SLAC Magnetic Measurements Date: 03-27-1995 Time: 10:19:22 Magnet Name (Serial #): 103 Bar Code Number: 454 Project: PEP II High Energy Ring Quadrupoles Test Stand: IR8, Q1 Measurement Coil: # 2 Operator: bmd Run Number: 3 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: 03-27-1995 Time: 11:06:53 Magnet Name: 103 Run Number: 3 FIELD HARMONICS Magnet Current, Imag = 9.998446 +- 3.815487E-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 0.00006 0.00000 -140.38 0.83 0.4107 0.0075 2 0.01485 0.00000 44.97 0.00 100.0000 0.0000 3 0.00001 0.00000 21.48 2.09 0.0626 0.0067 4 0.00000 0.00000 30.65 2.03 0.0115 0.0023 5 0.00000 0.00000 12.72 1.78 0.0175 0.0020 6 0.00003 0.00000 15.04 0.07 0.2193 0.0004 7 0.00000 0.00000 10.90 2.66 0.0054 0.0011 8 0.00000 0.00000 10.27 15.94 0.0020 0.0011 9 0.00000 0.00000 0.77 1.63 0.0118 0.0044 10 0.00004 0.00000 -9.07 0.02 0.3024 0.0010 11 0.00000 0.00000 6.93 8.00 0.0026 0.0010 12 0.00000 0.00000 -13.22 0.36 0.0057 0.0031 13 0.00000 0.00000 0.35 2.02 0.0105 0.0064 14 0.00004 0.00000 -6.40 0.01 0.2571 0.0033 15 0.00000 0.00000 -4.21 0.47 0.0140 0.0036 16 0.00000 0.00000 -1.47 5.75 0.0047 0.0016 The magnetic center is at X = 117.0 +- 3.0 microns Y = 141.3 +- 3.1 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: 03-27-1995 Time: 11:12:59 Magnet Name: 103 Run Number: 3 FIELD HARMONICS Magnet Current, Imag = 25.09838 +- 3.792004E-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 0.00000 -156.09 0.83 0.4096 0.0019 2 0.03502 0.00001 44.97 0.00 100.0000 0.0000 3 0.00002 0.00000 19.42 1.18 0.0536 0.0056 4 0.00000 0.00000 41.36 1.74 0.0127 0.0015 5 0.00001 0.00000 12.87 2.46 0.0156 0.0015 6 0.00008 0.00000 15.00 0.07 0.2246 0.0017 7 0.00000 0.00000 10.11 1.62 0.0067 0.0003 8 0.00000 0.00000 -0.21 21.25 0.0109 0.0010 9 0.00000 0.00000 1.24 1.77 0.0120 0.0054 10 0.00011 0.00000 -9.06 0.02 0.3015 0.0027 11 0.00000 0.00000 -2.90 3.32 0.0036 0.0010 12 0.00000 0.00000 -1.58 5.21 0.0031 0.0023 13 0.00001 0.00000 0.28 0.24 0.0235 0.0039 14 0.00009 0.00000 -6.42 0.03 0.2564 0.0017 15 0.00000 0.00000 -8.69 1.26 0.0099 0.0018 16 0.00000 0.00000 2.96 2.12 0.0087 0.0019 The magnetic center is at X = 74.2 +- 2.5 microns Y = 167.3 +- 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: 03-27-1995 Time: 11:19:11 Magnet Name: 103 Run Number: 3 FIELD HARMONICS Magnet Current, Imag = 50.06197 +- 6.251886E-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 0.00029 0.00000 -162.39 0.54 0.4212 0.0061 2 0.06902 0.00002 44.97 0.00 100.0000 0.0000 3 0.00004 0.00000 18.50 2.35 0.0527 0.0037 4 0.00000 0.00000 20.46 36.23 0.0065 0.0022 5 0.00001 0.00000 12.98 1.67 0.0182 0.0024 6 0.00016 0.00000 15.00 0.06 0.2253 0.0013 7 0.00000 0.00000 10.74 2.48 0.0061 0.0010 8 0.00000 0.00000 1.34 17.50 0.0028 0.0009 9 0.00001 0.00000 0.53 0.73 0.0137 0.0029 10 0.00021 0.00000 -9.08 0.03 0.3041 0.0013 11 0.00000 0.00000 -3.49 5.31 0.0031 0.0014 12 0.00000 0.00000 0.42 13.33 0.0065 0.0006 13 0.00002 0.00000 0.75 1.28 0.0246 0.0039 14 0.00017 0.00000 -6.43 0.02 0.2528 0.0014 15 0.00001 0.00000 -3.02 8.19 0.0134 0.0020 