.0010 16 0.00000 0.00000 2.01 2.24 0.0054 0.0030 The magnetic center is at X = -114.3 +- 2.3 microns Y = -152.2 +- 2.7 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: 03-28-1995 Time: 11:33:29 Magnet Name: 147 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 50.06737 +- 5.825256E-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 46.75 0.45 0.4132 0.0060 2 0.06881 0.00001 44.95 0.00 100.0000 0.0000 3 0.00004 0.00000 23.99 1.60 0.0588 0.0040 4 0.00003 0.00000 18.00 0.87 0.0391 0.0018 5 0.00001 0.00000 5.55 1.67 0.0196 0.0015 6 0.00015 0.00000 14.96 0.05 0.2202 0.0017 7 0.00000 0.00000 9.63 2.41 0.0041 0.0014 8 0.00000 0.00000 18.20 0.25 0.0057 0.0011 9 0.00001 0.00000 -15.06 0.82 0.0108 0.0014 10 0.00021 0.00000 -9.15 0.03 0.3064 0.0023 11 0.00000 0.00000 13.66 0.94 0.0028 0.0011 12 0.00001 0.00000 6.45 12.34 0.0140 0.0035 13 0.00001 0.00000 -10.64 0.21 0.0129 0.0010 14 0.00018 0.00000 -6.44 0.06 0.2611 0.0027 15 0.00001 0.00000 -8.51 1.50 0.0092 0.0033 16 0.00001 0.00000 6.36 2.14 0.0084 0.0061 The magnetic center is at X = -134.4 +- 2.2 microns Y = -126.5 +- 2.1 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: 03-28-1995 Time: 11:39:45 Magnet Name: 147 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 100.0612 +- 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 0.00057 0.00001 49.58 0.92 0.4141 0.0055 2 0.13729 0.00004 44.95 0.00 100.0000 0.0000 3 0.00008 0.00000 23.01 2.23 0.0552 0.0030 4 0.00005 0.00000 18.15 0.44 0.0386 0.0017 5 0.00003 0.00000 5.63 1.14 0.0199 0.0021 6 0.00030 0.00000 14.97 0.04 0.2206 0.0019 7 0.00001 0.00000 12.20 0.86 0.0041 0.0003 8 0.00001 0.00000 18.88 1.90 0.0050 0.0002 9 0.00001 0.00000 -14.85 1.26 0.0094 0.0011 10 0.00042 0.00001 -9.16 0.05 0.3063 0.0039 11 0.00000 0.00000 -1.45 13.21 0.0028 0.0018 12 0.00002 0.00001 10.64 2.40 0.0148 0.0048 13 0.00001 0.00000 -10.75 1.70 0.0108 0.0023 14 0.00037 0.00000 -6.41 0.10 0.2666 0.0025 15 0.00001 0.00001 -8.30 2.40 0.0073 0.0056 16 0.00001 0.00000 1.12 2.95 0.0087 0.0021 The magnetic center is at X = -140.8 +- 2.7 microns Y = -119.9 +- 2.8 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: 03-28-1995 Time: 11:46:00 Magnet Name: 147 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 150.0748 +- 3.967285E-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 0.00086 0.00000 50.50 0.76 0.4181 0.0020 2 0.20554 0.00003 44.93 0.00 100.0000 0.0000 3 0.00011 0.00001 23.59 1.05 0.0556 0.0053 4 0.00008 0.00000 18.30 0.21 0.0401 0.0019 5 0.00004 0.00001 5.95 0.69 0.0192 0.0030 6 0.00044 0.00000 14.95 0.08 0.2123 0.0008 7 0.00001 0.00000 9.02 2.19 0.0059 0.0010 8 0.00001 0.00000 7.71 17.06 0.0047 0.0008 9 0.00002 0.00001 -15.09 1.51 0.0091 0.0025 10 0.00064 0.00000 -9.15 0.02 0.3111 0.0006 11 0.00001 0.00000 -1.51 14.58 0.0025 0.0009 12 0.00002 0.00001 12.86 0.72 0.0117 0.0025 13 0.00002 0.00000 -9.37 1.44 0.0102 0.0014 14 0.00054 0.00001 -6.44 0.03 0.2613 0.0035 15 0.00002 0.00001 -10.51 0.84 0.0092 0.0025 16 0.00002 0.00001 1.63 4.91 0.0084 0.0035 The magnetic center is at X = -144.1 +- 1.7 microns Y = -118.8 +- 2.0 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: 03-28-1995 Time: 11:52:15 Magnet Name: 147 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 200.3216 +- 3.185215E-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 0.00114 0.00001 51.49 0.68 0.4174 0.0043 2 0.27325 0.00003 44.93 0.00 100.0000 0.0000 3 0.00015 0.00001 21.56 1.23 0.0556 0.0031 4 0.00010 0.00000 23.54 0.50 0.0384 0.0015 5 0.00005 0.00000 6.58 1.53 0.0200 0.0016 6 0.00056 0.00000 14.97 0.08 0.2055 0.0007 7 0.00002 