SLAC Magnetic Measurements Date: 07-30-1996 Time: 14:57:26 Magnet Name (Serial #): 107 Bar Code Number: 468 Project: PEP II High Energy Ring Quadrupoles Test Stand: IR8, Q1 Measurement Coil: # 2 Operator: dan Run Number: 2 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: 07-30-1996 Time: 15:39:34 Magnet Name: 107 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 9.980576 +- 3.249025E-04 A Coil Radius, Rcoil = .0446588 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 0.00003 0.00000 26.75 0.43 0.2341 0.0015 2 0.01491 0.00000 -45.13 0.00 100.0000 0.0000 3 0.00002 0.00000 -4.50 0.34 0.1349 0.0040 4 0.00000 0.00000 -25.99 2.62 0.0155 0.0021 5 0.00000 0.00000 -21.11 4.38 0.0104 0.0009 6 0.00003 0.00000 -15.28 0.08 0.2087 0.0017 7 0.00000 0.00000 -20.08 2.65 0.0126 0.0026 8 0.00000 0.00000 7.09 11.21 0.0035 0.0011 9 0.00000 0.00000 -14.59 0.90 0.0097 0.0020 10 0.00004 0.00000 8.70 0.19 0.2978 0.0079 11 0.00000 0.00000 7.61 4.88 0.0030 0.0010 12 0.00000 0.00000 1.49 6.68 0.0141 0.0088 13 0.00000 0.00000 -11.43 0.76 0.0128 0.0032 14 0.00004 0.00000 6.24 0.08 0.2602 0.0028 15 0.00000 0.00000 -6.00 4.26 0.0054 0.0020 16 0.00000 0.00000 -3.89 5.94 0.0070 0.0026 The magnetic center is at X = 47.1 +- 0.8 microns Y = 93.3 +- 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 ^ | S N --> x N S Date: 07-30-1996 Time: 15:45:40 Magnet Name: 107 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 25.05595 +- 1.722816E-03 A Coil Radius, Rcoil = .0446588 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 0.00013 0.00000 24.89 0.32 0.3606 0.0023 2 0.03493 0.00000 -45.13 0.00 100.0000 0.0000 3 0.00003 0.00000 -15.81 0.50 0.0804 0.0036 4 0.00001 0.00000 -28.27 1.91 0.0180 0.0011 5 0.00000 0.00000 -16.25 1.60 0.0107 0.0018 6 0.00007 0.00000 -15.22 0.08 0.2132 0.0016 7 0.00000 0.00000 -17.61 3.74 0.0075 0.0026 8 0.00000 0.00000 0.56 20.41 0.0093 0.0020 9 0.00000 0.00000 -16.27 1.44 0.0105 0.0032 10 0.00010 0.00000 8.61 0.12 0.2925 0.0052 11 0.00000 0.00000 8.89 8.33 0.0049 0.0026 12 0.00001 0.00000 -3.36 1.23 0.0229 0.0083 13 0.00000 0.00000 -11.09 1.23 0.0109 0.0017 14 0.00009 0.00000 6.24 0.05 0.2570 0.0052 15 0.00000 0.00000 -3.19 7.99 0.0082 0.0016 16 0.00000 0.00000 -1.25 5.10 0.0065 0.0017 The magnetic center is at X = 67.8 +- 0.9 microns Y = 146.1 +- 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 ^ | S N --> x N S Date: 07-30-1996 Time: 15:51:52 Magnet Name: 107 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 49.94888 +- 7.79898E-04 A Coil Radius, Rcoil = .0446588 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 0.00027 0.00000 27.24 0.44 0.3914 0.0022 2 0.06883 0.00001 -45.13 0.00 100.0000 0.0000 3 0.00005 0.00000 -19.84 0.36 0.0748 0.0028 4 0.00001 0.00000 -25.70 2.12 0.0148 0.0041 5 0.00001 0.00000 -17.43 1.38 0.0104 0.0009 6 0.00015 0.00000 -15.14 0.03 0.2155 0.0014 7 0.00000 0.00000 -20.30 3.15 0.0020 0.0006 8 0.00000 0.00000 9.16 14.28 0.0033 0.0004 9 0.00001 0.00000 -15.40 0.81 0.0110 0.0020 10 0.00020 0.00000 8.67 0.08 0.2947 0.0054 11 0.00000 0.00000 10.05 0.29 0.0061 0.0015 12 0.00001 0.00001 -5.10 3.83 0.0178 0.0100 13 0.00001 0.00000 -11.18 1.36 0.0119 0.0007 14 0.00018 0.00000 6.15 0.14 0.2582 0.0014 15 0.00001 0.00000 -5.72 1.49 0.0091 0.0039 16 0.00001 0.00000 -7.16 3.21 0.0075 0.0038 The magnetic center is at X = 80.0 +- 1.3 microns Y = 155.4 +- 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 ^ | S N --> x N S Date: 07-30-1996 Time: 15:58:08 Magnet Name: 107 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 99.81911 +- 5.366264E-04 A Coil Radius, Rcoil = .0446588 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 0.00055 0.00000 29.30 0.18 0.4022 0.0015 2 0.13732 0.00001 -45.13 0.00 100.0000 0.0000 3 0.00010 0.00001 -21.03 0.32 0.0724 0.0037 4 0.00002 0.00000 -25.06 1.55 0.0181 0.0013 5 0.00002 0.00000 -16.38 1.16 0.0122 0.0021 6 0.00029 0.00000 -15.13 0.04 0.2136 0.0019 7 0.00001 0.00000 -18.25 2.40 0.0043 0.0016 8 0.00000 0.00000 -14.34 4.45 0.0022 0.0007 9 0.00001 0.00000 -16.45 0.93 0.0099 0.0001 10 0.00041 0.00001 8.74 0.17 0.2983 0.0073 11 0.00001 0.00000 5.83 10.67 0.0041 0.0022 12 0.00003 0.00001 -2.37 7.26 0.0241 0.0072 13 0.00002 0.00000 -10.91 0.31 0.0134 0.0018 14 0.00036 0.00001 6.21 0.11 0.2587 0.0087 15 0.00002 0.00001 -9.18 1.69 0.0121 0.0070 16 0.00001 0.00001 -6.70 4.24 0.0057 0.0048 The magnetic center is at X = 87.9 +- 0.6 microns Y = 156.7 +- 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 ^ | S N --> x N S Date: 07-30-1996 Time: 16:04:23 Magnet Name: 107 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 149.7116 +- 1.459071E-03 A Coil Radius, Rcoil = .0446588 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 0.00078 0.00000 28.78 0.42 0.3784 0.0016 2 0.20547 0.00002 -45.16 0.00 100.0000 0.0000 3 0.00015 0.00000 -22.26 0.85 0.0738 0.0021 4 0.00003 0.00000 -23.83 1.97 0.0169 0.0015 5 0.00003 0.00000 -16.51 1.63 0.0137 0.0010 6 0.00042 0.00000 -15.14 0.05 0.2054 0.0014 7 0.00001 0.00000 -16.94 4.63 0.0030 0.0012 8 0.00001 0.00000 -4.73 15.86 0.0032 0.0021 9 0.00002 0.00000 -15.47 0.64 0.0109 0.0015 10 0.00063 0.00002 8.65 0.09 0.3044 0.0080 11 0.00001 0.00001 11.68 2.16 0.0063 0.0027 12 0.00003 0.00002 -2.64 5.76 0.0168 0.0084 13 0.00002 0.00001 -10.22 0.58 0.0096 0.0038 14 0.00054 0.00001 6.22 0.08 0.2620 0.0044 15 0.00001 0.00001 -2.99 6.67 0.0040 0.0033 16 0.00002 0.00001 0.15 10.70 0.0112 0.0034 The magnetic center is at X = 81.4 +- 1.1 microns Y = 148.1 +- 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 ^ | S N --> x N S Date: 07-30-1996 Time: 16:10:38 Magnet Name: 107 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 199.8391 +- 5.154219E-04 A Coil Radius, Rcoil = .0446588 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 0.00104 0.00001 27.99 0.45 0.3825 0.0025 2 0.27301 0.00003 -45.16 0.00 100.0000 0.0000 3 0.00020 0.00001 -23.87 0.42 0.0716 0.0031 4 0.00006 0.00001 -34.39 1.30 0.0219 0.0027 5 0.00003 0.00000 -17.14 1.11 0.0107 0.0010 6 0.00054 0.00000 -15.20 0.06 0.1994 0.0015 7 0.00000 0.00000 -16.70 4.99 0.0016 0.0008 8 0.00002 0.00000 0.67 2.30 0.0057 0.0015 9 0.00003 0.00000 -16.46 0.72 0.0109 0.0008 10 0.00082 0.00000 8.68 0.06 0.3012 0.0014 11 0.00002 0.00001 10.47 1.78 0.0058 0.0023 12 0.00005 0.00001 -5.09 1.45 0.0175 0.0031 13 0.00004 0.00001 -11.48 0.70 0.0133 0.0027 14 0.00071 0.00001 6.20 0.08 0.2608 0.0028 15 0.00003 0.00001 -0.48 7.45 0.0121 0.0055 16 0.00002 0.00001 0.53 10.46 0.0076 0.0031 The magnetic center is at X = 80.2 +- 1.3 microns Y = 150.8 +- 