16 0.00001 0.00000 1.46 6.15 0.0104 0.0047 The magnetic center is at X = 56.9 +- 1.9 microns Y = 179.3 +- 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: 03-27-1995 Time: 11:25:26 Magnet Name: 103 Run Number: 3 FIELD HARMONICS Magnet Current, Imag = 100.0573 +- 5.212753E-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 0.00059 0.00001 -164.93 0.70 0.4266 0.0056 2 0.13773 0.00002 44.97 0.00 100.0000 0.0000 3 0.00007 0.00001 18.30 2.02 0.0512 0.0039 4 0.00001 0.00000 0.36 40.93 0.0062 0.0010 5 0.00002 0.00000 12.22 1.87 0.0179 0.0019 6 0.00031 0.00000 15.02 0.06 0.2254 0.0014 7 0.00001 0.00000 8.59 1.49 0.0065 0.0008 8 0.00000 0.00000 10.30 18.49 0.0026 0.0007 9 0.00002 0.00000 2.30 1.46 0.0117 0.0017 10 0.00042 0.00000 -9.08 0.02 0.3054 0.0010 11 0.00000 0.00000 -2.05 1.30 0.0031 0.0013 12 0.00001 0.00000 13.33 1.73 0.0051 0.0022 13 0.00003 0.00000 0.24 0.49 0.0200 0.0034 14 0.00035 0.00000 -6.42 0.04 0.2558 0.0007 15 0.00002 0.00000 -2.66 8.40 0.0119 0.0020 16 0.00000 0.00000 0.52 4.55 0.0035 0.0007 The magnetic center is at X = 49.5 +- 2.3 microns Y = 184.0 +- 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 Date: 03-27-1995 Time: 11:31:41 Magnet Name: 103 Run Number: 3 FIELD HARMONICS Magnet Current, Imag = 150.0725 +- 5.925933E-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 0.00088 0.00001 -165.13 0.58 0.4247 0.0059 2 0.20613 0.00004 44.95 0.00 100.0000 0.0000 3 0.00010 0.00002 19.29 0.93 0.0472 0.0077 4 0.00001 0.00001 3.96 38.93 0.0055 0.0025 5 0.00004 0.00000 12.54 1.71 0.0179 0.0015 6 0.00045 0.00000 15.04 0.14 0.2167 0.0010 7 0.00001 0.00000 9.84 1.10 0.0060 0.0002 8 0.00001 0.00000 -9.83 18.07 0.0034 0.0013 9 0.00003 0.00000 2.79 0.92 0.0143 0.0024 10 0.00063 0.00000 -9.12 0.03 0.3080 0.0014 11 0.00001 0.00000 -3.53 2.64 0.0041 0.0009 12 0.00002 0.00000 0.01 14.06 0.0077 0.0007 13 0.00004 0.00001 0.18 0.94 0.0211 0.0048 14 0.00053 0.00000 -6.49 0.01 0.2566 0.0020 15 0.00002 0.00001 -6.54 2.08 0.0101 0.0032 16 0.00001 0.00000 -2.78 8.02 0.0051 0.0020 The magnetic center is at X = 48.7 +- 2.0 microns Y = 183.3 +- 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: 03-27-1995 Time: 11:37:57 Magnet Name: 103 Run Number: 3 FIELD HARMONICS Magnet Current, Imag = 200.3162 +- 2.437827E-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 0.00118 0.00001 -164.39 0.48 0.4290 0.0053 2 0.27408 0.00006 44.95 0.00 100.0000 0.0000 3 0.00013 0.00002 19.06 1.38 0.0461 0.0067 4 0.00006 0.00001 0.27 44.26 0.0208 0.0026 5 0.00005 0.00001 13.36 1.41 0.0174 0.0023 6 0.00057 0.00000 15.01 0.06 0.2078 0.0006 7 0.00002 0.00000 10.95 1.13 0.0069 0.0010 8 0.00001 0.00000 0.99 2.23 0.0049 0.0009 9 0.00004 0.00001 2.37 0.40 0.0128 0.0024 10 0.00085 0.00000 -9.11 0.03 0.3098 0.0013 11 0.00001 0.00000 7.53 4.50 0.0031 0.0018 12 0.00001 0.00000 6.82 10.76 0.0042 0.0003 13 0.00005 0.00001 2.75 1.08 0.0178 0.0049 14 0.00070 0.00000 -6.48 0.02 0.2538 0.0013 15 0.00005 0.00001 -6.46 1.13 0.0170 0.0037 16 0.00002 0.00001 7.59 1.37 0.0091 0.0031 The magnetic center is at X = 51.5 +- 1.7 microns Y = 184.5 +- 2.3 