SLAC Magnetic Measurements Date: 04-28-1995 Time: 09:08:45 Magnet Name (Serial #): 157 Bar Code Number: 289 Project: PEP II High Energy Ring Quadrupoles Test Stand: IR8, Q1 Measurement Coil: # 2 Operator: mkl Run Number: 2 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: 04-28-1995 Time: 09:55:51 Magnet Name: 157 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 10.00368 +- 1.902724E-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 0.00007 0.00000 -144.76 0.50 0.4560 0.0040 2 0.01489 0.00000 45.00 0.00 100.0000 0.0000 3 0.00001 0.00000 20.00 0.29 0.0499 0.0054 4 0.00000 0.00000 25.23 1.86 0.0310 0.0037 5 0.00000 0.00000 20.81 3.07 0.0222 0.0044 6 0.00003 0.00000 14.81 0.23 0.2217 0.0057 7 0.00000 0.00000 10.65 10.35 0.0034 0.0015 8 0.00000 0.00000 -8.60 9.29 0.0040 0.0026 9 0.00000 0.00000 2.94 0.57 0.0089 0.0007 10 0.00004 0.00000 -9.00 0.02 0.2970 0.0016 11 0.00000 0.00000 5.66 3.34 0.0031 0.0016 12 0.00000 0.00000 -1.12 10.08 0.0040 0.0010 13 0.00000 0.00000 1.31 0.96 0.0186 0.0046 14 0.00004 0.00000 -6.39 0.03 0.2598 0.0024 15 0.00000 0.00000 -0.66 3.87 0.0090 0.0013 16 0.00000 0.00000 -0.81 3.75 0.0066 0.0021 The magnetic center is at X = 117.5 +- 1.8 microns Y = 166.3 +- 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 Date: 04-28-1995 Time: 10:01:58 Magnet Name: 157 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 25.10713 +- 4.090518E-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 -160.64 0.62 0.3853 0.0042 2 0.03500 0.00001 45.00 0.00 100.0000 0.0000 3 0.00002 0.00000 34.13 1.79 0.0544 0.0009 4 0.00001 0.00000 27.20 1.87 0.0246 0.0033 5 0.00001 0.00000 15.76 2.49 0.0181 0.0021 6 0.00008 0.00000 14.97 0.20 0.2203 0.0032 7 0.00000 0.00000 -0.46 17.49 0.0037 0.0025 8 0.00000 0.00000 8.47 17.23 0.0091 0.0044 9 0.00000 0.00000 3.03 0.75 0.0097 0.0009 10 0.00010 0.00000 -9.01 0.03 0.2982 0.0020 11 0.00000 0.00000 0.60 0.85 0.0032 0.0006 12 0.00000 0.00000 -2.14 5.27 0.0107 0.0054 13 0.00001 0.00000 1.66 0.92 0.0251 0.0025 14 0.00009 0.00000 -6.46 0.07 0.2563 0.0038 15 0.00000 0.00000 -1.42 8.44 0.0069 0.0037 16 0.00000 0.00000 -0.25 6.73 0.0136 0.0061 The magnetic center is at X = 57.0 +- 1.9 microns Y = 162.4 +- 1.9 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: 04-28-1995 Time: 10:08:09 Magnet Name: 157 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 50.07305 +- 4.753165E-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 0.00026 0.00000 -167.71 0.52 0.3722 0.0024 2 0.06890 0.00003 45.00 0.00 100.0000 0.0000 3 0.00004 0.00000 37.83 0.82 0.0617 0.0036 4 0.00002 0.00000 23.86 0.74 0.0221 0.0016 5 0.00001 0.00000 17.51 1.09 0.0171 0.0025 6 0.00015 0.00000 14.96 0.08 0.2198 0.0024 7 0.00000 0.00000 16.22 3.75 0.0026 0.0002 8 0.00000 0.00000 4.97 6.41 0.0047 0.0028 9 0.00001 0.00000 2.16 1.54 0.0074 0.0004 10 0.00021 0.00000 -8.99 0.04 0.2997 0.0008 11 0.00000 0.00000 3.16 2.57 0.0057 0.0021 12 0.00000 0.00000 -2.63 3.39 0.0058 0.0025 13 0.00002 0.00000 1.90 0.87 0.0220 0.0027 14 0.00017 0.00000 -6.44 0.06 0.2525 0.0038 15 0.00000 0.00000 -4.65 