0.00000 10.27 1.46 0.0057 0.0014 8 0.00001 0.00000 5.20 1.37 0.0050 0.0012 9 0.00002 0.00000 -14.80 1.05 0.0086 0.0012 10 0.00085 0.00001 -9.18 0.04 0.3128 0.0021 11 0.00001 0.00000 6.18 12.31 0.0029 0.0003 12 0.00003 0.00001 13.57 1.44 0.0099 0.0052 13 0.00003 0.00000 -9.56 0.84 0.0125 0.0013 14 0.00072 0.00000 -6.49 0.08 0.2635 0.0016 15 0.00003 0.00001 -8.51 1.01 0.0096 0.0020 16 0.00002 0.00001 7.61 2.05 0.0068 0.0033 The magnetic center is at X = -145.9 +- 2.0 microns Y = -116.1 +- 2.1 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: 03-28-1995 Time: 11:58:31 Magnet Name: 147 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 250.4217 +- 4.537406E-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 0.00140 0.00000 51.41 0.36 0.4144 0.0013 2 0.33813 0.00001 44.93 0.00 100.0000 0.0000 3 0.00019 0.00000 22.74 0.68 0.0549 0.0011 4 0.00013 0.00000 22.06 0.35 0.0391 0.0012 5 0.00007 0.00001 6.08 2.25 0.0197 0.0023 6 0.00062 0.00001 15.06 0.08 0.1845 0.0015 7 0.00002 0.00000 11.40 2.32 0.0051 0.0008 8 0.00004 0.00001 19.54 0.92 0.0109 0.0015 9 0.00003 0.00001 -14.36 0.85 0.0087 0.0019 10 0.00105 0.00001 -9.17 0.03 0.3114 0.0018 11 0.00001 0.00000 14.07 1.43 0.0037 0.0013 12 0.00003 0.00001 9.76 2.51 0.0084 0.0041 13 0.00003 0.00000 -9.13 0.61 0.0103 0.0015 14 0.00088 0.00002 -6.43 0.05 0.2614 0.0051 15 0.00003 0.00001 -9.31 1.00 0.0077 0.0017 16 0.00002 0.00001 3.68 5.61 0.0048 0.0029 The magnetic center is at X = -144.7 +- 0.9 microns Y = -115.5 +- 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: 03-28-1995 Time: 12:04:47 Magnet Name: 147 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 300.4079 +- 5.357987E-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 0.00169 0.00003 50.05 0.60 0.4338 0.0072 2 0.39012 0.00011 44.93 0.00 100.0000 0.0000 3 0.00022 0.00001 26.58 2.46 0.0553 0.0032 4 0.00015 0.00001 20.04 0.90 0.0381 0.0014 5 0.00008 0.00001 5.40 0.50 0.0200 0.0027 6 0.00052 0.00001 15.11 0.15 0.1336 0.0019 7 0.00003 0.00000 9.21 2.29 0.0067 0.0010 8 0.00004 0.00001 20.29 0.30 0.0106 0.0015 9 0.00003 0.00000 -14.03 1.46 0.0077 0.0011 10 0.00126 0.00001 -9.15 0.07 0.3235 0.0033 11 0.00001 0.00001 4.69 11.86 0.0026 0.0013 12 0.00004 0.00001 8.01 3.83 0.0091 0.0035 13 0.00004 0.00001 -10.42 0.89 0.0113 0.0025 14 0.00102 0.00002 -6.48 0.04 0.2619 0.0061 15 0.00003 0.00001 -9.79 1.16 0.0083 0.0034 16 0.00003 0.00002 2.31 1.74 0.0074 0.0045 The magnetic center is at X = -148.5 +- 2.8 microns Y = -124.4 +- 2.6 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: 03-28-1995 Time: 12:11:02 Magnet Name: 147 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 350.4147 +- 1.555349E-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 0.00191 0.00002 48.39 0.84 0.4477 0.0041 2 0.42661 0.00010 44.93 0.00 100.0000 0.0000 3 0.00024 0.00002 30.82 1.59 0.0552 0.0057 4 0.00016 0.00001 20.75 0.58 0.0367 0.0014 5 0.00008 0.00001 6.29 0.84 0.0195 0.0015 6 0.00033 0.00001 15.13 0.31 0.0764 0.0016 7 0.00002 0.00000 9.19 1.24 0.0054 0.0005 8 0.00004 0.00000 20.03 0.90 0.0083 0.0003 9 0.00004 0.00000 -14.55 0.92 0.0086 0.0010 10 0.00144 0.00001 -9.20 0.03 0.3365 0.0026 11 0.00001 0.00000 5.62 12.34 0.0029 0.0008 12 0.00004 0.00002 5.85 12.06 0.0102 0.0051 13 0.00004 0.00001 -9.75 0.54 0.0096 0.0025 14 0.00112 0.00001 -6.43 0.06 0.2635 0.0027 15 0.00004 0.00001 -4.44 7.36 0.0083 0.0033 16 0.00005 0.00001 1.97 2.17 0.0117 0.0021 The magnetic center is at X = -149.5 +- 2.4 microns Y = -132.8 +- 2.5 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 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)