SLAC Magnetic Measurements Date: 07-31-1996 Time: 19:30:09 Magnet Name (Serial #): 125 Bar Code Number: 609 Project: PEP II High Energy Ring Quadrupoles Test Stand: IR8, Q1 Measurement Coil: # 2 Operator: gum 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: 07-31-1996 Time: 20:12:10 Magnet Name: 125 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 9.982325 +- 1.204757E-04 A Coil Radius, Rcoil = .0446588 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 0.00001 0.00000 89.71 1.28 0.0592 0.0025 2 0.01483 0.00000 -45.12 0.00 100.0000 0.0000 3 0.00001 0.00000 -10.21 1.02 0.0550 0.0027 4 0.00002 0.00000 21.38 0.43 0.1223 0.0019 5 0.00000 0.00000 -28.81 1.36 0.0215 0.0029 6 0.00003 0.00000 -15.14 0.10 0.2038 0.0032 7 0.00000 0.00000 -23.02 1.40 0.0102 0.0026 8 0.00000 0.00000 10.44 4.11 0.0056 0.0027 9 0.00000 0.00000 -10.73 0.49 0.0117 0.0009 10 0.00004 0.00000 8.89 0.08 0.2870 0.0093 11 0.00000 0.00000 -5.89 2.35 0.0068 0.0024 12 0.00000 0.00000 -2.72 7.72 0.0177 0.0115 13 0.00000 0.00000 -4.74 1.47 0.0119 0.0017 14 0.00004 0.00000 6.22 0.08 0.2597 0.0061 15 0.00000 0.00000 0.84 2.21 0.0125 0.0036 16 0.00000 0.00000 -6.21 6.15 0.0065 0.0016 The magnetic center is at X = 26.4 +- 1.1 microns Y = 0.1 +- 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: 07-31-1996 Time: 20:18:16 Magnet Name: 125 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 25.06513 +- 9.663074E-04 A Coil Radius, Rcoil = .0446588 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 0.00005 0.00000 71.61 2.61 0.1520 0.0042 2 0.03484 0.00008 -45.12 0.00 100.0000 0.0000 3 0.00001 0.00000 -33.12 2.83 0.0396 0.0087 4 0.00004 0.00000 22.25 0.34 0.1215 0.0027 5 0.00001 0.00000 -28.29 2.37 0.0164 0.0028 6 0.00007 0.00000 -15.14 0.09 0.2074 0.0021 7 0.00000 0.00000 -20.53 2.14 0.0087 0.0020 8 0.00000 0.00000 18.38 0.57 0.0132 0.0012 9 0.00000 0.00000 -10.04 0.65 0.0113 0.0013 10 0.00010 0.00000 8.87 0.21 0.2989 0.0064 11 0.00000 0.00000 -6.04 1.92 0.0067 0.0022 12 0.00001 0.00001 6.01 3.13 0.0217 0.0146 13 0.00000 0.00000 -5.02 0.73 0.0094 0.0014 14 0.00009 0.00000 6.32 0.03 0.2491 0.0055 15 0.00000 0.00000 2.77 2.05 0.0107 0.0017 16 0.00000 0.00000 -3.43 8.59 0.0056 0.0025 The magnetic center is at X = 64.4 +- 2.1 microns Y = 21.4 +- 3.0 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 ^ | S N --> x N S Date: 07-31-1996 Time: 20:24:28 Magnet Name: 125 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 49.96535 +- 1.079312E-03 A Coil Radius, Rcoil = .0446588 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 72.32 1.08 0.1907 0.0024 2 0.06878 0.00001 -45.12 0.00 100.0000 0.0000 3 0.00003 0.00000 -39.62 1.43 0.0502 0.0041 4 0.00008 0.00000 21.81 0.32 0.1230 0.0018 5 0.00001 0.00000 -27.90 1.37 0.0150 0.0029 6 0.00014 0.00000 -15.20 0.11 0.2082 0.0029 7 0.00001 0.00000 -20.97 2.51 0.0073 0.0018 8 0.00001 0.00000 14.61 0.83 0.0094 0.0018 9 0.00001 0.00000 -10.78 0.93 0.0113 0.0013 10 0.00020 0.00000 8.91 0.03 0.2964 0.0032 11 0.00000 0.00000 -7.14 0.48 0.0050 0.0013 12 0.00000 0.00000 7.70 1.99 0.0068 0.0034 13 0.00001 0.00000 -5.74 0.35 0.0096 0.0015 14 0.00017 0.00000 6.32 0.06 0.2507 0.0029 15 0.00001 0.00000 1.83 1.19 0.0119 0.0034 16 0.00000 