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: 03-27-1995 Time: 11:44:14 Magnet Name: 103 Run Number: 3 FIELD HARMONICS Magnet Current, Imag = 250.4166 +- 1.061802E-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 0.00151 0.00001 -164.96 0.16 0.4439 0.0027 2 0.33920 0.00003 44.95 0.00 100.0000 0.0000 3 0.00017 0.00001 14.53 1.33 0.0506 0.0031 4 0.00004 0.00001 1.29 42.64 0.0106 0.0019 5 0.00006 0.00001 13.03 1.76 0.0179 0.0031 6 0.00062 0.00000 14.99 0.07 0.1836 0.0010 7 0.00002 0.00000 9.20 1.85 0.0056 0.0008 8 0.00003 0.00001 -0.48 21.48 0.0076 0.0015 9 0.00005 0.00000 1.33 1.15 0.0134 0.0007 10 0.00106 0.00000 -9.13 0.02 0.3139 0.0010 11 0.00001 0.00001 -1.65 1.69 0.0029 0.0019 12 0.00001 0.00001 -3.91 2.89 0.0033 0.0018 13 0.00006 0.00001 1.41 0.78 0.0175 0.0041 14 0.00086 0.00000 -6.47 0.03 0.2542 0.0009 15 0.00005 0.00001 -7.11 1.07 0.0142 0.0035 16 0.00002 0.00001 3.13 7.32 0.0057 0.0036 The magnetic center is at X = 51.4 +- 0.6 microns Y = 191.5 +- 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: 03-27-1995 Time: 11:50:29 Magnet Name: 103 Run Number: 3 FIELD HARMONICS Magnet Current, Imag = 300.4038 +- 7.965322E-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 0.00180 0.00002 -167.06 0.60 0.4603 0.0050 2 0.39125 0.00007 44.95 0.00 100.0000 0.0000 3 0.00026 0.00001 13.74 1.93 0.0652 0.0019 4 0.00002 0.00001 0.79 37.80 0.0042 0.0013 5 0.00008 0.00001 12.85 1.50 0.0194 0.0029 6 0.00051 0.00001 15.05 0.07 0.1294 0.0021 7 0.00003 0.00000 9.93 0.54 0.0070 0.0012 8 0.00004 0.00000 10.48 18.82 0.0094 0.0010 9 0.00005 0.00001 1.61 0.67 0.0134 0.0021 10 0.00127 0.00001 -9.11 0.01 0.3258 0.0032 11 0.00002 0.00000 -2.06 4.48 0.0039 0.0007 12 0.00001 0.00000 -0.65 11.13 0.0015 0.0005 13 0.00008 0.00001 1.63 1.56 0.0216 0.0032 14 0.00100 0.00001 -6.44 0.04 0.2551 0.0019 15 0.00006 0.00002 -7.91 0.92 0.0157 0.0048 16 0.00004 0.00002 2.07 2.50 0.0107 0.0043 The magnetic center is at X = 46.1 +- 2.2 microns Y = 200.4 +- 2.2 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: 03-27-1995 Time: 11:56:45 Magnet Name: 103 Run Number: 3 FIELD HARMONICS Magnet Current, Imag = 350.4081 +- 4.541893E-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 0.00199 0.00002 -167.34 0.45 0.4657 0.0052 2 0.42756 0.00017 44.95 0.00 100.0000 0.0000 3 0.00030 0.00001 12.94 1.75 0.0690 0.0031 4 0.00003 0.00001 -21.69 34.41 0.0062 0.0015 5 0.00008 0.00001 12.38 1.42 0.0176 0.0026 6 0.00030 0.00001 15.17 0.20 0.0703 0.0017 7 0.00003 0.00000 11.91 2.01 0.0071 0.0010 8 0.00003 0.00000 0.77 21.18 0.0067 0.0002 9 0.00006 0.00000 2.30 0.64 0.0134 0.0007 10 0.00143 0.00000 -9.10 0.03 0.3337 0.0008 11 0.00001 0.00000 -0.26 9.18 0.0025 0.0008 12 0.00002 0.00001 -0.19 12.70 0.0056 0.0016 13 0.00007 0.00001 0.13 0.96 0.0172 0.0033 14 0.00108 0.00001 -6.42 0.01 0.2533 0.0033 15 0.00004 0.00002 -7.39 1.43 0.0087 0.0043 16 0.00004 0.00002 1.63 1.63 0.0093 0.0054 The magnetic center is at X = 45.6 +- 1.7 microns Y = 203.0 +- 2.3 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 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)