SLAC Magnetic Measurements Date: 04-10-1995 Time: 14:09:15 Magnet Name (Serial #): 130 Bar Code Number: 522 Project: PEP II High Energy Ring Quadrupoles Test Stand: IR8, Q1 Measurement Coil: # 2 Operator: mkl 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: 04-10-1995 Time: 14:56:24 Magnet Name: 130 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 10.00521 +- 2.585618E-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 0.00002 0.00000 -136.39 1.74 0.1641 0.0025 2 0.01495 0.00000 45.01 0.00 100.0000 0.0000 3 0.00002 0.00000 21.01 0.44 0.1391 0.0019 4 0.00000 0.00000 22.62 2.12 0.0181 0.0022 5 0.00000 0.00000 9.52 1.08 0.0240 0.0030 6 0.00003 0.00000 15.11 0.08 0.2117 0.0014 7 0.00000 0.00000 9.09 2.20 0.0066 0.0013 8 0.00000 0.00000 15.18 3.97 0.0024 0.0014 9 0.00000 0.00000 6.25 0.45 0.0067 0.0016 10 0.00004 0.00000 -9.06 0.03 0.3009 0.0014 11 0.00000 0.00000 -6.74 13.23 0.0042 0.0016 12 0.00000 0.00000 7.27 10.64 0.0043 0.0015 13 0.00000 0.00000 5.11 0.62 0.0077 0.0014 14 0.00004 0.00000 -6.44 0.03 0.2600 0.0007 15 0.00000 0.00000 -7.23 1.17 0.0115 0.0023 16 0.00000 0.00000 2.12 5.04 0.0072 0.0027 The magnetic center is at X = 50.6 +- 1.8 microns Y = 53.1 +- 1.7 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: 04-10-1995 Time: 15:02:29 Magnet Name: 130 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 25.11041 +- 4.723394E-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 -165.76 0.80 0.1805 0.0036 2 0.03502 0.00001 45.01 0.00 100.0000 0.0000 3 0.00004 0.00000 19.04 0.55 0.1224 0.0034 4 0.00001 0.00000 27.99 2.36 0.0182 0.0025 5 0.00001 0.00000 9.28 1.74 0.0207 0.0030 6 0.00008 0.00000 15.14 0.04 0.2153 0.0013 7 0.00000 0.00000 8.07 3.36 0.0070 0.0005 8 0.00000 0.00000 20.98 0.49 0.0105 0.0013 9 0.00000 0.00000 6.26 1.17 0.0075 0.0005 10 0.00010 0.00000 -9.03 0.05 0.2995 0.0019 11 0.00000 0.00000 -12.51 3.18 0.0027 0.0007 12 0.00000 0.00000 4.99 3.17 0.0045 0.0020 13 0.00000 0.00000 4.54 1.06 0.0083 0.0007 14 0.00009 0.00000 -6.47 0.03 0.2597 0.0024 15 0.00000 0.00000 -6.52 0.96 0.0119 0.0046 16 0.00000 0.00000 1.38 1.67 0.0072 0.0008 The magnetic center is at X = 19.8 +- 1.2 microns Y = 78.2 +- 1.6 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: 04-10-1995 Time: 15:08:41 Magnet Name: 130 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 50.07475 +- 3.702714E-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 -174.86 0.73 0.1993 0.0041 2 0.06896 0.00001 45.01 0.00 100.0000 0.0000 3 0.00008 0.00000 18.02 0.54 0.1172 0.0047 4 0.00001 0.00000 22.47 2.03 0.0151 0.0023 5 0.00001 0.00000 9.43 1.80 0.0186 0.0020 6 0.00015 0.00000 15.09 0.07 0.2135 0.0024 7 0.00000 0.00000 9.71 1.47 0.0064 0.0013 8 0.00000 0.00000 11.42 3.44 0.0028 0.0015 9 0.00001 0.00000 5.91 0.74 0.0083 0.0004 10 0.00021 0.00000 -9.04 0.02 0.3019 0.0017 11 0.00000 0.00000 -0.05 13.22 0.0031 0.0014 12 0.00000 0.00000 4.75 10.18 0.0047 0.0016 13 0.00000 0.00000 6.92 0.94 0.0057 0.0015 14 0.00018 0.00000 -6.46 0.02 0.2582 0.0019 15 0.00001 0.00000 -6.82 1.24 0.0102 0.0036 16 0.00000 0.00000 0.53 7.01 