SLAC Magnetic Measurements Date: 04-12-1995 Time: 12:10:57 Magnet Name (Serial #): 153 Bar Code Number: 489 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: 04-12-1995 Time: 12:58:05 Magnet Name: 153 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 10.00992 +- 6.668107E-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 -0.58 0.88 0.1530 0.0030 2 0.01502 0.00000 45.00 0.00 100.0000 0.0000 3 0.00002 0.00000 45.69 0.59 0.1249 0.0022 4 0.00001 0.00000 24.24 0.51 0.0436 0.0026 5 0.00000 0.00000 11.77 1.15 0.0243 0.0008 6 0.00003 0.00000 15.10 0.09 0.2129 0.0011 7 0.00000 0.00000 7.67 1.28 0.0068 0.0006 8 0.00000 0.00000 5.47 4.41 0.0015 0.0011 9 0.00000 0.00000 -0.04 13.82 0.0016 0.0004 10 0.00004 0.00000 -9.06 0.05 0.2984 0.0017 11 0.00000 0.00000 4.94 1.99 0.0022 0.0008 12 0.00000 0.00000 -1.22 11.33 0.0048 0.0031 13 0.00000 0.00000 -3.88 4.28 0.0064 0.0014 14 0.00004 0.00000 -6.35 0.04 0.2560 0.0026 15 0.00000 0.00000 -4.17 2.79 0.0089 0.0039 16 0.00000 0.00000 3.50 8.53 0.0064 0.0008 The magnetic center is at X = 0.7 +- 1.0 microns Y = -68.3 +- 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: 04-12-1995 Time: 13:04:11 Magnet Name: 153 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 25.11616 +- 3.055645E-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 171.04 1.99 0.0626 0.0033 2 0.03504 0.00000 45.00 0.00 100.0000 0.0000 3 0.00001 0.00000 32.28 2.14 0.0368 0.0024 4 0.00001 0.00000 26.35 1.04 0.0383 0.0020 5 0.00001 0.00000 13.00 1.84 0.0191 0.0033 6 0.00008 0.00000 15.14 0.06 0.2149 0.0022 7 0.00000 0.00000 13.76 0.97 0.0073 0.0006 8 0.00000 0.00000 18.91 1.05 0.0088 0.0010 9 0.00000 0.00000 -9.26 5.77 0.0027 0.0011 10 0.00010 0.00000 -9.03 0.05 0.2962 0.0018 11 0.00000 0.00000 5.69 4.41 0.0027 0.0008 12 0.00000 0.00000 2.25 1.26 0.0057 0.0025 13 0.00000 0.00000 -3.05 1.04 0.0074 0.0029 14 0.00009 0.00000 -6.37 0.02 0.2556 0.0018 15 0.00000 0.00000 -5.21 0.74 0.0095 0.0020 16 0.00000 0.00000 2.67 6.80 0.0037 0.0010 The magnetic center is at X = -4.4 +- 1.0 microns Y = 27.6 +- 1.5 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: 04-12-1995 Time: 13:10:23 Magnet Name: 153 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 50.07813 +- 4.434124E-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 0.00007 0.00000 158.99 0.50 0.1065 0.0026 2 0.06889 0.00001 45.00 0.00 100.0000 0.0000 3 0.00002 0.00000 27.55 0.73 0.0326 0.0027 4 0.00002 0.00000 24.20 0.97 0.0331 0.0017 5 0.00001 0.00000 13.90 2.08 0.0192 0.0032 6 0.00015 0.00000 15.09 0.11 0.2136 0.0019 7 0.00001 0.00000 13.23 0.89 0.0089 0.0008 8 0.00000 0.00000 8.65 1.51 0.0041 0.0008 9 0.00000 0.00000 3.35 7.32 0.0031 0.0010 10 0.00021 0.00000 -9.05 0.05 0.2990 0.0005 11 0.00000 0.00000 0.06 2.86 0.0031 0.0008 12 0.00000 0.00000 0.73 14.09 0.0054 