SLAC Magnetic Measurements Date: 03-13-1995 Time: 08:27:46 Magnet Name (Serial #): 113 Bar Code Number: 409 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: 03-13-1995 Time: 09:15:56 Magnet Name: 113 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 9.999969 +- 3.103683E-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 -112.38 0.23 0.2940 0.0011 2 0.01490 0.00001 44.96 0.00 100.0000 0.0000 3 0.00001 0.00000 30.57 0.55 0.0361 0.0017 4 0.00000 0.00000 -22.24 1.98 0.0169 0.0030 5 0.00000 0.00000 15.83 1.54 0.0137 0.0024 6 0.00003 0.00000 14.98 0.05 0.2126 0.0017 7 0.00000 0.00000 10.23 2.98 0.0041 0.0014 8 0.00000 0.00000 -15.24 3.59 0.0036 0.0002 9 0.00000 0.00000 3.99 1.37 0.0036 0.0013 10 0.00004 0.00000 -9.05 0.02 0.3004 0.0013 11 0.00000 0.00000 -10.01 1.90 0.0045 0.0023 12 0.00000 0.00000 -1.95 2.12 0.0029 0.0008 13 0.00000 0.00000 1.02 1.20 0.0055 0.0015 14 0.00004 0.00000 -6.45 0.04 0.2566 0.0043 15 0.00000 0.00000 -0.54 9.87 0.0150 0.0037 16 0.00000 0.00000 3.71 2.38 0.0049 0.0026 The magnetic center is at X = 121.4 +- 0.5 microns Y = 50.0 +- 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: 03-13-1995 Time: 09:22:07 Magnet Name: 113 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 25.09943 +- 5.830952E-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 -143.34 0.41 0.2354 0.0031 2 0.03496 0.00002 44.95 0.00 100.0000 0.0000 3 0.00002 0.00000 26.63 0.79 0.0456 0.0043 4 0.00001 0.00000 -33.00 1.46 0.0243 0.0016 5 0.00000 0.00000 15.43 1.70 0.0143 0.0018 6 0.00008 0.00000 15.05 0.09 0.2156 0.0013 7 0.00000 0.00000 11.69 2.40 0.0035 0.0007 8 0.00000 0.00000 -3.12 4.82 0.0016 0.0008 9 0.00000 0.00000 1.74 1.40 0.0041 0.0010 10 0.00011 0.00000 -9.07 0.01 0.3021 0.0010 11 0.00000 0.00000 -10.11 2.89 0.0030 0.0016 12 0.00000 0.00000 -0.06 1.13 0.0043 0.0014 13 0.00000 0.00000 -0.35 0.72 0.0074 0.0022 14 0.00009 0.00000 -6.43 0.05 0.2524 0.0018 15 0.00000 0.00000 -6.48 2.85 0.0055 0.0018 16 0.00000 0.00000 -1.34 8.37 0.0050 0.0020 The magnetic center is at X = 62.8 +- 1.0 microns Y = 84.3 +- 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: 03-13-1995 Time: 09:28:23 Magnet Name: 113 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 50.06174 +- 4.773938E-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 0.00016 0.00000 -154.42 0.15 0.2326 0.0009 2 0.06889 0.00001 44.95 0.00 100.0000 0.0000 3 0.00003 0.00000 26.09 0.97 0.0429 0.0018 4 0.00001 0.00000 -25.24 1.43 0.0201 0.0011 5 0.00001 0.00000 15.65 1.79 0.0134 0.0015 6 0.00015 0.00000 15.00 0.09 0.2180 0.0008 7 0.00000 0.00000 12.71 3.49 0.0036 0.0006 8 0.00000 0.00000 -9.09 0.70 0.0019 0.0008 9 0.00000 0.00000 1.43 3.15 0.0045 0.0010 10 0.00021 0.00000 -9.05 0.01 0.3020 0.0014 11 0.00000 0.00000 -9.79 1.82 0.0036 0.0010 12 0.00000 0.00000 -3.27 2.10 0.0033 0.0010 13 0.00000 0.00000 -0.16 1.27 0.0066 0.0008 14 0.00018 0.00000 -6.45 0.04 0.2563 0.0048 15 0.00000 0.00000 -1.74 7.42 0.0065 0.0046 16 0.00000 0.00000 1.40 6.40 0.0044 0.0020 The magnetic center is at X = 44.8 +- 