SLAC Magnetic Measurements Date: 03-09-1995 Time: 14:41:44 Magnet Name (Serial #): 141 Bar Code Number: 371 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: 03-09-1995 Time: 15:28:52 Magnet Name: 141 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 10.00261 +- 2.020878E-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 0.00009 0.00000 -30.63 0.07 0.5793 0.0022 2 0.01481 0.00000 -45.02 0.00 100.0000 0.0000 3 0.00002 0.00000 -39.27 0.40 0.1198 0.0021 4 0.00001 0.00000 -19.92 0.57 0.0617 0.0023 5 0.00000 0.00000 -17.97 0.30 0.0265 0.0020 6 0.00003 0.00000 -15.03 0.05 0.2216 0.0015 7 0.00000 0.00000 0.57 1.33 0.0077 0.0017 8 0.00000 0.00000 -14.07 4.66 0.0034 0.0012 9 0.00000 0.00000 18.03 1.70 0.0050 0.0009 10 0.00004 0.00000 8.99 0.02 0.3032 0.0013 11 0.00000 0.00000 2.81 2.65 0.0022 0.0015 12 0.00000 0.00000 -8.84 1.61 0.0077 0.0011 13 0.00000 0.00000 6.67 11.60 0.0112 0.0021 14 0.00004 0.00000 6.42 0.05 0.2533 0.0018 15 0.00000 0.00000 2.05 7.74 0.0039 0.0022 16 0.00000 0.00000 -2.04 5.64 0.0035 0.0009 The magnetic center is at X = -131.9 +- 0.6 microns Y = 222.7 +- 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: 03-09-1995 Time: 15:35:00 Magnet Name: 141 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 25.10311 +- 1.595204E-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 -13.55 0.11 0.3897 0.0014 2 0.03490 0.00000 -45.02 0.00 100.0000 0.0000 3 0.00002 0.00000 -37.18 0.49 0.0614 0.0007 4 0.00002 0.00000 -24.79 0.97 0.0605 0.0023 5 0.00001 0.00000 -19.50 0.71 0.0220 0.0018 6 0.00008 0.00000 -15.05 0.12 0.2208 0.0013 7 0.00000 0.00000 -7.64 3.57 0.0048 0.0011 8 0.00000 0.00000 -6.47 2.99 0.0032 0.0020 9 0.00000 0.00000 0.23 18.81 0.0079 0.0015 10 0.00011 0.00000 9.01 0.03 0.3032 0.0010 11 0.00000 0.00000 6.57 8.29 0.0021 0.0018 12 0.00000 0.00000 -7.31 1.92 0.0073 0.0017 13 0.00000 0.00000 6.19 11.45 0.0113 0.0016 14 0.00009 0.00000 6.46 0.05 0.2537 0.0023 15 0.00000 0.00000 6.43 2.05 0.0055 0.0024 16 0.00000 0.00000 0.99 9.88 0.0049 0.0013 The magnetic center is at X = -40.8 +- 0.4 microns Y = 169.2 +- 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: 03-09-1995 Time: 15:41:14 Magnet Name: 141 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 50.06454 +- 4.470119E-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 0.00022 0.00000 -5.79 0.19 0.3261 0.0036 2 0.06880 0.00002 -45.02 0.00 100.0000 0.0000 3 0.00003 0.00000 -31.53 0.72 0.0452 0.0025 4 0.00004 0.00000 -21.23 0.53 0.0594 0.0010 5 0.00001 0.00000 -19.70 1.32 0.0202 0.0028 6 0.00015 0.00000 -15.01 0.04 0.2208 0.0005 7 0.00000 0.00000 -6.54 3.56 0.0040 0.0013 8 0.00000 0.00000 -9.34 1.72 0.0037 0.0012 9 0.00000 0.00000 0.18 19.11 0.0062 0.0011 10 0.00021 0.00000 8.97 0.03 0.3036 0.0005 11 0.00000 0.00000 5.77 0.33 0.0027 0.0009 12 0.00000 0.00000 -8.43 2.09 0.0063 0.0020 13 0.00001 0.00000 12.73 0.75 0.0098 0.0009 14 0.00017 0.00000 6.43 0.09 0.2541 0.0026 15 0.00000 0.00000 7.39 2.05 0.0033 0.0009 16 0.00000 0.00000 -2.30 8.00 0.0032 0.0013 The magnetic center is at X = -14.7 +- 0.5 microns Y = 144.9 +- 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 ^ | S N --> x N S Date: 03-09-1995 Time: 15:47:33 Magnet Name: 141 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 100.0558 +- 6.686284E-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 0.00041 0.00000 -2.32 0.22 0.2954 0.0029 2 0.13730 0.00002 -45.02 0.00 100.0000 0.0000 3 0.00006 0.00000 -26.62 1.17 0.0431 0.0030 4 0.00008 0.00000 -21.25 0.56 0.0614 0.0016 5 0.00003 0.00000 -19.70 1.49 0.0198 0.0018 6 0.00031 0.00000 -14.96 0.07 0.2223 0.0020 7 0.00001 0.00000 -8.44 2.45 0.0040 0.0014 8 0.00000 0.00000 -14.11 1.51 0.0034 0.0013 9 0.00001 0.00000 0.77 19.09 0.0059 0.0012 10 0.00042 0.00000 8.99 0.01 0.3037 0.0013 11 0.00000 0.00000 4.14 2.86 0.0024 0.0013 12 0.00001 0.00000 -10.32 1.43 0.0079 0.0020 13 0.00001 0.00000 12.85 0.41 0.0094 0.0012 14 0.00035 0.00000 6.44 0.04 0.2525 0.0022 15 0.00001 0.00000 5.23 2.03 0.0049 0.0013 16 0.00000 0.00000 -0.76 6.98 0.0019 0.0011 The magnetic center is at X = -5.3 +- 0.5 microns Y = 131.8 +- 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 Date: 03-09-1995 Time: 15:53:52 Magnet Name: 141 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 150.0678 +- 4.340716E-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 0.00001 -2.58 0.35 0.2752 0.0032 2 0.20545 0.00004 -45.04 0.00 100.0000 0.0000 3 0.00009 0.00000 -26.07 0.93 0.0448 0.0009 4 0.00012 0.00000 -21.20 0.38 0.0600 0.0019 5 0.00004 0.00000 -21.02 0.51 0.0190 0.0022 6 0.00044 0.00000 -14.97 0.11 0.2148 0.0013 7 0.00001 0.00000 -10.22 1.88 0.0042 0.0016 8 0.00001 0.00000 -8.85 4.18 0.0027 0.0016 9 0.00002 0.00000 18.72 0.79 0.0075 0.0008 10 0.00062 0.00000 8.96 0.03 0.3037 0.0009 11 0.00001 0.00000 1.22 2.82 0.0029 0.0012 12 0.00002 0.00001 -11.19 1.15 0.0111 0.0026 13 0.00002 0.00000 6.50 11.74 0.0096 0.0008 14 0.00052 0.00000 6.42 0.06 0.2554 0.0010 15 0.00001 0.00001 5.77 2.30 0.0035 0.0027 16 0.00001 0.00000 -0.84 0.90 0.0057 0.0020 The magnetic center is at X = -5.5 +- 0.8 microns Y = 122.8 +- 1.4 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 ^ | S N --> x N S Date: 03-09-1995 Time: 16:00:11 Magnet Name: 141 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 200.3102 +- 9.198721E-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 0.00000 -0.57 0.36 0.2659 0.0015 2 0.27317 0.00008 -45.04 0.00 100.0000 0.0000 3 0.00011 0.00000 -25.08 0.92 0.0407 0.0014 4 0.00016 0.00000 -21.31 0.36 0.0569 0.0011 5 0.00005 0.00000 -20.33 0.83 0.0191 0.0012 6 0.00057 0.00000 -15.00 0.06 0.2074 0.0011 7 0.00001 0.00000 -14.15 2.56 0.0036 0.0008 8 0.00001 0.00000 -8.98 3.92 0.0042 0.0010 9 0.00002 0.00000 18.88 0.98 0.0065 0.0018 10 0.00084 0.00000 8.98 0.02 0.3088 0.0009 11 0.00001 0.00000 3.05 2.59 0.0030 0.0005 12 0.00002 0.00000 -10.06 1.49 0.0063 0.0012 13 0.00003 0.00000 12.67 0.51 0.0093 0.0011 14 0.00070 0.00000 6.39 0.04 0.2565 0.0018 15 0.00001 0.00000 5.37 3.10 0.0032 0.0017 16 0.00001 0.00000 -5.84 6.87 0.0040 0.0009 The magnetic center is at X = -1.2 +- 0.7 microns Y = 118.7 +- 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: 