SLAC Magnetic Measurements Date: 10-19-1995 Time: 11:01:28 Magnet Name (Serial #): 163 Bar Code Number: 491 Project: PEP II High Energy Ring Quadrupoles Test Stand: IR8, Q1 Measurement Coil: # 2 Operator: pdr Run Number: 11 Comment: Standardization studies; 10A-350A Standardization Currents (A): 350.0 10.0 350.0 10.0 350.0 10.0 Test Currents (A): 150.0 200.0 250.0 300.0 340.0 Harmonics Measurements Date: 10-19-1995 Time: 11:22:55 Magnet Name: 163 Run Number: 11 FIELD HARMONICS Magnet Current, Imag = 150.1764 +- 1.180117E-03 A Coil Radius, Rcoil = .044646 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 0.00155 0.00000 -145.58 0.17 0.5654 0.0011 2 0.27420 0.00003 44.88 0.00 100.0000 0.0000 3 0.00019 0.00000 21.62 0.47 0.0689 0.0002 4 0.00005 0.00001 20.25 36.58 0.0191 0.0021 5 0.00005 0.00000 5.40 0.67 0.0192 0.0005 6 0.00060 0.00001 15.02 0.09 0.2180 0.0022 7 0.00002 0.00001 9.13 6.09 0.0087 0.0029 8 0.00001 0.00000 -0.64 3.06 0.0052 0.0017 9 0.00006 0.00001 6.02 1.02 0.0206 0.0033 10 0.00083 0.00001 -9.15 0.06 0.3012 0.0026 11 0.00001 0.00000 1.11 10.86 0.0023 0.0007 12 0.00003 0.00001 4.12 9.50 0.0095 0.0040 13 0.00005 0.00001 3.33 0.36 0.0174 0.0029 14 0.00073 0.00001 -6.51 0.10 0.2680 0.0028 15 0.00001 0.00001 -3.80 7.76 0.0048 0.0028 16 0.00002 0.00001 2.61 6.42 0.0070 0.0032 The magnetic center is at X = 142.7 +- 0.7 microns Y = 208.2 +- 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: 10-19-1995 Time: 11:29:11 Magnet Name: 163 Run Number: 11 FIELD HARMONICS Magnet Current, Imag = 200.4537 +- 8.639089E-04 A Coil Radius, Rcoil = .044646 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 0.00204 0.00001 -145.77 0.09 0.5587 0.0015 2 0.36466 0.00007 44.88 0.00 100.0000 0.0000 3 0.00025 0.00001 22.61 0.45 0.0684 0.0023 4 0.00005 0.00001 30.00 4.24 0.0139 0.0019 5 0.00007 0.00001 5.51 0.34 0.0204 0.0016 6 0.00075 0.00001 14.98 0.09 0.2068 0.0024 7 0.00003 0.00001 9.09 2.64 0.0077 0.0019 8 0.00004 0.00001 -20.39 1.28 0.0115 0.0035 9 0.00007 0.00001 6.66 0.86 0.0192 0.0023 10 0.00110 0.00001 -9.15 0.05 0.3009 0.0016 11 0.00001 0.00000 -0.05 10.03 0.0029 0.0011 12 0.00003 0.00001 1.95 3.03 0.0072 0.0018 13 0.00007 0.00001 3.46 0.67 0.0187 0.0024 14 0.00096 0.00001 -6.52 0.06 0.2643 0.0035 15 0.00004 0.00001 -7.96 1.20 0.0097 0.0035 16 0.00003 0.00000 3.00 1.35 0.0092 0.0009 The magnetic center is at X = 140.3 +- 0.5 microns Y = 206.2 +- 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: 10-19-1995 Time: 11:35:29 Magnet Name: 163 Run Number: 11 FIELD HARMONICS Magnet Current, Imag = 250.5727 +- 7.974816E-04 A Coil Radius, Rcoil = .044646 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 0.00252 0.00001 -145.76 0.21 0.5572 0.0022 2 0.45190 0.00009 44.88 0.00 100.0000 0.0000 3 0.00032 0.00000 23.11 0.48 0.0707 0.0010 4 0.00003 