SLAC Magnetic Measurements Date: 03-17-1995 Time: 07:32:47 Magnet Name (Serial #): 123 Bar Code Number: 466 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: 03-17-1995 Time: 08:20:06 Magnet Name: 123 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 9.998031 +- 1.678589E-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 55.59 1.55 0.1166 0.0012 2 0.01486 0.00001 44.94 0.00 100.0000 0.0000 3 0.00001 0.00000 26.80 1.78 0.0418 0.0017 4 0.00001 0.00000 19.42 0.85 0.0491 0.0021 5 0.00000 0.00000 8.03 0.49 0.0246 0.0012 6 0.00003 0.00000 15.15 0.05 0.2224 0.0013 7 0.00000 0.00000 9.16 2.83 0.0061 0.0003 8 0.00000 0.00000 12.06 3.10 0.0046 0.0016 9 0.00000 0.00000 -11.16 0.97 0.0072 0.0011 10 0.00004 0.00000 -9.10 0.03 0.3014 0.0013 11 0.00000 0.00000 -0.80 14.54 0.0098 0.0015 12 0.00000 0.00000 -0.67 6.46 0.0027 0.0005 13 0.00000 0.00000 -9.34 0.97 0.0092 0.0022 14 0.00004 0.00000 -6.48 0.04 0.2565 0.0014 15 0.00000 0.00000 -6.69 1.15 0.0039 0.0015 16 0.00000 0.00000 0.34 5.75 0.0055 0.0025 The magnetic center is at X = -43.0 +- 0.9 microns Y = -29.4 +- 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 Date: 03-17-1995 Time: 08:26:12 Magnet Name: 123 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 25.0984 +- 4.581936E-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 92.94 0.63 0.2631 0.0022 2 0.03495 0.00001 44.93 0.00 100.0000 0.0000 3 0.00003 0.00000 26.17 0.66 0.0742 0.0018 4 0.00002 0.00000 21.37 0.28 0.0445 0.0011 5 0.00001 0.00000 9.46 0.67 0.0251 0.0014 6 0.00008 0.00000 15.16 0.04 0.2267 0.0016 7 0.00000 0.00000 3.22 6.23 0.0038 0.0015 8 0.00000 0.00000 17.05 0.97 0.0067 0.0011 9 0.00000 0.00000 -11.83 0.38 0.0076 0.0005 10 0.00011 0.00000 -9.10 0.01 0.3042 0.0012 11 0.00000 0.00000 -15.99 0.05 0.0126 0.0025 12 0.00000 0.00000 0.78 1.25 0.0074 0.0007 13 0.00000 0.00000 -9.77 0.95 0.0122 0.0026 14 0.00009 0.00000 -6.56 0.04 0.2577 0.0018 15 0.00000 0.00000 -7.95 1.34 0.0060 0.0003 16 0.00000 0.00000 -4.62 5.06 0.0035 0.0009 The magnetic center is at X = -117.4 +- 1.0 microns Y = 6.0 +- 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: 03-17-1995 Time: 08:32:26 Magnet Name: 123 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 50.06083 +- 5.095942E-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 95.62 2.79 0.3167 0.0033 2 0.06857 0.00034 44.93 0.00 100.0000 0.0000 3 0.00006 0.00000 27.25 1.67 0.0810 0.0045 4 0.00003 0.00000 18.69 1.80 0.0454 0.0016 5 0.00002 0.00000 10.24 0.73 0.0248 0.0019 6 0.00015 0.00000 15.23 0.12 0.2249 0.0024 7 0.00000 0.00000 9.71 3.86 0.0025 0.0006 8 0.00000 0.00000 14.86 1.88 0.0060 0.0012 9 0.00000 0.00000 -10.84 0.60 0.0067 0.0011 10 0.00021 0.00000 -9.09 0.03 0.3063 0.0011 11 0.00001 0.00000 7.61 13.27 0.0089 0.0006 12 0.00000 0.00000 3.98 6.57 0.0018 0.0009 13 0.00001 0.00000 -8.61 1.75 0.0079 0.0014 14 0.00018 0.00000 -6.56 0.05 0.2577 0.0022 15 0.00000 0.00000 -7.51 1.51 0.0071 0.0013 16 0.00001 0.00000 0.45 3.14 0.0075 0.0031 The magnetic center is at X = -140.8 +- 2.0 microns Y = 13.8 +- 