SLAC Magnetic Measurements Date: 03-08-1995 Time: 13:41:29 Magnet Name (Serial #): 186 Bar Code Number: 561 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: 03-08-1995 Time: 14:28:46 Magnet Name: 186 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 10.00095 +- 5.053655E-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 0.00007 0.00000 -123.72 0.28 0.4855 0.0009 2 0.01486 0.00000 44.99 0.00 100.0000 0.0000 3 0.00000 0.00000 -7.98 1.44 0.0297 0.0012 4 0.00000 0.00000 26.54 3.98 0.0160 0.0045 5 0.00000 0.00000 19.02 2.98 0.0048 0.0021 6 0.00003 0.00000 15.15 0.09 0.2206 0.0027 7 0.00000 0.00000 17.22 1.42 0.0120 0.0007 8 0.00000 0.00000 -7.56 16.56 0.0032 0.0017 9 0.00000 0.00000 4.41 0.67 0.0093 0.0014 10 0.00004 0.00000 -8.99 0.01 0.3000 0.0008 11 0.00000 0.00000 -12.33 2.21 0.0031 0.0015 12 0.00000 0.00000 2.03 3.16 0.0081 0.0015 13 0.00000 0.00000 1.87 0.36 0.0141 0.0017 14 0.00004 0.00000 -6.34 0.06 0.2507 0.0026 15 0.00000 0.00000 -3.57 4.85 0.0037 0.0010 16 0.00000 0.00000 3.90 4.52 0.0037 0.0013 The magnetic center is at X = 180.3 +- 0.7 microns Y = 120.4 +- 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: 03-08-1995 Time: 14:34:54 Magnet Name: 186 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 25.10097 +- 4.896688E-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 0.00013 0.00000 -145.99 0.28 0.3685 0.0044 2 0.03492 0.00001 44.99 0.00 100.0000 0.0000 3 0.00002 0.00000 27.08 0.69 0.0695 0.0024 4 0.00001 0.00000 36.46 5.37 0.0168 0.0051 5 0.00000 0.00000 16.08 1.14 0.0130 0.0016 6 0.00008 0.00000 15.07 0.12 0.2238 0.0018 7 0.00000 0.00000 16.80 2.36 0.0068 0.0006 8 0.00000 0.00000 -2.41 8.13 0.0029 0.0023 9 0.00000 0.00000 3.06 0.57 0.0093 0.0016 10 0.00010 0.00000 -8.99 0.03 0.2996 0.0018 11 0.00000 0.00000 -9.90 1.90 0.0018 0.0017 12 0.00000 0.00000 -0.43 0.97 0.0071 0.0043 13 0.00001 0.00000 2.03 0.30 0.0169 0.0021 14 0.00009 0.00000 -6.32 0.07 0.2550 0.0020 15 0.00000 0.00000 -3.70 2.29 0.0060 0.0022 16 0.00000 0.00000 2.30 7.95 0.0033 0.0018 The magnetic center is at X = 92.0 +- 1.3 microns Y = 136.4 +- 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: 03-08-1995 Time: 14:41:08 Magnet Name: 186 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 50.06258 +- 7.549102E-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 0.00024 0.00000 -155.07 0.11 0.3507 0.0017 2 0.06879 0.00003 44.99 0.00 100.0000 0.0000 3 0.00006 0.00000 30.45 0.23 0.0901 0.0018 4 0.00001 0.00000 34.57 1.77 0.0106 0.0016 5 0.00001 0.00000 16.19 1.88 0.0156 0.0024 6 0.00015 0.00000 15.03 0.08 0.2241 0.0017 7 0.00000 0.00000 17.46 1.53 0.0050 0.0012 8 0.00000 0.00000 -3.69 2.80 0.0018 0.0007 9 0.00000 0.00000 2.67 1.09 0.0073 0.0008 10 0.00021 0.00000 -9.03 0.02 0.3024 0.0012 11 0.00000 0.00000 -13.49 1.43 0.0041 0.0005 12 0.00001 0.00000 1.08 5.51 0.0076 0.0016 13 0.00001 0.00000 1.49 0.25 0.0131 0.0019 14 0.00017 0.00001 -6.38 0.08 0.2509 0.0076 15 0.00000 0.00000 -7.17 0.58 0.0055 0.0022 16 0.00000 0.00000 -2.03 3.45 0.0040 0.0016 The magnetic