5.07 0.0043 0.0021 16 0.00001 0.00000 -1.65 6.21 0.0094 0.0050 The magnetic center is at X = 35.4 +- 1.5 microns Y = 162.4 +- 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: 04-28-1995 Time: 10:14:26 Magnet Name: 157 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 100.0713 +- 8.743566E-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 0.00053 0.00001 -171.40 0.68 0.3838 0.0055 2 0.13744 0.00003 45.00 0.00 100.0000 0.0000 3 0.00009 0.00000 36.39 1.77 0.0623 0.0031 4 0.00003 0.00000 22.96 1.53 0.0212 0.0018 5 0.00002 0.00000 16.55 1.99 0.0149 0.0013 6 0.00030 0.00000 15.06 0.04 0.2214 0.0013 7 0.00000 0.00000 21.12 1.73 0.0025 0.0012 8 0.00001 0.00000 -0.03 6.02 0.0042 0.0018 9 0.00001 0.00000 0.59 1.49 0.0085 0.0013 10 0.00041 0.00000 -8.99 0.04 0.3001 0.0010 11 0.00001 0.00000 4.59 2.90 0.0051 0.0008 12 0.00001 0.00000 -7.03 5.25 0.0070 0.0028 13 0.00003 0.00000 2.81 1.23 0.0236 0.0023 14 0.00035 0.00000 -6.45 0.04 0.2532 0.0020 15 0.00001 0.00000 -5.59 2.12 0.0087 0.0031 16 0.00001 0.00000 1.30 8.64 0.0047 0.0019 The magnetic center is at X = 25.6 +- 2.0 microns Y = 169.5 +- 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: 04-28-1995 Time: 10:20:41 Magnet Name: 157 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 150.0909 +- 1.927234E-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 0.00076 0.00001 -170.20 0.42 0.3717 0.0049 2 0.20572 0.00005 44.98 0.00 100.0000 0.0000 3 0.00013 0.00001 36.34 1.08 0.0636 0.0046 4 0.00004 0.00000 21.91 0.75 0.0206 0.0024 5 0.00003 0.00001 17.66 1.16 0.0170 0.0043 6 0.00044 0.00000 14.98 0.03 0.2128 0.0011 7 0.00001 0.00000 16.48 4.57 0.0037 0.0017 8 0.00001 0.00000 5.64 5.36 0.0068 0.0017 9 0.00002 0.00000 1.42 0.66 0.0083 0.0015 10 0.00062 0.00001 -9.03 0.03 0.2996 0.0028 11 0.00001 0.00000 0.52 9.52 0.0032 0.0007 12 0.00001 0.00001 -2.80 9.48 0.0061 0.0033 13 0.00003 0.00001 2.18 1.39 0.0158 0.0058 14 0.00052 0.00001 -6.52 0.04 0.2546 0.0027 15 0.00001 0.00001 -0.48 7.73 0.0069 0.0059 16 0.00002 0.00001 -0.60 9.86 0.0112 0.0038 The magnetic center is at X = 28.3 +- 1.3 microns Y = 163.6 +- 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: 04-28-1995 Time: 10:26:57 Magnet Name: 157 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 200.3416 +- 1.476303E-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 0.00100 0.00002 -170.67 0.54 0.3661 0.0055 2 0.27342 0.00007 44.98 0.00 100.0000 0.0000 3 0.00017 0.00001 36.85 1.33 0.0634 0.0032 4 0.00007 0.00001 31.52 1.64 0.0272 0.0026 5 0.00004 0.00001 15.86 2.13 0.0163 0.0019 6 0.00056 0.00000 15.04 0.03 0.2044 0.0017 7 0.00001 0.00000 8.07 18.82 0.0028 0.0011 8 0.00002 0.00001 0.26 0.69 0.0091 0.0028 9 0.00002 0.00001 2.09 1.01 0.0082 0.0022 10 0.00083 0.00000 -9.03 0.04 0.3052 0.0007 11 0.00001 0.00000 5.41 4.28 0.0037 0.0017 12 0.00001 0.00000 -5.68 5.69 0.0038 0.0015 13 0.00005 0.00001 2.65 0.33 0.0174 0.0032 14 0.00070 0.00000 -6.48 0.02 0.2565 0.0004 15 0.00003 0.00001 -5.44 2.53 0.0100 0.0024 16 0.00002 0.00001 0.51 9.09 0.0089 0.0043 The magnetic center is at X = 26.5 +- 1.6 microns Y = 161.4 +- 2.5 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: 04-28-1995 Time: 10:33:13 Magnet Name: 157 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 250.4478 +- 7.981018E-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 0.00120 0.00000 -169.77 0.81 0.3555 0.0014 2 0.33842 0.00005 44.98 0.00 100.0000 0.0000 3 0.00021 0.00002 38.63 1.09 0.0632 0.0050 4 0.00008 0.00001 27.55 1.93 0.0233 0.0021 5 0.00006 0.00001 15.86 2.27 0.0185 0.0024 6 0.00062 0.00000 15.00 0.13 0.1822 0.0009 7 0.00001 0.00000 5.97 17.76 0.0034 0.0009 8 0.00001 0.00001 5.79 16.61 0.0037 0.0021 9 0.00003 0.00000 2.82 0.95 0.0091 0.0014 10 0.00104 0.00001 -9.02 0.04 0.3074 0.0027 11 0.00001 0.00001 7.24 5.30 0.0030 0.0015 12 0.00004 0.00001 0.62 2.92 0.0108 0.0034 13 0.00006 0.00001 1.54 0.70 0.0166 0.0027 14 0.00086 0.00001 -6.48 0.10 0.2546 0.0032 15 0.00002 0.00001 -2.49 3.52 0.0069 0.0030 16 0.00004 0.00001 -0.04 9.40 0.0125 0.0042 The magnetic center is at X = 28.2 +- 2.2 microns Y = 156.3 +- 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: 04-28-1995 Time: 10:39:29 Magnet Name: 157 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 300.4381 +- 8.157389E-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 0.00146 0.00003 -167.82 0.55 0.3745 0.0066 2 0.39045 0.00004 44.98 0.00 100.0000 0.0000 3 0.00020 0.00002 37.11 1.68 0.0509 0.0040 4 0.00008 0.00001 26.13 1.89 0.0212 0.0023 5 0.00006 0.00001 14.10 2.06 0.0160 0.0019 6 0.00051 0.00001 15.07 0.11 0.1301 0.0013 7 0.00001 0.00001 18.10 3.83 0.0033 0.0014 8 0.00003 0.00001 20.58 0.97 0.0077 0.0018 9 0.00003 0.00000 1.86 0.76 0.0077 0.0009 10 0.00124 0.00000 -9.03 0.04 0.3175 0.0008 11 0.00001 0.00000 0.74 3.37 0.0024 0.0006 12 0.00002 0.00000 2.50 5.31 0.0050 0.0012 13 0.00008 0.00002 1.56 0.37 0.0201 0.0045 14 0.00100 0.00000 -6.44 0.05 0.2553 0.0004 15 0.00003 0.00001 -0.77 7.89 0.0068 0.0032 16 0.00003 0.00001 0.34 3.89 0.0080 0.0032 The magnetic center is at X = 35.3 +- 1.7 microns Y = 163.5 +- 2.9 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: 04-28-1995 Time: 10:45:45 Magnet Name: 157 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 350.4474 +- 1.346064E-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 0.00166 0.00003 -166.86 0.45 0.3880 0.0064 2 0.42681 0.00004 44.98 0.00 100.0000 0.0000 3 0.00019 0.00002 35.13 1.76 0.0444 0.0045 4 0.00009 0.00001 25.75 1.63 0.0213 0.0014 5 0.00007 0.00001 14.71 1.64 0.0174 0.0020 6 0.00030 0.00001 15.13 0.28 0.0712 0.0029 7 0.00002 0.00001 19.28 2.09 0.0042 0.0012 8 0.00001 0.00001 5.62 16.18 0.0022 0.0026 9 0.00004 0.00000 1.56 0.97 0.0096 0.0011 10 0.00140 0.00001 -9.02 0.03 0.3278 0.0013 11 0.00001 0.00001 -0.43 9.82 0.0020 0.0018 12 0.00003 0.00001 -6.26 7.63 0.0070 0.0031 13 0.00008 0.00002 2.56 0.86 0.0182 0.0039 14 0.00107 0.00002 -6.41 0.09 0.2517 0.0058 15 0.00004 0.00002 -5.88 1.06 0.0086 0.0043 16 0.00003 0.00002 -0.70 3.25 0.0080 0.0045 The magnetic center is at X = 39.4 +- 1.5 microns Y = 168.8 +- 2.8 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)