6.9 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: 03-17-1995 Time: 08:38:44 Magnet Name: 123 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 100.0558 +- 6.659133E-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 0.00047 0.00000 99.97 0.38 0.3393 0.0016 2 0.13724 0.00025 44.93 0.00 100.0000 0.0000 3 0.00011 0.00000 25.69 0.52 0.0808 0.0018 4 0.00006 0.00000 17.92 0.69 0.0458 0.0024 5 0.00003 0.00000 10.00 0.38 0.0255 0.0009 6 0.00031 0.00000 15.20 0.10 0.2262 0.0014 7 0.00000 0.00000 6.12 1.59 0.0030 0.0004 8 0.00001 0.00000 12.89 2.19 0.0051 0.0006 9 0.00001 0.00000 -11.54 0.98 0.0067 0.0017 10 0.00042 0.00000 -9.08 0.01 0.3060 0.0002 11 0.00001 0.00000 7.60 13.15 0.0106 0.0022 12 0.00000 0.00000 5.20 2.73 0.0027 0.0014 13 0.00001 0.00000 -9.20 0.77 0.0074 0.0031 14 0.00036 0.00000 -6.53 0.05 0.2591 0.0027 15 0.00001 0.00000 -7.58 1.49 0.0065 0.0023 16 0.00001 0.00000 -2.21 4.17 0.0057 0.0030 The magnetic center is at X = -149.3 +- 1.0 microns Y = 26.2 +- 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: 03-17-1995 Time: 08:45:00 Magnet Name: 123 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 150.0684 +- 1.007745E-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 0.00071 0.00000 100.83 0.36 0.3475 0.0019 2 0.20558 0.00026 44.91 0.00 100.0000 0.0000 3 0.00017 0.00001 25.30 0.41 0.0832 0.0037 4 0.00009 0.00000 16.84 0.43 0.0442 0.0022 5 0.00005 0.00000 10.31 0.55 0.0250 0.0016 6 0.00045 0.00000 15.14 0.03 0.2165 0.0012 7 0.00001 0.00001 11.69 5.39 0.0056 0.0026 8 0.00001 0.00000 11.57 0.80 0.0051 0.0007 9 0.00001 0.00000 -9.56 0.51 0.0056 0.0015 10 0.00063 0.00000 -9.11 0.02 0.3045 0.0011 11 0.00002 0.00000 7.76 12.87 0.0113 0.0011 12 0.00001 0.00000 6.05 11.54 0.0063 0.0012 13 0.00002 0.00001 -9.39 1.74 0.0095 0.0031 14 0.00054 0.00000 -6.57 0.01 0.2624 0.0007 15 0.00002 0.00001 -3.06 8.68 0.0084 0.0035 16 0.00001 0.00000 0.07 1.29 0.0044 0.0018 The magnetic center is at X = -152.5 +- 0.9 microns Y = 29.2 +- 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: 03-17-1995 Time: 08:51:17 Magnet Name: 123 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 200.3117 +- 3.839792E-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 0.00096 0.00000 101.96 0.13 0.3521 0.0014 2 0.27340 0.00022 44.91 0.00 100.0000 0.0000 3 0.00022 0.00000 24.14 0.73 0.0821 0.0008 4 0.00010 0.00000 20.63 0.55 0.0374 0.0006 5 0.00007 0.00000 10.50 0.35 0.0253 0.0017 6 0.00057 0.00001 15.15 0.05 0.2099 0.0024 7 0.00001 0.00000 4.32 4.31 0.0032 0.0012 8 0.00002 0.00000 4.42 1.23 0.0090 0.0014 9 0.00002 0.00000 -10.11 1.33 0.0072 0.0003 10 0.00085 0.00000 -9.13 0.02 0.3097 0.0009 11 0.00004 0.00001 8.50 13.23 0.0129 0.0025 12 0.00001 0.00000 -6.68 11.51 0.0027 0.0011 13 0.00004 0.00001 -9.59 1.25 0.0141 0.0027 14 0.00072 0.00001 -6.53 0.04 0.2621 0.0028 15 0.00002 0.00001 -6.58 1.40 0.0075 0.0025 16 0.00003 0.00001 -0.64 1.22 0.0102 0.0026 The magnetic center is at X = -153.9 +- 0.7 microns Y = 32.6 +- 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: 