center is at X = 66.0 +- 0.4 microns Y = 142.0 +- 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 ^ | N S --> x S N Date: 03-08-1995 Time: 14:47:28 Magnet Name: 186 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 100.0545 +- 1.150117E-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 0.00048 0.00000 -158.51 0.12 0.3472 0.0028 2 0.13726 0.00004 44.99 0.00 100.0000 0.0000 3 0.00013 0.00000 31.24 0.64 0.0947 0.0015 4 0.00001 0.00000 30.53 4.30 0.0064 0.0011 5 0.00002 0.00000 15.98 1.55 0.0167 0.0030 6 0.00031 0.00000 15.09 0.07 0.2248 0.0014 7 0.00001 0.00000 17.27 3.50 0.0040 0.0012 8 0.00000 0.00000 -18.15 2.80 0.0024 0.0009 9 0.00001 0.00000 2.29 0.61 0.0074 0.0006 10 0.00042 0.00000 -9.01 0.03 0.3024 0.0003 11 0.00000 0.00000 -13.57 1.07 0.0032 0.0008 12 0.00001 0.00000 1.50 2.23 0.0082 0.0035 13 0.00002 0.00000 1.28 0.24 0.0117 0.0018 14 0.00034 0.00001 -6.31 0.08 0.2502 0.0042 15 0.00001 0.00000 -2.84 8.29 0.0045 0.0021 16 0.00001 0.00000 3.57 3.85 0.0050 0.0023 The magnetic center is at X = 56.8 +- 0.5 microns Y = 144.3 +- 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: 03-08-1995 Time: 14:53:46 Magnet Name: 186 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 150.066 +- 8.594167E-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 0.00000 -158.95 0.45 0.3365 0.0010 2 0.20537 0.00004 44.97 0.00 100.0000 0.0000 3 0.00020 0.00000 31.10 0.28 0.0969 0.0008 4 0.00001 0.00000 25.11 10.55 0.0058 0.0023 5 0.00003 0.00000 15.79 0.21 0.0152 0.0016 6 0.00045 0.00000 15.14 0.08 0.2191 0.0018 7 0.00001 0.00000 16.62 4.81 0.0037 0.0012 8 0.00000 0.00000 -8.89 2.33 0.0015 0.0007 9 0.00002 0.00000 2.67 1.28 0.0073 0.0008 10 0.00062 0.00000 -9.03 0.02 0.3008 0.0014 11 0.00001 0.00000 1.65 14.00 0.0036 0.0012 12 0.00001 0.00000 3.83 7.05 0.0069 0.0013 13 0.00002 0.00000 1.57 0.15 0.0112 0.0007 14 0.00053 0.00001 -6.36 0.06 0.2572 0.0068 15 0.00001 0.00000 -8.53 1.84 0.0042 0.0007 16 0.00001 0.00000 1.80 1.57 0.0072 0.0023 The magnetic center is at X = 54.0 +- 1.1 microns Y = 140.3 +- 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: 03-08-1995 Time: 15:00:05 Magnet Name: 186 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 200.309 +- 3.773273E-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 0.00091 0.00000 -159.27 0.23 0.3349 0.0013 2 0.27307 0.00004 44.97 0.00 100.0000 0.0000 3 0.00027 0.00000 31.12 0.26 0.0977 0.0013 4 0.00001 0.00001 18.31 35.48 0.0039 0.0019 5 0.00004 0.00000 15.37 1.90 0.0156 0.0009 6 0.00057 0.00001 15.09 0.03 0.2075 0.0022 7 0.00001 0.00000 19.36 1.95 0.0034 0.0013 8 0.00000 0.00000 5.49 14.56 0.0015 0.0006 9 0.00002 0.00000 1.72 1.48 0.0072 0.0008 10 0.00084 0.00000 -9.02 0.02 0.3085 0.0015 11 0.00001 0.00000 -0.77 13.76 0.0028 0.0010 12 0.00002 0.00001 0.21 1.21 0.0067 0.0037 13 0.00004 0.00000 1.37 0.98 0.0148 0.0013 14 0.00069 0.00000 -6.32 0.07 0.2535 0.0005 15 0.00002 0.00000 -6.87 1.93 0.0058 0.0015 16 0.00001 0.00001 -3.32 5.14 0.0032 0.0028 The magnetic center is at X = 52.9 +- 0.6 microns Y = 139.9 +- 