0.00002 -5.35 5.85 0.0074 0.0034 5 0.00009 0.00001 6.93 0.64 0.0207 0.0024 6 0.00080 0.00001 15.09 0.08 0.1770 0.0022 7 0.00004 0.00001 7.35 1.62 0.0088 0.0023 8 0.00005 0.00001 -10.42 17.24 0.0117 0.0014 9 0.00010 0.00001 6.07 0.85 0.0211 0.0019 10 0.00138 0.00001 -9.19 0.04 0.3060 0.0032 11 0.00002 0.00000 -0.35 5.26 0.0040 0.0011 12 0.00006 0.00003 -5.04 9.43 0.0137 0.0056 13 0.00008 0.00001 3.30 1.00 0.0168 0.0014 14 0.00118 0.00003 -6.39 0.13 0.2621 0.0069 15 0.00002 0.00002 -2.82 7.48 0.0054 0.0044 16 0.00003 0.00001 4.84 3.77 0.0068 0.0021 The magnetic center is at X = 140.0 +- 0.9 microns Y = 205.6 +- 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 ^ | N S --> x S N Date: 10-19-1995 Time: 11:41:46 Magnet Name: 163 Run Number: 11 FIELD HARMONICS Magnet Current, Imag = 300.5643 +- 1.610869E-03 A Coil Radius, Rcoil = .044646 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 0.00296 0.00001 -143.60 0.07 0.5626 0.0016 2 0.52522 0.00004 44.88 0.00 100.0000 0.0000 3 0.00032 0.00002 22.61 0.71 0.0601 0.0033 4 0.00004 0.00001 -31.34 8.44 0.0069 0.0025 5 0.00013 0.00002 6.64 0.59 0.0248 0.0030 6 0.00069 0.00001 15.07 0.22 0.1321 0.0023 7 0.00005 0.00001 7.34 2.57 0.0089 0.0024 8 0.00004 0.00002 -16.96 2.30 0.0075 0.0038 9 0.00012 0.00002 6.72 0.31 0.0235 0.0042 10 0.00169 0.00003 -9.14 0.01 0.3224 0.0058 11 0.00003 0.00001 9.19 3.31 0.0058 0.0010 12 0.00006 0.00001 -5.13 9.43 0.0121 0.0018 13 0.00009 0.00002 3.07 1.00 0.0179 0.0041 14 0.00139 0.00003 -6.49 0.09 0.2638 0.0063 15 0.00008 0.00001 -2.68 8.54 0.0147 0.0025 16 0.00003 0.00002 5.06 2.10 0.0066 0.0033 The magnetic center is at X = 149.1 +- 0.5 microns Y = 202.2 +- 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: 10-19-1995 Time: 11:48:01 Magnet Name: 163 Run Number: 11 FIELD HARMONICS Magnet Current, Imag = 340.5687 +- 2.601791E-03 A Coil Radius, Rcoil = .044646 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 0.00321 0.00001 -141.90 0.09 0.5648 0.0012 2 0.56757 0.00006 44.88 0.00 100.0000 0.0000 3 0.00030 0.00001 22.66 0.35 0.0534 0.0019 4 0.00005 0.00001 29.84 8.66 0.0095 0.0009 5 0.00014 0.00001 6.05 0.91 0.0244 0.0022 6 0.00048 0.00002 15.43 0.35 0.0837 0.0032 7 0.00007 0.00002 9.24 1.86 0.0123 0.0033 8 0.00003 0.00002 -18.20 3.24 0.0056 0.0038 9 0.00014 0.00002 6.71 0.57 0.0248 0.0032 10 0.00186 0.00004 -9.14 0.04 0.3285 0.0064 11 0.00003 0.00001 9.75 4.21 0.0047 0.0025 12 0.00006 0.00002 7.75 8.61 0.0104 0.0036 13 0.00010 0.00001 2.37 0.64 0.0183 0.0020 14 0.00149 0.00003 -6.45 0.06 0.2620 0.0061 15 0.00008 0.00002 -4.39 7.47 0.0136 0.0042 16 0.00004 0.00002 1.90 4.51 0.0073 0.0031 The magnetic center is at X = 155.6 +- 0.5 microns Y = 198.4 +- 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 ^ | 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)