03-17-1995 Time: 08:57:34 Magnet Name: 123 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 250.4096 +- 3.589871E-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 0.00115 0.00001 104.06 0.20 0.3390 0.0021 2 0.33849 0.00033 44.91 0.00 100.0000 0.0000 3 0.00026 0.00000 22.47 0.35 0.0767 0.0007 4 0.00011 0.00000 21.23 1.20 0.0335 0.0012 5 0.00009 0.00001 11.09 0.47 0.0263 0.0018 6 0.00063 0.00001 15.13 0.08 0.1869 0.0016 7 0.00001 0.00001 11.01 4.09 0.0026 0.0018 8 0.00002 0.00000 14.49 3.70 0.0046 0.0005 9 0.00003 0.00000 -9.64 0.48 0.0079 0.0010 10 0.00106 0.00000 -9.12 0.02 0.3139 0.0009 11 0.00005 0.00001 0.69 15.54 0.0134 0.0019 12 0.00002 0.00000 -1.35 1.53 0.0046 0.0010 13 0.00005 0.00001 -10.00 0.58 0.0138 0.0024 14 0.00088 0.00001 -6.57 0.01 0.2592 0.0024 15 0.00003 0.00000 -8.06 2.13 0.0078 0.0005 16 0.00002 0.00000 -0.09 5.39 0.0047 0.0011 The magnetic center is at X = -146.9 +- 1.0 microns Y = 36.8 +- 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: 03-17-1995 Time: 09:03:51 Magnet Name: 123 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 300.3957 +- 7.200791E-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 0.00111 0.00000 107.44 0.38 0.2850 0.0012 2 0.39027 0.00029 44.91 0.00 100.0000 0.0000 3 0.00019 0.00000 18.26 0.66 0.0498 0.0009 4 0.00012 0.00001 17.50 1.40 0.0315 0.0026 5 0.00009 0.00001 9.66 0.82 0.0222 0.0018 6 0.00054 0.00001 15.28 0.02 0.1376 0.0014 7 0.00002 0.00001 11.36 2.01 0.0039 0.0016 8 0.00004 0.00001 20.04 0.48 0.0099 0.0016 9 0.00003 0.00000 -9.80 1.04 0.0077 0.0005 10 0.00126 0.00000 -9.15 0.01 0.3237 0.0014 11 0.00004 0.00001 -14.06 0.45 0.0111 0.0024 12 0.00002 0.00000 1.43 0.07 0.0048 0.0009 13 0.00006 0.00002 -8.26 0.86 0.0161 0.0047 14 0.00101 0.00000 -6.55 0.03 0.2591 0.0009 15 0.00002 0.00002 -7.71 0.69 0.0059 0.0040 16 0.00006 0.00000 -0.56 0.34 0.0160 0.0009 The magnetic center is at X = -121.5 +- 0.6 microns Y = 38.2 +- 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: 03-17-1995 Time: 09:10:09 Magnet Name: 123 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 350.3987 +- 4.577637E-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 0.00108 0.00000 109.25 0.33 0.2531 0.0010 2 0.42671 0.00025 44.90 0.00 100.0000 0.0000 3 0.00015 0.00001 13.16 1.03 0.0341 0.0028 4 0.00013 0.00001 15.58 0.74 0.0315 0.0018 5 0.00010 0.00001 9.23 0.54 0.0227 0.0012 6 0.00034 0.00001 15.53 0.05 0.0788 0.0025 7 0.00002 0.00001 10.54 1.15 0.0048 0.0019 8 0.00003 0.00000 9.48 17.92 0.0069 0.0009 9 0.00003 0.00001 -8.96 1.49 0.0080 0.0018 10 0.00142 0.00001 -9.14 0.01 0.3336 0.0012 11 0.00007 0.00001 -12.92 1.73 0.0166 0.0026 12 0.00002 0.00000 -1.29 2.04 0.0046 0.0011 13 0.00011 0.00001 -8.47 0.63 0.0261 0.0014 14 0.00110 0.00001 -6.61 0.02 0.2582 0.0016 15 0.00003 0.00002 -6.68 2.73 0.0062 0.0042 16 0.00008 0.00001 -0.69 0.47 0.0187 0.0023 The magnetic center is at X = -106.7 +- 0.5 microns Y = 37.3 +- 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 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)