SLAC Magnetic Measurements Date: 03-14-1995 Time: 13:13:01 Magnet Name (Serial #): 187 Bar Code Number: 213 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: 03-14-1995 Time: 14:00:14 Magnet Name: 187 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 10.00377 +- 2.906407E-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 0.00006 0.00000 -120.95 0.21 0.3870 0.0024 2 0.01480 0.00001 45.00 0.00 100.0000 0.0000 3 0.00001 0.00000 -55.58 0.87 0.0674 0.0032 4 0.00001 0.00000 10.59 0.91 0.0477 0.0023 5 0.00000 0.00000 12.42 0.59 0.0143 0.0021 6 0.00003 0.00000 15.20 0.09 0.2270 0.0015 7 0.00000 0.00000 6.85 1.47 0.0050 0.0007 8 0.00000 0.00000 11.47 3.68 0.0029 0.0016 9 0.00000 0.00000 0.85 0.58 0.0127 0.0026 10 0.00004 0.00000 -8.99 0.02 0.2991 0.0011 11 0.00000 0.00000 -10.41 1.79 0.0054 0.0007 12 0.00000 0.00000 0.12 8.58 0.0038 0.0023 13 0.00000 0.00000 0.68 0.27 0.0152 0.0018 14 0.00004 0.00000 -6.44 0.01 0.2503 0.0022 15 0.00000 0.00000 -4.28 5.78 0.0096 0.0018 16 0.00000 0.00000 -0.77 6.24 0.0037 0.0015 The magnetic center is at X = 148.3 +- 1.0 microns Y = 88.9 +- 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: 03-14-1995 Time: 14:06:24 Magnet Name: 187 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 25.1061 +- 1.997259E-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 0.00016 0.00000 -151.14 0.14 0.4474 0.0014 2 0.03479 0.00001 45.00 0.00 100.0000 0.0000 3 0.00000 0.00000 -21.72 0.76 0.0141 0.0012 4 0.00001 0.00000 14.86 1.29 0.0343 0.0016 5 0.00000 0.00000 17.69 0.63 0.0136 0.0006 6 0.00008 0.00000 15.15 0.06 0.2276 0.0017 7 0.00000 0.00000 9.07 19.18 0.0017 0.0005 8 0.00000 0.00000 7.85 4.16 0.0039 0.0022 9 0.00001 0.00000 1.70 0.78 0.0146 0.0014 10 0.00010 0.00000 -8.95 0.03 0.3003 0.0009 11 0.00000 0.00000 -8.92 0.85 0.0059 0.0011 12 0.00000 0.00000 5.19 3.05 0.0044 0.0015 13 0.00001 0.00000 1.25 0.50 0.0148 0.0011 14 0.00009 0.00000 -6.46 0.05 0.2531 0.0023 15 0.00000 0.00000 -1.84 4.97 0.0058 0.0023 16 0.00000 0.00000 9.40 1.50 0.0080 0.0009 The magnetic center is at X = 96.4 +- 0.5 microns Y = 175.0 +- 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: 03-14-1995 Time: 14:12:39 Magnet Name: 187 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 50.06812 +- 4.533034E-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 0.00032 0.00000 -157.86 0.06 0.4679 0.0004 2 0.06854 0.00003 45.00 0.00 100.0000 0.0000 3 0.00001 0.00000 -10.73 1.58 0.0191 0.0017 4 0.00003 0.00000 11.65 0.90 0.0430 0.0026 5 0.00001 0.00000 19.77 0.23 0.0136 0.0018 6 0.00016 0.00000 15.13 0.08 0.2289 0.0007 7 0.00000 0.00000 17.98 3.03 0.0033 0.0010 8 0.00000 0.00000 6.74 3.44 0.0028 0.0006 9 0.00001 0.00000 1.19 0.63 0.0146 0.0021 10 0.00021 0.00000 -8.96 0.03 0.2993 0.0013 11 0.00000 0.00000 -7.97 2.06 0.0043 0.0004 12 0.00000 0.00000 7.75 3.67 0.0029 0.0012 13 0.00001 0.00000 0.76 0.37 0.0139 0.0016 14 0.00017 0.00000 -6.40 0.04 0.2505 0.0029 15 0.00000 0.00000 2.75 5.48 0.0068 0.0022 16 0.00000 0.00000 2.96 7.42 0.0015 0.0012 The magnetic center is at X = 