0.00000 0.39 5.35 0.0046 0.0019 The magnetic center is at X = 81.2 +- 1.1 microns Y = 25.9 +- 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: 07-31-1996 Time: 20:30:44 Magnet Name: 125 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 99.8538 +- 8.24363E-04 A Coil Radius, Rcoil = .0446588 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 0.00030 0.00000 77.32 0.80 0.2153 0.0029 2 0.13724 0.00001 -45.12 0.00 100.0000 0.0000 3 0.00006 0.00000 -41.87 0.96 0.0430 0.0025 4 0.00017 0.00000 21.64 0.27 0.1243 0.0028 5 0.00002 0.00000 -29.62 0.43 0.0143 0.0015 6 0.00029 0.00000 -15.15 0.08 0.2092 0.0015 7 0.00001 0.00000 -19.76 1.64 0.0064 0.0012 8 0.00001 0.00000 13.42 0.80 0.0091 0.0020 9 0.00001 0.00000 -10.86 0.32 0.0097 0.0009 10 0.00041 0.00000 8.98 0.06 0.2985 0.0026 11 0.00001 0.00000 -7.74 1.04 0.0052 0.0015 12 0.00001 0.00001 8.30 2.38 0.0067 0.0037 13 0.00001 0.00000 -5.48 0.39 0.0091 0.0009 14 0.00035 0.00000 6.41 0.07 0.2549 0.0022 15 0.00002 0.00001 0.97 1.05 0.0134 0.0040 16 0.00001 0.00000 -3.80 4.20 0.0062 0.0014 The magnetic center is at X = 93.8 +- 1.3 microns Y = 21.1 +- 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: 07-31-1996 Time: 20:36:59 Magnet Name: 125 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 149.7612 +- 8.293611E-04 A Coil Radius, Rcoil = .0446588 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 0.00044 0.00000 88.82 0.36 0.2134 0.0020 2 0.20539 0.00001 -45.14 0.00 100.0000 0.0000 3 0.00006 0.00001 -41.70 0.91 0.0312 0.0025 4 0.00026 0.00001 21.58 0.37 0.1253 0.0038 5 0.00003 0.00000 -29.51 1.95 0.0154 0.0014 6 0.00041 0.00000 -15.18 0.13 0.1993 0.0013 7 0.00002 0.00000 -21.55 2.04 0.0084 0.0018 8 0.00002 0.00000 14.03 2.53 0.0076 0.0014 9 0.00002 0.00001 -10.68 1.39 0.0105 0.0026 10 0.00061 0.00002 8.79 0.14 0.2966 0.0111 11 0.00001 0.00000 -4.42 3.50 0.0062 0.0018 12 0.00004 0.00001 -2.28 7.54 0.0206 0.0050 13 0.00002 0.00000 -5.04 0.54 0.0115 0.0009 14 0.00052 0.00002 6.32 0.19 0.2527 0.0082 15 0.00005 0.00002 2.49 0.85 0.0222 0.0076 16 0.00002 0.00001 -1.59 7.53 0.0084 0.0029 The magnetic center is at X = 95.3 +- 0.9 microns Y = 2.0 +- 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 ^ | S N --> x N S Date: 07-31-1996 Time: 20:43:14 Magnet Name: 125 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 199.8992 +- 4.470851E-04 A Coil Radius, Rcoil = .0446588 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 0.00058 0.00000 89.48 0.63 0.2135 0.0013 2 0.27312 0.00003 -45.15 0.00 100.0000 0.0000 3 0.00010 0.00001 -42.59 1.10 0.0354 0.0031 4 0.00034 0.00000 23.44 0.31 0.1241 0.0014 5 0.00004 0.00001 -28.72 1.41 0.0151 0.0021 6 0.00053 0.00000 -15.19 0.06 0.1928 0.0007 7 0.00002 0.00000 -21.29 1.90 0.0056 0.0012 8 0.00003 0.00001 7.01 1.76 0.0095 0.0020 9 0.00003 0.00000 -9.80 1.08 0.0118 0.0014 10 0.00083 0.00004 8.76 0.11 0.3043 0.0133 11 0.00002 0.00000 -4.60 1.36 0.0074 0.0013 12 0.00006 0.00002 0.16 4.93 0.0215 0.0077 13 0.00003 0.00000 -4.61 0.36 0.0126 0.0011 14 0.00070 0.00001 6.36 0.15 0.2545 0.0019 15 0.00005 0.00002 3.36 0.98 0.0187 0.0078 16 0.00003 0.00001 -1.25 6.90 0.0101 0.0027 The magnetic center is at X = 95.3 +- 0.6 microns Y = 0.9 +- 