SLAC Magnetic Measurements Date: 05-04-1995 Time: 08:55:39 Magnet Name (Serial #): 103 Bar Code Number: 454 Project: PEP II High Energy Ring Quadrupoles Test Stand: IR8, Q1 Measurement Coil: # 2 Operator: pdr Run Number: 7 Comment: Measure Reference Magnet 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: 05-04-1995 Time: 09:32:46 Magnet Name: 103 Run Number: 7 FIELD HARMONICS Magnet Current, Imag = 10.00387 +- 4.447833E-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 0.00008 0.00000 -128.47 0.59 0.5212 0.0040 2 0.01485 0.00000 44.95 0.00 100.0000 0.0000 3 0.00001 0.00000 26.18 1.80 0.0535 0.0023 4 0.00000 0.00000 35.00 3.33 0.0086 0.0026 5 0.00000 0.00000 13.26 3.00 0.0161 0.0014 6 0.00003 0.00000 15.03 0.11 0.2183 0.0019 7 0.00000 0.00000 14.01 2.17 0.0025 0.0010 8 0.00000 0.00000 11.50 7.90 0.0022 0.0017 9 0.00000 0.00000 2.57 0.55 0.0135 0.0011 10 0.00004 0.00000 -9.09 0.03 0.3006 0.0020 11 0.00000 0.00000 0.98 0.85 0.0081 0.0011 12 0.00000 0.00000 -5.85 9.44 0.0045 0.0033 13 0.00000 0.00000 1.38 0.63 0.0269 0.0037 14 0.00004 0.00000 -6.52 0.03 0.2549 0.0032 15 0.00000 0.00000 -5.98 4.99 0.0048 0.0008 16 0.00000 0.00000 -1.18 6.27 0.0081 0.0019 The magnetic center is at X = 182.3 +- 2.1 microns Y = 144.8 +- 2.2 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: 05-04-1995 Time: 09:38:51 Magnet Name: 103 Run Number: 7 FIELD HARMONICS Magnet Current, Imag = 25.10898 +- 3.726939E-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 0.00017 0.00000 -140.99 0.58 0.4936 0.0048 2 0.03502 0.00001 44.95 0.00 100.0000 0.0000 3 0.00002 0.00000 23.82 1.57 0.0444 0.0035 4 0.00000 0.00000 -22.01 37.25 0.0130 0.0033 5 0.00001 0.00000 13.08 1.20 0.0174 0.0028 6 0.00008 0.00000 14.93 0.11 0.2233 0.0029 7 0.00000 0.00000 12.31 3.24 0.0030 0.0012 8 0.00000 0.00000 21.43 0.86 0.0111 0.0006 9 0.00001 0.00000 2.95 0.37 0.0147 0.0011 10 0.00010 0.00000 -9.04 0.03 0.2995 0.0017 11 0.00000 0.00000 -0.77 1.77 0.0101 0.0016 12 0.00000 0.00000 1.80 3.13 0.0085 0.0013 13 0.00001 0.00000 1.85 0.32 0.0294 0.0045 14 0.00009 0.00000 -6.46 0.07 0.2575 0.0022 15 0.00000 0.00000 -6.27 1.34 0.0082 0.0037 16 0.00000 0.00000 4.96 4.55 0.0061 0.0010 The magnetic center is at X = 138.8 +- 2.2 microns Y = 171.3 +- 2.2 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: 05-04-1995 Time: 09:45:04 Magnet Name: 103 Run Number: 7 FIELD HARMONICS Magnet Current, Imag = 50.07505 +- 5.343402E-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 0.00034 0.00000 -146.84 0.13 0.4929 0.0036 2 0.06900 0.00001 44.95 0.00 100.0000 0.0000 3 0.00003 0.00000 22.85 0.97 0.0478 0.0011 4 0.00000 0.00000 -36.03 3.64 0.0063 0.0026 5 0.00001 0.00000 12.70 1.40 0.0180 0.0015 6 0.00015 0.00000 14.99 0.11 0.2216 0.0016 7 0.00000 0.00000 11.10 1.75 0.0040 0.0015 8 0.00000 0.00000 1.58 20.56 0.0036 0.0011 9 0.00001 0.00000 2.77 0.29 0.0136 0.0010 10 0.00021 0.00000 -9.07 0.01 0.3021 0.0008 11 0.00000 0.00000 1.20 2.33 0.0063 0.0015 12 0.00000 0.00000 0.99 4.94 0.0035 0.0013 13 0.00002 0.00000 2.50 0.96 0.0234 0.0024 14 0.00018 0.00000 -6.54 0.02 0.2552 0.0004 15 0.00000 0.00000 -5.79 3.31 0.0060 0.0042 16 0.00000 0.00000 2.33 4.32 0.0049 0.0023 The magnetic center is at X = 120.4 +- 1.0 microns Y = 184.3 +- 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 ^ | N S --> x S N Date: 05-04-1995 Time: 09:51:19 Magnet Name: 103 Run Number: 7 FIELD HARMONICS Magnet Current, Imag = 100.0759 +- 5.537753E-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 0.00066 0.00000 -148.18 0.16 0.4825 0.0016 2 0.13769 0.00003 44.95 0.00 100.0000 0.0000 3 0.00005 0.00000 26.30 0.40 0.0397 0.0014 4 0.00001 0.00000 -36.17 4.73 0.0077 0.0014 5 0.00002 0.00000 12.26 1.10 0.0165 0.0022 6 0.00031 0.00000 15.05 0.05 0.2230 0.0012 7 0.00001 0.00000 10.88 1.94 0.0041 0.0010 8 0.00000 0.00000 1.09 15.33 0.0012 0.0004 9 0.00002 0.00000 2.49 0.22 0.0125 0.0010 10 0.00042 0.00000 -9.07 0.01 0.3031 0.0019 11 0.00001 0.00000 2.33 2.09 0.0062 0.0008 12 0.00001 0.00000 0.37 8.43 0.0054 0.0018 13 0.00003 0.00000 1.85 0.55 0.0248 0.0012 14 0.00035 0.00001 -6.53 0.07 0.2538 0.0040 15 0.00001 0.00000 -4.56 8.55 0.0052 0.0013 16 0.00001 0.00001 -0.85 4.04 0.0089 0.0046 The magnetic center is at X = 113.6 +- 0.6 microns Y = 183.1 +- 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: 05-04-1995 Time: 09:57:33 Magnet Name: 103 Run Number: 7 FIELD HARMONICS Magnet Current, Imag = 150.0956 +- 7.8679E-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 0.00103 0.00001 -149.29 0.27 0.4987 0.0025 2 0.20605 0.00005 44.93 0.00 100.0000 0.0000 3 0.00008 0.00000 20.85 0.40 0.0406 0.0017 4 0.00001 0.00000 -25.41 3.21 0.0053 0.0021 5 0.00003 0.00000 12.19 2.09 0.0161 0.0024 6 0.00044 0.00000 14.89 0.04 0.2136 0.0010 7 0.00001 0.00000 6.83 2.10 0.0049 0.0016 8 0.00000 0.00000 -5.24 6.83 0.0016 0.0010 9 0.00003 0.00000 2.97 0.57 0.0140 0.0018 10 0.00063 0.00000 -9.10 0.04 0.3052 0.0021 11 0.00001 0.00000 1.60 1.90 0.0071 0.0017 12 0.00001 0.00000 1.12 10.71 0.0050 0.0006 13 0.00006 0.00001 1.73 1.11 0.0291 0.0034 14 0.00053 0.00000 -6.56 0.03 0.2572 0.0017 15 0.00001 0.00000 1.80 8.75 0.0063 0.0022 16 0.00001 0.00000 -1.92 4.33 0.0050 0.0017 The magnetic center is at X = 113.7 +- 1.1 microns Y = 191.5 +- 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: 05-04-1995 Time: 10:03:49 Magnet Name: 103 Run Number: 7 FIELD HARMONICS Magnet Current, Imag = 200.3515 +- 4.60363E-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 0.00136 0.00001 -148.40 0.47 0.4981 0.0033 2 0.27396 0.00004 44.93 0.00 100.0000 0.0000 3 0.00010 0.00001 22.39 1.84 0.0382 0.0046 4 0.00005 0.00001 -42.56 2.59 0.0191 0.0028 5 0.00005 0.00001 12.75 1.38 0.0171 0.0018 6 0.00056 0.00000 14.96 0.08 0.2052 0.0010 7 0.00001 0.00000 10.57 2.54 0.0050 0.0015 8 0.00002 0.00001 1.64 0.95 0.0072 0.0021 9 0.00004 0.00000 2.16 0.71 0.0136 0.0006 10 0.00084 0.00001 -9.10 0.03 0.3080 0.0021 11 0.00002 0.00001 3.51 2.58 0.0058 0.0029 12 0.00001 0.00000 -2.13 8.44 0.0048 0.0008 13 0.00006 0.00002 1.81 0.85 0.0235 0.0057 14 0.00071 0.00001 -6.56 0.05 0.2582 0.0029 15 0.00002 0.00001 -4.25 2.63 0.0063 0.0020 16 0.00003 0.00001 -4.90 6.09 0.0097 0.0022 The magnetic center is at X = 116.6 +- 1.7 