0.3 microns Y = 93.7 +- 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 Date: 03-13-1995 Time: 09:34:43 Magnet Name: 113 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 100.054 +- 8.305622E-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 -159.41 0.27 0.2305 0.0012 2 0.13748 0.00005 44.95 0.00 100.0000 0.0000 3 0.00005 0.00000 26.44 1.29 0.0395 0.0021 4 0.00003 0.00000 -24.26 2.17 0.0184 0.0014 5 0.00002 0.00000 15.12 1.89 0.0139 0.0020 6 0.00030 0.00000 15.03 0.04 0.2198 0.0009 7 0.00001 0.00000 11.38 5.90 0.0040 0.0010 8 0.00000 0.00000 -5.77 15.01 0.0024 0.0016 9 0.00001 0.00000 1.25 1.99 0.0044 0.0010 10 0.00042 0.00000 -9.06 0.02 0.3028 0.0010 11 0.00001 0.00000 -8.13 2.61 0.0040 0.0008 12 0.00000 0.00000 -3.06 3.74 0.0031 0.0005 13 0.00001 0.00000 0.18 0.72 0.0055 0.0008 14 0.00036 0.00000 -6.46 0.07 0.2588 0.0024 15 0.00001 0.00000 -0.38 9.81 0.0082 0.0024 16 0.00001 0.00000 4.30 1.03 0.0066 0.0016 The magnetic center is at X = 36.2 +- 0.5 microns Y = 96.4 +- 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: 03-13-1995 Time: 09:41:02 Magnet Name: 113 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 150.0663 +- 7.916944E-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 0.00043 0.00000 -159.84 0.42 0.2110 0.0020 2 0.20576 0.00004 44.93 0.00 100.0000 0.0000 3 0.00008 0.00000 29.01 1.40 0.0389 0.0021 4 0.00004 0.00001 -23.04 1.81 0.0191 0.0032 5 0.00003 0.00000 13.63 3.00 0.0135 0.0016 6 0.00044 0.00000 14.97 0.09 0.2128 0.0015 7 0.00001 0.00000 6.69 1.66 0.0031 0.0017 8 0.00000 0.00000 -19.93 0.78 0.0019 0.0013 9 0.00001 0.00000 0.08 2.32 0.0043 0.0006 10 0.00062 0.00000 -9.08 0.02 0.3000 0.0015 11 0.00001 0.00000 -10.99 2.41 0.0053 0.0011 12 0.00001 0.00000 -9.99 5.58 0.0035 0.0019 13 0.00001 0.00000 -0.91 0.95 0.0062 0.0018 14 0.00053 0.00001 -6.49 0.06 0.2563 0.0056 15 0.00001 0.00001 2.76 5.58 0.0070 0.0051 16 0.00002 0.00001 1.13 0.86 0.0109 0.0025 The magnetic center is at X = 32.5 +- 0.7 microns Y = 88.5 +- 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: 03-13-1995 Time: 09:47:22 Magnet Name: 113 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 200.3078 +- 6.441306E-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 0.00000 -160.98 0.34 0.2092 0.0014 2 0.27331 0.00007 44.93 0.00 100.0000 0.0000 3 0.00010 0.00000 28.72 0.76 0.0383 0.0008 4 0.00005 0.00001 -24.66 2.19 0.0171 0.0029 5 0.00003 0.00001 14.92 1.69 0.0127 0.0020 6 0.00056 0.00000 15.01 0.05 0.2031 0.0016 7 0.00001 0.00000 14.34 6.66 0.0031 0.0015 8 0.00001 0.00000 -6.96 2.96 0.0025 0.0008 9 0.00001 0.00000 2.58 1.24 0.0028 0.0011 10 0.00084 0.00000 -9.06 0.02 0.3071 0.0012 11 0.00001 0.00001 -9.83 1.60 0.0041 0.0020 12 0.00001 0.00001 0.50 6.99 0.0028 0.0020 13 0.00002 0.00000 0.98 0.80 0.0059 0.0010 14 0.00071 0.00001 -6.50 0.03 0.2592 0.0025 15 0.00002 0.00001 -6.79 4.40 0.0088 0.0037 16 0.00001 0.00000 -1.35 9.19 0.0047 0.0015 The magnetic center is at X = 30.5 +- 0.6 microns Y = 88.3 +- 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: 