0.0029 0.0014 The magnetic center is at X = 8.0 +- 1.1 microns Y = 88.7 +- 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: 04-10-1995 Time: 15:14:57 Magnet Name: 130 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 100.0689 +- 1.152449E-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 0.00030 0.00000 -0.17 179.69 0.2153 0.0011 2 0.13754 0.00002 45.01 0.00 100.0000 0.0000 3 0.00016 0.00000 17.27 0.11 0.1182 0.0013 4 0.00002 0.00000 22.72 1.69 0.0142 0.0023 5 0.00002 0.00000 8.69 1.17 0.0171 0.0017 6 0.00030 0.00000 15.08 0.10 0.2150 0.0027 7 0.00001 0.00000 8.76 1.99 0.0070 0.0022 8 0.00000 0.00000 10.26 2.83 0.0032 0.0005 9 0.00001 0.00000 6.88 0.71 0.0079 0.0019 10 0.00042 0.00000 -9.04 0.05 0.3025 0.0014 11 0.00000 0.00000 -7.02 13.49 0.0035 0.0014 12 0.00001 0.00001 9.51 2.86 0.0063 0.0037 13 0.00001 0.00000 5.98 0.46 0.0068 0.0028 14 0.00035 0.00000 -6.46 0.03 0.2558 0.0030 15 0.00002 0.00000 -7.97 0.88 0.0156 0.0029 16 0.00001 0.00000 -1.24 6.26 0.0039 0.0011 The magnetic center is at X = 0.3 +- 301.6 microns Y = -96.1 +- 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 ^ | N S --> x S N Date: 04-10-1995 Time: 15:21:13 Magnet Name: 130 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 150.0847 +- 4.119873E-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 0.00044 0.00001 178.76 0.70 0.2137 0.0057 2 0.20577 0.00004 44.98 0.00 100.0000 0.0000 3 0.00024 0.00001 17.63 0.29 0.1186 0.0041 4 0.00003 0.00000 22.11 2.42 0.0141 0.0023 5 0.00004 0.00000 10.55 0.75 0.0173 0.0014 6 0.00042 0.00000 15.13 0.07 0.2034 0.0017 7 0.00002 0.00000 8.20 1.14 0.0082 0.0020 8 0.00001 0.00000 15.66 3.01 0.0034 0.0013 9 0.00002 0.00001 4.98 1.12 0.0075 0.0025 10 0.00063 0.00000 -9.07 0.02 0.3056 0.0019 11 0.00001 0.00000 0.77 14.50 0.0031 0.0015 12 0.00001 0.00000 -0.85 12.61 0.0049 0.0017 13 0.00001 0.00001 4.82 1.84 0.0070 0.0031 14 0.00052 0.00000 -6.50 0.04 0.2544 0.0005 15 0.00002 0.00001 -8.77 1.94 0.0121 0.0057 16 0.00001 0.00000 -2.16 5.87 0.0039 0.0015 The magnetic center is at X = -2.1 +- 1.2 microns Y = 95.4 +- 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: 04-10-1995 Time: 15:27:28 Magnet Name: 130 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 200.3358 +- 3.793275E-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 0.00061 0.00000 0.41 179.40 0.2232 0.0013 2 0.27342 0.00005 44.98 0.00 100.0000 0.0000 3 0.00031 0.00000 15.91 0.24 0.1133 0.0014 4 0.00005 0.00001 36.14 1.99 0.0184 0.0023 5 0.00004 0.00001 9.48 1.92 0.0164 0.0024 6 0.00054 0.00000 15.05 0.04 0.1981 0.0018 7 0.00002 0.00000 11.12 1.70 0.0068 0.0012 8 0.00002 0.00000 1.98 2.00 0.0067 0.0014 9 0.00002 0.00000 6.68 1.23 0.0081 0.0015 10 0.00084 0.00001 -9.06 0.04 0.3090 0.0029 11 0.00001 0.00000 6.67 12.53 0.0041 0.0013 12 0.00002 0.00001 -1.48 11.60 0.0065 0.0026 13 0.00002 0.00001 3.80 1.05 0.0065 0.0030 14 0.00071 0.00001 -6.46 0.04 0.2588 0.0026 15 0.00003 0.00001 -8.68 0.33 0.0120 0.0030 16 0.00002 0.00001 1.34 7.35 0.0061 0.0026 The magnetic center is at X = -0.7 +- 312.0 microns Y = -99.7 +- 