SLAC Magnetic Measurements Date: 02-24-1995 Time: 15:06:43 Magnet Name (Serial #): 189 Bar Code Number: 508 Project: PEP II High Energy Ring Quadrupoles Test Stand: IR8, Q1 Measurement Coil: # 2 Operator: bmd 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: 02-24-1995 Time: 15:54:01 Magnet Name: 189 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 10.00126 +- 1.826398E-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 143.66 0.19 0.4520 0.0017 2 0.01483 0.00000 45.09 0.00 100.0000 0.0000 3 0.00002 0.00000 29.54 0.38 0.1073 0.0016 4 0.00001 0.00000 -13.72 0.74 0.0429 0.0015 5 0.00000 0.00000 16.07 1.09 0.0142 0.0033 6 0.00003 0.00000 15.31 0.05 0.2158 0.0033 7 0.00000 0.00000 -1.02 12.96 0.0023 0.0012 8 0.00000 0.00000 -14.61 2.50 0.0040 0.0009 9 0.00000 0.00000 -2.35 0.92 0.0133 0.0012 10 0.00004 0.00000 -8.87 0.02 0.3025 0.0019 11 0.00000 0.00000 -0.69 9.45 0.0020 0.0014 12 0.00000 0.00000 -8.07 2.20 0.0051 0.0020 13 0.00000 0.00000 -3.57 0.70 0.0181 0.0026 14 0.00004 0.00000 -6.35 0.04 0.2551 0.0028 15 0.00000 0.00000 1.96 6.30 0.0037 0.0011 16 0.00000 0.00000 -1.19 6.75 0.0046 0.0021 The magnetic center is at X = -119.6 +- 0.7 microns Y = 162.6 +- 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 ^ | N S --> x S N Date: 02-24-1995 Time: 16:00:06 Magnet Name: 189 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 25.1014 +- 6.099364E-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 0.00018 0.00000 148.04 0.19 0.5032 0.0020 2 0.03493 0.00001 45.09 0.00 100.0000 0.0000 3 0.00003 0.00000 30.63 0.16 0.0850 0.0016 4 0.00001 0.00000 -16.38 0.64 0.0405 0.0015 5 0.00000 0.00000 17.87 1.50 0.0136 0.0021 6 0.00008 0.00000 15.33 0.08 0.2184 0.0009 7 0.00000 0.00000 -0.75 15.77 0.0033 0.0019 8 0.00000 0.00000 -21.08 0.94 0.0107 0.0020 9 0.00000 0.00000 -1.39 0.52 0.0134 0.0009 10 0.00011 0.00000 -8.85 0.02 0.3017 0.0024 11 0.00000 0.00000 -2.68 11.21 0.0034 0.0012 12 0.00000 0.00000 -2.10 1.10 0.0059 0.0015 13 0.00001 0.00000 -2.63 0.74 0.0147 0.0012 14 0.00009 0.00000 -6.33 0.04 0.2530 0.0012 15 0.00000 0.00000 1.14 4.14 0.0071 0.0025 16 0.00000 0.00000 -1.46 4.80 0.0050 0.0039 The magnetic center is at X = -119.0 +- 0.8 microns Y = 190.7 +- 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 ^ | N S --> x S N Date: 02-24-1995 Time: 16:06:16 Magnet Name: 189 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 50.06138 +- 4.19196E-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 0.00036 0.00000 153.10 0.12 0.5168 0.0019 2 0.06881 0.00001 45.09 0.00 100.0000 0.0000 3 0.00005 0.00000 31.05 0.53 0.0766 0.0016 4 0.00003 0.00000 -15.36 0.81 0.0442 0.0020 5 0.00001 0.00000 14.47 2.98 0.0099 0.0009 6 0.00015 0.00000 15.34 0.14 0.2195 0.0028 7 0.00000 0.00000 9.97 2.39 0.0033 0.0020 8 0.00000 0.00000 -6.79 16.26 0.0021 0.0011 9 0.00001 0.00000 -2.14 0.66 0.0147 0.0013 10 0.00021 0.00000 -8.87 0.04 0.3019 0.0019 11 0.00000 0.00000 -6.37 1.34 0.0030 0.0013 12 0.00000 0.00000 -6.25 2.46 0.0040 0.0004 13 0.00001 0.00000 -2.98 0.75 0.0174 0.0022 14 0.00017 0.00000 -6.33 0.03 0.2523 0.0034 15 0.00001 0.00000 -3.71 3.56 0.0086 