03-13-1995 Time: 09:53:42 Magnet Name: 113 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 250.407 +- 8.24716E-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 0.00069 0.00001 -159.94 0.84 0.2040 0.0020 2 0.33823 0.00021 44.93 0.00 100.0000 0.0000 3 0.00012 0.00000 31.00 0.51 0.0360 0.0005 4 0.00007 0.00000 -34.27 1.58 0.0204 0.0015 5 0.00004 0.00000 12.59 0.79 0.0132 0.0014 6 0.00060 0.00000 15.03 0.08 0.1766 0.0012 7 0.00001 0.00000 6.89 2.78 0.0039 0.0011 8 0.00002 0.00000 -2.58 1.26 0.0063 0.0006 9 0.00002 0.00001 1.03 0.22 0.0049 0.0017 10 0.00106 0.00001 -9.06 0.01 0.3130 0.0017 11 0.00001 0.00000 -11.03 1.14 0.0028 0.0008 12 0.00001 0.00000 -4.82 5.12 0.0035 0.0014 13 0.00002 0.00000 -0.34 0.79 0.0066 0.0007 14 0.00086 0.00001 -6.49 0.01 0.2529 0.0027 15 0.00002 0.00000 -3.19 7.93 0.0050 0.0009 16 0.00002 0.00000 9.47 0.52 0.0052 0.0011 The magnetic center is at X = 31.3 +- 1.3 microns Y = 85.6 +- 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: 03-13-1995 Time: 10:00:01 Magnet Name: 113 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 300.3909 +- 1.195748E-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 0.00079 0.00001 -156.66 0.69 0.2021 0.0019 2 0.38976 0.00021 44.93 0.00 100.0000 0.0000 3 0.00012 0.00000 32.51 0.44 0.0306 0.0013 4 0.00006 0.00001 -31.73 1.72 0.0146 0.0028 5 0.00005 0.00000 12.85 1.63 0.0131 0.0007 6 0.00051 0.00001 14.98 0.14 0.1317 0.0014 7 0.00002 0.00001 8.55 1.86 0.0047 0.0016 8 0.00002 0.00000 -20.79 1.45 0.0053 0.0005 9 0.00002 0.00001 3.00 0.39 0.0048 0.0015 10 0.00126 0.00000 -9.08 0.01 0.3225 0.0007 11 0.00001 0.00001 -10.33 2.03 0.0034 0.0014 12 0.00003 0.00000 -0.98 0.54 0.0079 0.0008 13 0.00003 0.00001 1.71 1.55 0.0072 0.0014 14 0.00099 0.00001 -6.48 0.03 0.2533 0.0022 15 0.00003 0.00002 -4.08 9.03 0.0078 0.0044 16 0.00002 0.00000 3.78 8.76 0.0055 0.0008 The magnetic center is at X = 35.8 +- 1.0 microns Y = 82.9 +- 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: 03-13-1995 Time: 10:06:22 Magnet Name: 113 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 350.3967 +- 1.111066E-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 0.00088 0.00000 -154.70 0.37 0.2054 0.0011 2 0.42619 0.00017 44.93 0.00 100.0000 0.0000 3 0.00012 0.00000 32.75 1.19 0.0291 0.0009 4 0.00005 0.00000 -29.89 1.72 0.0128 0.0011 5 0.00006 0.00000 11.52 1.12 0.0135 0.0008 6 0.00032 0.00000 15.03 0.10 0.0749 0.0008 7 0.00002 0.00000 5.06 2.57 0.0039 0.0008 8 0.00004 0.00000 -10.34 18.57 0.0094 0.0011 9 0.00002 0.00001 1.47 0.72 0.0052 0.0012 10 0.00142 0.00001 -9.07 0.02 0.3331 0.0013 11 0.00001 0.00000 -8.87 0.72 0.0030 0.0007 12 0.00003 0.00000 -0.82 0.57 0.0061 0.0009 13 0.00003 0.00000 0.32 1.06 0.0078 0.0011 14 0.00106 0.00001 -6.46 0.03 0.2492 0.0022 15 0.00003 0.00002 -2.92 9.01 0.0063 0.0038 16 0.00003 0.00001 2.12 1.50 0.0077 0.0031 The magnetic center is at X = 39.2 +- 0.6 microns Y = 82.9 +- 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 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)