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: 03-08-1995 Time: 15:06:23 Magnet Name: 186 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 250.4071 +- 1.52397E-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 0.00110 0.00001 -159.97 0.36 0.3256 0.0031 2 0.33804 0.00010 44.97 0.00 100.0000 0.0000 3 0.00033 0.00001 30.92 0.38 0.0987 0.0027 4 0.00006 0.00001 0.11 43.09 0.0185 0.0016 5 0.00005 0.00001 15.54 1.55 0.0142 0.0022 6 0.00061 0.00001 15.14 0.13 0.1811 0.0016 7 0.00001 0.00000 12.34 16.51 0.0018 0.0014 8 0.00001 0.00000 -4.46 6.29 0.0022 0.0012 9 0.00003 0.00000 2.28 1.54 0.0079 0.0010 10 0.00105 0.00000 -9.02 0.03 0.3116 0.0009 11 0.00001 0.00000 -4.80 11.79 0.0028 0.0014 12 0.00003 0.00001 1.10 0.76 0.0103 0.0042 13 0.00005 0.00000 1.83 0.88 0.0141 0.0014 14 0.00084 0.00001 -6.34 0.07 0.2496 0.0039 15 0.00001 0.00001 -7.13 0.46 0.0043 0.0021 16 0.00002 0.00001 5.43 7.96 0.0060 0.0020 The magnetic center is at X = 49.8 +- 1.0 microns Y = 136.6 +- 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: 03-08-1995 Time: 15:12:42 Magnet Name: 186 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 300.3898 +- 9.751309E-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 0.00133 0.00000 -164.40 0.16 0.3411 0.0007 2 0.39007 0.00006 44.97 0.00 100.0000 0.0000 3 0.00043 0.00001 28.95 0.27 0.1097 0.0020 4 0.00004 0.00001 0.69 42.66 0.0115 0.0019 5 0.00006 0.00001 17.04 1.46 0.0151 0.0018 6 0.00054 0.00001 15.14 0.13 0.1376 0.0018 7 0.00001 0.00001 -9.02 18.83 0.0030 0.0013 8 0.00004 0.00001 -21.19 0.85 0.0098 0.0014 9 0.00003 0.00001 0.86 1.23 0.0076 0.0019 10 0.00125 0.00001 -9.04 0.03 0.3208 0.0015 11 0.00002 0.00001 -6.00 12.94 0.0040 0.0018 12 0.00004 0.00001 -1.15 0.56 0.0115 0.0029 13 0.00004 0.00001 1.31 0.82 0.0103 0.0019 14 0.00099 0.00001 -6.39 0.09 0.2531 0.0018 15 0.00001 0.00001 -5.73 2.63 0.0036 0.0019 16 0.00001 0.00001 1.61 1.59 0.0033 0.0017 The magnetic center is at X = 41.0 +- 0.4 microns Y = 146.8 +- 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: 03-08-1995 Time: 15:19:01 Magnet Name: 186 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 350.3919 +- 5.154219E-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 0.00149 0.00001 -167.15 0.19 0.3501 0.0027 2 0.42652 0.00009 44.97 0.00 100.0000 0.0000 3 0.00051 0.00001 27.53 0.21 0.1188 0.0020 4 0.00004 0.00001 -18.68 35.44 0.0096 0.0034 5 0.00007 0.00000 16.45 0.96 0.0159 0.0011 6 0.00035 0.00000 15.14 0.28 0.0809 0.0005 7 0.00001 0.00000 -17.94 6.28 0.0030 0.0012 8 0.00004 0.00000 -20.00 1.00 0.0084 0.0007 9 0.00004 0.00000 0.90 0.41 0.0086 0.0008 10 0.00142 0.00000 -9.03 0.03 0.3331 0.0004 11 0.00001 0.00001 -10.82 3.87 0.0028 0.0012 12 0.00005 0.00001 -0.69 1.54 0.0128 0.0034 13 0.00005 0.00001 1.52 0.88 0.0108 0.0019 14 0.00107 0.00002 -6.30 0.08 0.2504 0.0055 15 0.00001 0.00000 -4.73 2.94 0.0035 0.0010 16 0.00003 0.00001 2.30 1.01 0.0073 0.0013 The magnetic center is at X = 34.8 +- 0.6 microns Y = 152.4 +- 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)