0.0040 16 0.00000 0.00000 -0.92 7.67 0.0039 0.0026 The magnetic center is at X = -104.5 +- 0.6 microns Y = 205.9 +- 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: 02-24-1995 Time: 16:12:31 Magnet Name: 189 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 100.0517 +- 4.316849E-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 0.00074 0.00000 151.20 0.05 0.5417 0.0016 2 0.13729 0.00002 45.09 0.00 100.0000 0.0000 3 0.00011 0.00000 30.48 0.39 0.0802 0.0017 4 0.00006 0.00000 -15.35 0.67 0.0452 0.0010 5 0.00001 0.00000 16.02 0.33 0.0105 0.0018 6 0.00030 0.00000 15.34 0.04 0.2192 0.0030 7 0.00000 0.00000 10.46 5.00 0.0032 0.0017 8 0.00000 0.00000 -15.30 4.77 0.0029 0.0012 9 0.00002 0.00000 -2.50 0.72 0.0128 0.0014 10 0.00042 0.00000 -8.89 0.03 0.3031 0.0021 11 0.00000 0.00000 -7.33 6.24 0.0022 0.0008 12 0.00000 0.00000 -4.03 10.04 0.0032 0.0016 13 0.00002 0.00000 -2.81 0.52 0.0168 0.0015 14 0.00035 0.00000 -6.32 0.03 0.2549 0.0034 15 0.00001 0.00001 -3.06 3.51 0.0068 0.0041 16 0.00000 0.00000 -0.71 2.79 0.0026 0.0013 The magnetic center is at X = -116.6 +- 0.4 microns Y = 212.0 +- 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: 02-24-1995 Time: 16:18:44 Magnet Name: 189 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 150.0611 +- 5.908718E-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 0.00114 0.00000 150.89 0.14 0.5522 0.0010 2 0.20554 0.00002 45.07 0.00 100.0000 0.0000 3 0.00017 0.00000 29.12 0.70 0.0811 0.0014 4 0.00009 0.00000 -15.35 0.75 0.0451 0.0020 5 0.00002 0.00000 16.72 1.65 0.0109 0.0010 6 0.00043 0.00000 15.31 0.07 0.2110 0.0020 7 0.00001 0.00000 10.18 6.24 0.0033 0.0012 8 0.00001 0.00001 -0.51 13.60 0.0036 0.0026 9 0.00003 0.00000 -2.31 0.68 0.0133 0.0013 10 0.00063 0.00001 -8.89 0.04 0.3077 0.0026 11 0.00001 0.00000 0.97 8.49 0.0031 0.0006 12 0.00001 0.00000 -2.63 10.25 0.0042 0.0023 13 0.00004 0.00000 -2.70 0.23 0.0177 0.0019 14 0.00052 0.00001 -6.38 0.06 0.2524 0.0048 15 0.00001 0.00000 1.75 6.80 0.0072 0.0021 16 0.00001 0.00000 -5.20 8.17 0.0044 0.0022 The magnetic center is at X = -120.0 +- 0.6 microns Y = 215.5 +- 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: 02-24-1995 Time: 16:24:57 Magnet Name: 189 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 200.3007 +- 3.194339E-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 0.00152 0.00001 150.14 0.24 0.5566 0.0024 2 0.27320 0.00002 45.07 0.00 100.0000 0.0000 3 0.00022 0.00001 28.92 0.44 0.0795 0.0025 4 0.00011 0.00000 -19.24 0.66 0.0391 0.0014 5 0.00003 0.00000 15.63 1.10 0.0094 0.0012 6 0.00056 0.00000 15.37 0.05 0.2039 0.0017 7 0.00001 0.00000 12.06 6.84 0.0026 0.0011 8 0.00002 0.00000 -2.54 1.20 0.0060 0.0016 9 0.00004 0.00000 -1.75 0.51 0.0146 0.0008 10 0.00085 0.00000 -8.88 0.06 0.3094 0.0015 11 0.00001 0.00000 -5.96 6.31 0.0024 0.0010 12 0.00001 0.00001 -7.51 2.44 0.0040 0.0024 13 0.00005 0.00000 -2.80 0.37 0.0178 0.0011 14 0.00069 0.00001 -6.38 0.03 0.2513 0.0036 15 0.00001 0.00001 -3.04 2.86 0.0051 0.0026 16 0.00002 0.00000 -5.13 8.15 0.0083 0.0018 The magnetic center is at X = -123.8 +- 1.0 microns Y = 215.6 +- 