03-09-1995 Time: 16:06:30 Magnet Name: 141 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 250.4086 +- 1.077421E-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 0.00084 0.00000 3.94 0.40 0.2488 0.0008 2 0.33827 0.00009 -45.05 0.00 100.0000 0.0000 3 0.00010 0.00001 -19.75 1.61 0.0305 0.0035 4 0.00019 0.00001 -24.65 0.46 0.0566 0.0017 5 0.00006 0.00001 -21.25 1.73 0.0184 0.0029 6 0.00061 0.00001 -14.99 0.09 0.1791 0.0025 7 0.00001 0.00000 -10.70 2.50 0.0021 0.0008 8 0.00001 0.00000 -5.85 2.49 0.0041 0.0005 9 0.00002 0.00000 -9.27 15.82 0.0064 0.0014 10 0.00106 0.00001 8.95 0.02 0.3136 0.0015 11 0.00001 0.00000 2.86 3.83 0.0018 0.0007 12 0.00001 0.00000 -4.92 4.68 0.0032 0.0009 13 0.00003 0.00001 5.66 11.25 0.0089 0.0021 14 0.00085 0.00001 6.41 0.01 0.2522 0.0022 15 0.00002 0.00001 7.37 3.32 0.0053 0.0031 16 0.00002 0.00001 -4.57 8.67 0.0069 0.0018 The magnetic center is at X = 7.6 +- 0.8 microns Y = 110.9 +- 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 ^ | S N --> x N S Date: 03-09-1995 Time: 16:12:49 Magnet Name: 141 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 300.3921 +- 8.813189E-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 0.00105 0.00001 9.71 0.14 0.2693 0.0014 2 0.39008 0.00007 -45.05 0.00 100.0000 0.0000 3 0.00005 0.00001 -24.02 3.61 0.0138 0.0019 4 0.00020 0.00001 -23.02 0.77 0.0514 0.0026 5 0.00007 0.00001 -21.09 1.48 0.0177 0.0018 6 0.00052 0.00001 -14.96 0.16 0.1340 0.0023 7 0.00002 0.00000 -10.78 2.71 0.0046 0.0013 8 0.00002 0.00000 -19.98 1.13 0.0062 0.0012 9 0.00002 0.00000 -18.61 0.61 0.0063 0.0009 10 0.00126 0.00001 8.94 0.03 0.3237 0.0016 11 0.00001 0.00001 2.96 1.47 0.0031 0.0018 12 0.00003 0.00001 -4.95 1.80 0.0067 0.0031 13 0.00003 0.00001 12.01 0.65 0.0083 0.0022 14 0.00098 0.00001 6.45 0.07 0.2511 0.0015 15 0.00002 0.00001 -0.20 6.59 0.0050 0.0027 16 0.00002 0.00001 4.64 8.59 0.0039 0.0022 The magnetic center is at X = 20.3 +- 0.3 microns Y = 118.5 +- 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: 03-09-1995 Time: 16:19:09 Magnet Name: 141 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 350.3947 +- 8.851413E-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 0.00122 0.00001 12.58 0.23 0.2866 0.0017 2 0.42629 0.00013 -45.05 0.00 100.0000 0.0000 3 0.00004 0.00001 -48.73 3.66 0.0100 0.0018 4 0.00022 0.00001 -22.40 0.66 0.0509 0.0026 5 0.00007 0.00001 -21.98 0.52 0.0166 0.0014 6 0.00032 0.00000 -14.76 0.17 0.0755 0.0007 7 0.00002 0.00000 -13.13 3.73 0.0047 0.0004 8 0.00003 0.00001 -21.23 1.59 0.0073 0.0014 9 0.00003 0.00000 19.69 0.32 0.0078 0.0009 10 0.00143 0.00001 8.94 0.01 0.3351 0.0017 11 0.00001 0.00000 1.47 4.24 0.0021 0.0008 12 0.00002 0.00001 -4.17 1.86 0.0055 0.0017 13 0.00004 0.00000 12.68 0.47 0.0090 0.0006 14 0.00106 0.00001 6.43 0.00 0.2479 0.0022 15 0.00002 0.00000 4.96 1.19 0.0045 0.0010 16 0.00003 0.00000 0.04 0.75 0.0061 0.0010 The magnetic center is at X = 27.9 +- 0.5 microns Y = 124.9 +- 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 ^ | 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)