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 ^ | S N --> x N S Date: 07-30-1996 Time: 16:16:55 Magnet Name: 107 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 249.8047 +- 7.534969E-04 A Coil Radius, Rcoil = .0446588 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 0.00136 0.00001 26.48 0.29 0.4039 0.0016 2 0.33758 0.00003 -45.16 0.00 100.0000 0.0000 3 0.00024 0.00000 -27.35 0.70 0.0712 0.0004 4 0.00005 0.00001 -31.98 2.51 0.0142 0.0022 5 0.00004 0.00001 -14.31 1.29 0.0108 0.0017 6 0.00059 0.00000 -15.26 0.09 0.1756 0.0011 7 0.00001 0.00000 -9.68 6.21 0.0030 0.0015 8 0.00003 0.00000 20.92 1.22 0.0085 0.0011 9 0.00004 0.00000 -16.52 1.71 0.0114 0.0011 10 0.00103 0.00004 8.78 0.13 0.3060 0.0117 11 0.00002 0.00001 9.93 2.98 0.0051 0.0032 12 0.00006 0.00002 -4.75 4.20 0.0188 0.0055 13 0.00005 0.00000 -11.98 0.91 0.0136 0.0007 14 0.00087 0.00001 6.11 0.12 0.2574 0.0019 15 0.00003 0.00002 4.12 7.48 0.0095 0.0072 16 0.00002 0.00001 -1.56 5.76 0.0074 0.0036 The magnetic center is at X = 80.4 +- 0.9 microns Y = 161.4 +- 0.8 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 ^ | S N --> x N S Date: 07-30-1996 Time: 16:23:11 Magnet Name: 107 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 299.6825 +- 1.015025E-03 A Coil Radius, Rcoil = .0446588 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 0.00154 0.00001 27.72 0.09 0.3961 0.0016 2 0.38932 0.00008 -45.16 0.00 100.0000 0.0000 3 0.00025 0.00001 -25.32 0.68 0.0654 0.0030 4 0.00005 0.00001 -19.80 1.90 0.0132 0.0024 5 0.00004 0.00001 -16.49 2.57 0.0113 0.0015 6 0.00047 0.00001 -15.19 0.15 0.1217 0.0014 7 0.00001 0.00000 -2.82 9.36 0.0014 0.0002 8 0.00002 0.00001 9.16 16.81 0.0055 0.0027 9 0.00005 0.00001 -16.59 1.19 0.0122 0.0025 10 0.00124 0.00002 8.70 0.16 0.3183 0.0047 11 0.00001 0.00001 12.78 1.36 0.0036 0.0029 12 0.00006 0.00002 -4.15 4.54 0.0153 0.0060 13 0.00005 0.00001 -11.35 1.45 0.0126 0.0013 14 0.00101 0.00002 6.19 0.09 0.2586 0.0039 15 0.00004 0.00002 0.81 10.33 0.0103 0.0042 16 0.00003 0.00001 -1.08 3.91 0.0064 0.0014 The magnetic center is at X = 82.3 +- 0.4 microns Y = 156.6 +- 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 ^ | S N --> x N S Date: 07-30-1996 Time: 16:29:27 Magnet Name: 107 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 349.5658 +- 1.410922E-03 A Coil Radius, Rcoil = .0446588 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 0.00163 0.00001 28.38 0.38 0.3838 0.0030 2 0.42552 0.00003 -45.16 0.00 100.0000 0.0000 3 0.00030 0.00001 -23.75 1.12 0.0710 0.0015 4 0.00005 0.00002 -23.00 1.33 0.0106 0.0039 5 0.00005 0.00001 -19.08 1.19 0.0125 0.0021 6 0.00029 0.00001 -15.11 0.30 0.0672 0.0014 7 0.00001 0.00000 4.27 8.35 0.0020 0.0009 8 0.00002 0.00001 18.51 3.88 0.0055 0.0025 9 0.00005 0.00000 -14.91 1.49 0.0116 0.0004 10 0.00138 0.00004 8.68 0.04 0.3254 0.0102 11 0.00002 0.00001 10.15 2.43 0.0038 0.0024 12 0.00007 0.00003 -2.78 4.22 0.0158 0.0074 13 0.00005 0.00001 -5.22 10.50 0.0119 0.0021 14 0.00107 0.00001 6.19 0.10 0.2517 0.0023 15 0.00004 0.00002 0.85 9.14 0.0097 0.0036 16 0.00003 0.00001 -2.61 4.69 0.0069 0.0023 The magnetic center is at X = 81.5 +- 1.2 microns Y = 150.8 +- 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 ^ | S N --> x N S 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)