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: 02-24-1995 Time: 16:31:12 Magnet Name: 189 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 250.3974 +- 4.751098E-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 0.00188 0.00001 149.85 0.30 0.5548 0.0020 2 0.33805 0.00003 45.06 0.00 100.0000 0.0000 3 0.00027 0.00001 28.67 0.45 0.0789 0.0022 4 0.00013 0.00000 -17.95 0.58 0.0397 0.0014 5 0.00003 0.00001 15.39 2.54 0.0102 0.0018 6 0.00060 0.00001 15.31 0.06 0.1778 0.0023 7 0.00001 0.00000 6.47 3.29 0.0034 0.0012 8 0.00003 0.00001 0.34 21.44 0.0099 0.0025 9 0.00005 0.00000 -2.61 0.56 0.0149 0.0003 10 0.00105 0.00001 -8.90 0.02 0.3113 0.0021 11 0.00001 0.00000 -8.13 3.67 0.0027 0.0006 12 0.00003 0.00001 0.17 1.97 0.0083 0.0037 13 0.00005 0.00000 -2.88 0.30 0.0157 0.0011 14 0.00086 0.00001 -6.35 0.05 0.2543 0.0040 15 0.00002 0.00001 -1.52 5.19 0.0052 0.0036 16 0.00002 0.00001 -3.00 4.47 0.0049 0.0023 The magnetic center is at X = -124.5 +- 1.2 microns Y = 214.3 +- 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: 02-24-1995 Time: 16:37:26 Magnet Name: 189 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 300.3782 +- 6.724263E-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 0.00209 0.00001 147.86 0.25 0.5350 0.0015 2 0.39000 0.00005 45.06 0.00 100.0000 0.0000 3 0.00032 0.00001 32.51 0.35 0.0820 0.0034 4 0.00017 0.00000 -14.82 0.30 0.0435 0.0013 5 0.00003 0.00001 12.20 1.28 0.0088 0.0024 6 0.00049 0.00001 15.47 0.15 0.1257 0.0021 7 0.00001 0.00000 -4.11 6.98 0.0021 0.0005 8 0.00003 0.00001 -9.44 18.03 0.0066 0.0015 9 0.00006 0.00000 -2.50 0.68 0.0149 0.0011 10 0.00126 0.00001 -8.90 0.01 0.3235 0.0017 11 0.00001 0.00001 -8.02 2.01 0.0031 0.0021 12 0.00003 0.00002 -3.75 2.20 0.0076 0.0042 13 0.00007 0.00000 -3.23 0.27 0.0170 0.0009 14 0.00099 0.00001 -6.39 0.04 0.2531 0.0018 15 0.00002 0.00001 -1.59 1.67 0.0054 0.0022 16 0.00002 0.00001 4.22 4.60 0.0055 0.0026 The magnetic center is at X = -127.1 +- 1.0 microns Y = 202.3 +- 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 ^ | N S --> x S N Date: 02-24-1995 Time: 16:43:41 Magnet Name: 189 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 350.3788 +- 3.845094E-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 0.00222 0.00001 146.81 0.17 0.5196 0.0017 2 0.42642 0.00009 45.06 0.00 100.0000 0.0000 3 0.00037 0.00001 34.77 0.59 0.0859 0.0018 4 0.00018 0.00001 -14.53 0.73 0.0415 0.0022 5 0.00004 0.00001 7.05 1.16 0.0096 0.0025 6 0.00030 0.00001 15.83 0.27 0.0699 0.0019 7 0.00001 0.00000 -4.79 5.52 0.0031 0.0003 8 0.00003 0.00000 -0.04 21.99 0.0065 0.0004 9 0.00007 0.00000 -2.22 0.76 0.0158 0.0006 10 0.00143 0.00001 -8.90 0.03 0.3347 0.0015 11 0.00001 0.00000 -3.02 12.01 0.0022 0.0005 12 0.00001 0.00000 -8.50 2.13 0.0029 0.0009 13 0.00006 0.00001 -2.51 0.38 0.0131 0.0014 14 0.00107 0.00001 -6.40 0.03 0.2509 0.0020 15 0.00002 0.00000 -1.70 6.03 0.0039 0.0011 16 0.00002 0.00001 0.84 0.85 0.0039 0.0013 The magnetic center is at X = -127.1 +- 0.7 microns Y = 194.2 +- 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 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)