microns Y = 189.5 +- 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: 05-04-1995 Time: 10:10:06 Magnet Name: 103 Run Number: 7 FIELD HARMONICS Magnet Current, Imag = 250.4601 +- 1.237327E-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 0.00170 0.00002 -149.60 0.31 0.5020 0.0061 2 0.33910 0.00008 44.93 0.00 100.0000 0.0000 3 0.00013 0.00001 20.90 2.09 0.0393 0.0029 4 0.00004 0.00000 -38.18 2.60 0.0106 0.0012 5 0.00006 0.00001 12.90 1.19 0.0190 0.0025 6 0.00061 0.00000 14.96 0.04 0.1803 0.0009 7 0.00002 0.00000 11.13 2.68 0.0046 0.0013 8 0.00002 0.00001 10.87 18.25 0.0057 0.0017 9 0.00005 0.00001 3.26 0.20 0.0141 0.0020 10 0.00106 0.00001 -9.09 0.02 0.3125 0.0015 11 0.00003 0.00001 2.74 0.79 0.0074 0.0016 12 0.00003 0.00001 -1.48 1.46 0.0086 0.0021 13 0.00009 0.00001 2.08 0.98 0.0257 0.0042 14 0.00086 0.00000 -6.57 0.03 0.2540 0.0008 15 0.00003 0.00001 -4.11 3.87 0.0079 0.0018 16 0.00003 0.00001 0.02 9.96 0.0085 0.0042 The magnetic center is at X = 113.5 +- 1.7 microns Y = 193.4 +- 2.4 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: 05-04-1995 Time: 10:16:22 Magnet Name: 103 Run Number: 7 FIELD HARMONICS Magnet Current, Imag = 300.4502 +- 4.752323E-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 0.00202 0.00002 -151.28 0.24 0.5169 0.0040 2 0.39095 0.00015 44.93 0.00 100.0000 0.0000 3 0.00020 0.00002 17.49 1.53 0.0516 0.0053 4 0.00002 0.00001 -35.55 5.89 0.0063 0.0017 5 0.00006 0.00001 12.08 1.20 0.0161 0.0014 6 0.00050 0.00000 15.00 0.10 0.1286 0.0012 7 0.00001 0.00000 11.84 3.15 0.0038 0.0009 8 0.00003 0.00001 21.49 1.04 0.0082 0.0019 9 0.00005 0.00001 2.96 1.32 0.0133 0.0015 10 0.00126 0.00000 -9.11 0.03 0.3227 0.0012 11 0.00004 0.00001 1.16 0.88 0.0092 0.0032 12 0.00003 0.00001 1.77 2.75 0.0070 0.0025 13 0.00011 0.00001 2.23 1.14 0.0283 0.0022 14 0.00101 0.00001 -6.54 0.06 0.2572 0.0017 15 0.00003 0.00002 -2.78 4.17 0.0071 0.0058 16 0.00003 0.00001 -4.77 3.80 0.0073 0.0018 The magnetic center is at X = 110.9 +- 1.2 microns Y = 202.5 +- 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: 05-04-1995 Time: 10:22:39 Magnet Name: 103 Run Number: 7 FIELD HARMONICS Magnet Current, Imag = 350.4612 +- 7.849012E-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 0.00224 0.00002 -151.51 0.51 0.5246 0.0038 2 0.42718 0.00009 44.93 0.00 100.0000 0.0000 3 0.00022 0.00001 15.12 1.79 0.0516 0.0034 4 0.00003 0.00001 -33.16 7.54 0.0076 0.0035 5 0.00008 0.00001 11.66 1.64 0.0186 0.0027 6 0.00030 0.00000 15.04 0.10 0.0698 0.0010 7 0.00002 0.00000 11.48 2.41 0.0047 0.0011 8 0.00002 0.00000 9.12 17.38 0.0057 0.0005 9 0.00006 0.00000 2.61 0.90 0.0150 0.0010 10 0.00142 0.00001 -9.09 0.01 0.3322 0.0015 11 0.00003 0.00001 0.47 1.17 0.0078 0.0021 12 0.00002 0.00000 -2.66 11.02 0.0038 0.0012 13 0.00012 0.00001 1.66 0.33 0.0275 0.0033 14 0.00107 0.00001 -6.50 0.04 0.2502 0.0030 15 0.00003 0.00000 -4.42 1.87 0.0061 0.0011 16 0.00003 0.00001 0.76 1.18 0.0068 0.0023 The magnetic center is at X = 111.8 +- 2.0 microns Y = 205.9 +- 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 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)