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: 04-10-1995 Time: 15:33:44 Magnet Name: 130 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 250.4397 +- 4.309088E-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 0.00073 0.00001 -175.84 0.37 0.2146 0.0042 2 0.33822 0.00005 44.98 0.00 100.0000 0.0000 3 0.00036 0.00001 15.37 0.58 0.1052 0.0037 4 0.00004 0.00000 33.59 2.63 0.0120 0.0008 5 0.00005 0.00001 8.90 1.57 0.0156 0.0016 6 0.00059 0.00001 15.17 0.07 0.1734 0.0015 7 0.00002 0.00001 10.02 2.92 0.0064 0.0020 8 0.00002 0.00000 21.35 1.11 0.0070 0.0009 9 0.00003 0.00000 6.95 0.49 0.0084 0.0013 10 0.00106 0.00001 -9.09 0.02 0.3127 0.0015 11 0.00001 0.00001 -3.86 12.40 0.0033 0.0016 12 0.00002 0.00001 2.38 5.04 0.0069 0.0029 13 0.00003 0.00001 4.43 1.75 0.0080 0.0020 14 0.00087 0.00001 -6.48 0.03 0.2584 0.0043 15 0.00005 0.00001 -7.80 1.06 0.0153 0.0026 16 0.00002 0.00001 9.32 1.61 0.0066 0.0023 The magnetic center is at X = 6.9 +- 0.6 microns Y = 95.6 +- 1.9 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: 04-10-1995 Time: 15:40:01 Magnet Name: 130 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 300.4243 +- 5.850308E-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 0.00081 0.00001 -175.25 0.98 0.2076 0.0034 2 0.39006 0.00011 44.98 0.00 100.0000 0.0000 3 0.00041 0.00001 15.27 0.39 0.1055 0.0019 4 0.00002 0.00001 33.31 8.16 0.0048 0.0015 5 0.00006 0.00001 8.62 2.03 0.0160 0.0017 6 0.00047 0.00000 15.14 0.07 0.1204 0.0011 7 0.00003 0.00000 9.86 2.50 0.0070 0.0013 8 0.00003 0.00000 10.74 19.11 0.0075 0.0009 9 0.00003 0.00000 6.55 0.41 0.0083 0.0009 10 0.00126 0.00001 -9.07 0.03 0.3231 0.0014 11 0.00001 0.00000 -4.86 11.69 0.0022 0.0004 12 0.00002 0.00001 0.05 3.97 0.0048 0.0015 13 0.00003 0.00001 5.27 0.80 0.0078 0.0031 14 0.00101 0.00001 -6.49 0.02 0.2592 0.0029 15 0.00005 0.00002 -7.29 1.68 0.0136 0.0054 16 0.00002 0.00001 1.52 3.62 0.0051 0.0024 The magnetic center is at X = 7.7 +- 1.6 microns Y = 92.4 +- 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: 04-10-1995 Time: 15:46:18 Magnet Name: 130 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 350.4305 +- 1.143697E-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 0.00082 0.00001 -174.37 0.78 0.1927 0.0026 2 0.42657 0.00010 44.98 0.00 100.0000 0.0000 3 0.00042 0.00003 16.25 0.65 0.0980 0.0060 4 0.00002 0.00001 12.21 30.83 0.0052 0.0028 5 0.00007 0.00001 7.64 1.95 0.0165 0.0025 6 0.00026 0.00001 15.60 0.26 0.0607 0.0012 7 0.00003 0.00000 8.49 3.38 0.0073 0.0009 8 0.00003 0.00000 20.41 0.86 0.0062 0.0011 9 0.00003 0.00001 5.16 0.39 0.0081 0.0014 10 0.00142 0.00001 -9.08 0.04 0.3328 0.0018 11 0.00001 0.00000 -11.45 3.40 0.0021 0.0008 12 0.00002 0.00001 -4.63 9.91 0.0037 0.0015 13 0.00004 0.00001 4.77 0.58 0.0099 0.0016 14 0.00108 0.00000 -6.50 0.01 0.2543 0.0009 15 0.00006 0.00002 -8.50 1.05 0.0129 0.0045 16 0.00004 0.00001 1.64 2.14 0.0083 0.0031 The magnetic center is at X = 8.4 +- 1.2 microns Y = 85.6 +- 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 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)