78.7 +- 0.2 microns Y = 193.6 +- 0.2 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: 03-14-1995 Time: 14:18:58 Magnet Name: 187 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 100.0596 +- 1.283831E-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 0.00064 0.00000 -161.03 0.09 0.4698 0.0014 2 0.13671 0.00009 45.00 0.00 100.0000 0.0000 3 0.00002 0.00000 -9.06 1.96 0.0172 0.0012 4 0.00006 0.00000 11.53 0.85 0.0404 0.0017 5 0.00002 0.00000 18.98 1.72 0.0124 0.0016 6 0.00031 0.00000 15.18 0.03 0.2301 0.0023 7 0.00000 0.00000 -3.10 18.55 0.0021 0.0011 8 0.00000 0.00000 14.92 4.07 0.0028 0.0016 9 0.00002 0.00000 0.82 0.28 0.0141 0.0008 10 0.00041 0.00000 -8.97 0.01 0.3010 0.0013 11 0.00000 0.00000 -8.15 1.08 0.0035 0.0010 12 0.00001 0.00000 1.52 8.71 0.0050 0.0018 13 0.00002 0.00000 0.40 0.57 0.0153 0.0019 14 0.00034 0.00001 -6.44 0.05 0.2503 0.0043 15 0.00001 0.00000 -0.95 4.33 0.0080 0.0025 16 0.00000 0.00000 7.26 1.71 0.0025 0.0016 The magnetic center is at X = 68.2 +- 0.4 microns Y = 198.4 +- 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: 03-14-1995 Time: 14:25:17 Magnet Name: 187 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 150.072 +- 1.402647E-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 0.00095 0.00000 -160.89 0.21 0.4661 0.0013 2 0.20465 0.00007 44.98 0.00 100.0000 0.0000 3 0.00003 0.00001 -10.90 3.55 0.0149 0.0027 4 0.00008 0.00000 11.22 0.97 0.0409 0.0016 5 0.00003 0.00000 18.11 2.26 0.0134 0.0017 6 0.00046 0.00000 15.15 0.05 0.2225 0.0007 7 0.00001 0.00000 9.80 11.24 0.0025 0.0008 8 0.00001 0.00000 4.93 4.38 0.0029 0.0013 9 0.00003 0.00000 0.70 0.42 0.0147 0.0010 10 0.00061 0.00001 -8.98 0.02 0.2993 0.0026 11 0.00001 0.00000 -8.37 1.20 0.0041 0.0013 12 0.00001 0.00000 12.15 1.30 0.0048 0.0015 13 0.00003 0.00000 0.27 0.25 0.0140 0.0005 14 0.00052 0.00000 -6.43 0.03 0.2551 0.0017 15 0.00001 0.00001 1.86 2.95 0.0052 0.0041 16 0.00001 0.00000 0.52 1.12 0.0067 0.0009 The magnetic center is at X = 68.2 +- 0.8 microns Y = 196.7 +- 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: 03-14-1995 Time: 14:31:36 Magnet Name: 187 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 200.3172 +- 8.594505E-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 0.00128 0.00001 -161.39 0.21 0.4704 0.0021 2 0.27203 0.00010 44.98 0.00 100.0000 0.0000 3 0.00005 0.00001 -7.10 3.44 0.0178 0.0020 4 0.00010 0.00000 10.67 0.91 0.0381 0.0017 5 0.00003 0.00000 19.71 1.72 0.0122 0.0017 6 0.00058 0.00000 15.14 0.08 0.2130 0.0017 7 0.00001 0.00000 -13.90 8.69 0.0027 0.0013 8 0.00001 0.00000 8.01 7.79 0.0027 0.0016 9 0.00004 0.00000 0.29 0.26 0.0137 0.0015 10 0.00083 0.00000 -9.00 0.01 0.3048 0.0005 11 0.00001 0.00000 -8.08 2.86 0.0043 0.0012 12 0.00001 0.00001 -1.73 12.18 0.0043 0.0019 13 0.00004 0.00001 0.55 0.71 0.0146 0.0023 14 0.00069 0.00001 -6.45 0.05 0.2542 0.0039 15 0.00001 0.00001 0.80 6.33 0.0039 0.0021 16 0.00001 0.00001 3.34 7.74 0.0036 0.0032 The magnetic center is at X = 67.0 +- 0.8 microns Y = 199.1 +- 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: 