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 ^ | S N --> x N S Date: 07-31-1996 Time: 20:49:30 Magnet Name: 125 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 249.8797 +- 9.187008E-04 A Coil Radius, Rcoil = .0446588 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 88.62 0.57 0.2102 0.0010 2 0.33798 0.00006 -45.15 0.00 100.0000 0.0000 3 0.00012 0.00001 -43.58 0.74 0.0344 0.0043 4 0.00040 0.00001 22.72 0.36 0.1172 0.0023 5 0.00005 0.00001 -28.85 2.42 0.0134 0.0025 6 0.00058 0.00001 -15.13 0.10 0.1706 0.0019 7 0.00002 0.00000 -21.68 1.99 0.0055 0.0011 8 0.00004 0.00000 17.36 0.71 0.0110 0.0005 9 0.00003 0.00000 -10.71 0.84 0.0101 0.0013 10 0.00103 0.00003 8.76 0.14 0.3036 0.0093 11 0.00002 0.00000 -4.28 1.32 0.0059 0.0012 12 0.00007 0.00004 -1.24 3.84 0.0217 0.0117 13 0.00004 0.00000 -4.49 0.60 0.0122 0.0006 14 0.00086 0.00001 6.35 0.07 0.2556 0.0033 15 0.00006 0.00002 3.03 1.66 0.0176 0.0045 16 0.00002 0.00001 3.35 7.69 0.0074 0.0026 The magnetic center is at X = 93.8 +- 0.4 microns Y = 2.3 +- 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: 07-31-1996 Time: 20:55:46 Magnet Name: 125 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 299.773 +- 9.247632E-04 A Coil Radius, Rcoil = .0446588 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 0.00081 0.00001 90.80 0.33 0.2091 0.0018 2 0.38967 0.00005 -45.15 0.00 100.0000 0.0000 3 0.00012 0.00001 -39.44 2.01 0.0311 0.0028 4 0.00042 0.00001 21.91 0.27 0.1081 0.0033 5 0.00006 0.00001 -28.08 2.96 0.0153 0.0031 6 0.00046 0.00001 -15.16 0.12 0.1193 0.0024 7 0.00002 0.00001 -22.52 1.30 0.0062 0.0023 8 0.00004 0.00001 18.03 0.77 0.0100 0.0013 9 0.00005 0.00000 -11.06 0.73 0.0132 0.0013 10 0.00120 0.00006 8.83 0.19 0.3092 0.0146 11 0.00003 0.00001 -6.14 1.96 0.0076 0.0015 12 0.00011 0.00007 -2.13 6.51 0.0276 0.0169 13 0.00005 0.00001 -4.54 0.71 0.0134 0.0018 14 0.00100 0.00003 6.24 0.16 0.2573 0.0084 15 0.00006 0.00003 1.58 1.99 0.0146 0.0065 16 0.00003 0.00001 0.55 7.90 0.0066 0.0033 The magnetic center is at X = 93.4 +- 0.8 microns Y = -1.3 +- 0.5 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 ^ | S N --> x N S Date: 07-31-1996 Time: 21:02:02 Magnet Name: 125 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 349.6743 +- 7.398546E-04 A Coil Radius, Rcoil = .0446588 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 0.00090 0.00001 93.57 0.39 0.2119 0.0021 2 0.42595 0.00007 -45.15 0.00 100.0000 0.0000 3 0.00014 0.00001 -33.36 1.85 0.0323 0.0035 4 0.00043 0.00001 22.13 0.36 0.1020 0.0017 5 0.00006 0.00001 -28.26 2.04 0.0147 0.0020 6 0.00027 0.00001 -15.31 0.20 0.0640 0.0014 7 0.00003 0.00000 -20.32 1.27 0.0073 0.0008 8 0.00003 0.00001 16.32 1.69 0.0081 0.0025 9 0.00005 0.00001 -10.92 0.75 0.0121 0.0016 10 0.00136 0.00007 8.95 0.04 0.3202 0.0172 11 0.00003 0.00001 -4.34 1.66 0.0078 0.0014 12 0.00009 0.00004 0.19 10.71 0.0205 0.0086 13 0.00005 0.00000 -4.95 0.32 0.0120 0.0009 14 0.00109 0.00001 6.28 0.03 0.2551 0.0032 15 0.00010 0.00002 2.24 1.05 0.0238 0.0042 16 0.00005 0.00001 0.25 2.50 0.0111 0.0029 The magnetic center is at X = 94.4 +- 0.9 microns Y = -5.9 +- 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 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)