03-14-1995 Time: 14:37:55 Magnet Name: 187 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 250.4164 +- 5.439389E-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 0.00158 0.00001 -163.05 0.20 0.4703 0.0016 2 0.33697 0.00010 44.98 0.00 100.0000 0.0000 3 0.00007 0.00000 -1.82 1.09 0.0201 0.0014 4 0.00010 0.00001 14.28 0.64 0.0296 0.0027 5 0.00004 0.00001 18.72 1.55 0.0132 0.0016 6 0.00063 0.00001 15.18 0.06 0.1882 0.0015 7 0.00001 0.00000 -17.58 4.27 0.0019 0.0011 8 0.00001 0.00001 0.01 3.08 0.0042 0.0019 9 0.00005 0.00000 1.29 0.53 0.0139 0.0012 10 0.00104 0.00000 -9.01 0.01 0.3098 0.0007 11 0.00001 0.00000 -6.88 2.48 0.0042 0.0012 12 0.00001 0.00000 4.67 2.74 0.0041 0.0010 13 0.00006 0.00000 0.11 0.61 0.0171 0.0013 14 0.00084 0.00000 -6.45 0.04 0.2499 0.0012 15 0.00002 0.00002 -0.71 5.53 0.0056 0.0046 16 0.00002 0.00001 -0.59 9.19 0.0053 0.0021 The magnetic center is at X = 61.3 +- 0.7 microns Y = 200.9 +- 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: 03-14-1995 Time: 14:44:14 Magnet Name: 187 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 300.3994 +- 6.751906E-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 0.00187 0.00001 -165.35 0.16 0.4817 0.0018 2 0.38905 0.00016 44.98 0.00 100.0000 0.0000 3 0.00012 0.00001 2.54 0.68 0.0308 0.0019 4 0.00012 0.00001 11.07 0.75 0.0318 0.0015 5 0.00005 0.00000 18.38 1.42 0.0128 0.0010 6 0.00057 0.00001 15.25 0.06 0.1455 0.0014 7 0.00001 0.00000 -19.33 3.90 0.0026 0.0009 8 0.00002 0.00000 20.63 1.83 0.0057 0.0012 9 0.00006 0.00000 0.51 0.52 0.0152 0.0005 10 0.00124 0.00000 -9.00 0.02 0.3183 0.0008 11 0.00001 0.00000 -5.75 1.46 0.0034 0.0009 12 0.00002 0.00001 1.87 2.43 0.0061 0.0013 13 0.00006 0.00001 0.59 0.64 0.0154 0.0017 14 0.00097 0.00001 -6.48 0.02 0.2490 0.0031 15 0.00002 0.00001 -1.16 8.16 0.0052 0.0034 16 0.00002 0.00001 0.45 10.30 0.0058 0.0019 The magnetic center is at X = 54.4 +- 0.6 microns Y = 208.2 +- 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 Date: 03-14-1995 Time: 14:50:34 Magnet Name: 187 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 350.4025 +- 8.843518E-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 0.00208 0.00000 -166.02 0.14 0.4881 0.0004 2 0.42554 0.00010 44.98 0.00 100.0000 0.0000 3 0.00016 0.00001 3.72 1.18 0.0375 0.0012 4 0.00014 0.00001 9.29 0.74 0.0320 0.0026 5 0.00006 0.00000 18.09 1.24 0.0140 0.0008 6 0.00039 0.00001 15.44 0.26 0.0912 0.0016 7 0.00002 0.00001 -15.88 2.90 0.0035 0.0014 8 0.00004 0.00000 -0.18 20.94 0.0099 0.0011 9 0.00006 0.00001 0.02 0.37 0.0147 0.0020 10 0.00140 0.00001 -9.00 0.01 0.3301 0.0014 11 0.00002 0.00000 -7.32 1.89 0.0036 0.0007 12 0.00002 0.00000 1.05 1.09 0.0047 0.0008 13 0.00006 0.00001 0.26 0.72 0.0150 0.0018 14 0.00106 0.00001 -6.45 0.06 0.2484 0.0023 15 0.00002 0.00000 -4.22 3.94 0.0053 0.0011 16 0.00002 0.00001 1.02 1.55 0.0048 0.0012 The magnetic center is at X = 52.7 +- 0.5 microns Y = 211.6 +- 0.2 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 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)