0.0024 13 0.00001 0.00000 -2.55 2.00 0.0089 0.0017 14 0.00017 0.00000 -6.35 0.03 0.2530 0.0025 15 0.00001 0.00000 -5.58 1.95 0.0081 0.0036 16 0.00000 0.00000 3.93 6.07 0.0051 0.0027 The magnetic center is at X = -17.1 +- 0.6 microns Y = 44.4 +- 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: 04-12-1995 Time: 13:16:39 Magnet Name: 153 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 100.0713 +- 1.069939E-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 0.00017 0.00000 156.22 0.24 0.1259 0.0027 2 0.13739 0.00003 45.00 0.00 100.0000 0.0000 3 0.00004 0.00000 27.09 1.40 0.0298 0.0029 4 0.00004 0.00000 23.96 0.88 0.0319 0.0023 5 0.00002 0.00000 14.25 2.08 0.0164 0.0020 6 0.00029 0.00000 15.09 0.11 0.2146 0.0013 7 0.00001 0.00000 13.67 0.86 0.0068 0.0006 8 0.00001 0.00000 7.12 2.21 0.0038 0.0010 9 0.00000 0.00000 -6.09 11.62 0.0024 0.0006 10 0.00041 0.00000 -9.03 0.01 0.2995 0.0013 11 0.00000 0.00000 3.95 8.41 0.0021 0.0010 12 0.00000 0.00000 -1.88 9.93 0.0036 0.0021 13 0.00001 0.00000 -7.53 3.82 0.0042 0.0024 14 0.00035 0.00000 -6.38 0.03 0.2540 0.0031 15 0.00002 0.00000 -2.72 0.66 0.0118 0.0034 16 0.00001 0.00000 4.51 6.07 0.0053 0.0028 The magnetic center is at X = -22.7 +- 0.5 microns Y = 51.5 +- 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: 04-12-1995 Time: 13:22:54 Magnet Name: 153 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 150.0855 +- 1.120846E-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 0.00028 0.00000 155.85 0.85 0.1348 0.0016 2 0.20552 0.00005 44.97 0.00 100.0000 0.0000 3 0.00006 0.00000 23.50 1.04 0.0287 0.0007 4 0.00007 0.00000 23.70 0.90 0.0324 0.0013 5 0.00004 0.00001 14.42 1.29 0.0175 0.0033 6 0.00042 0.00000 15.07 0.12 0.2042 0.0012 7 0.00001 0.00001 13.52 1.62 0.0073 0.0025 8 0.00001 0.00000 10.74 1.35 0.0037 0.0014 9 0.00000 0.00000 3.01 7.73 0.0018 0.0010 10 0.00062 0.00000 -9.07 0.02 0.3036 0.0022 11 0.00001 0.00000 3.35 3.94 0.0026 0.0022 12 0.00002 0.00000 -7.03 10.50 0.0074 0.0017 13 0.00002 0.00000 -0.31 2.88 0.0083 0.0019 14 0.00052 0.00000 -6.41 0.03 0.2535 0.0023 15 0.00003 0.00001 -5.39 0.73 0.0136 0.0033 16 0.00001 0.00001 -1.05 8.10 0.0063 0.0033 The magnetic center is at X = -24.6 +- 0.9 microns Y = 54.9 +- 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: 04-12-1995 Time: 13:29:10 Magnet Name: 153 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 200.3372 +- 9.240705E-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 0.00038 0.00000 156.80 0.59 0.1378 0.0015 2 0.27311 0.00004 44.97 0.00 100.0000 0.0000 3 0.00007 0.00001 23.41 1.77 0.0259 0.0031 4 0.00010 0.00001 30.71 1.02 0.0355 0.0023 5 0.00004 0.00000 15.00 1.62 0.0157 0.0014 6 0.00054 0.00000 15.11 0.05 0.1968 0.0008 7 0.00002 0.00000 14.37 1.54 0.0070 0.0007 8 0.00003 0.00000 1.94 1.02 0.0102 0.0010 9 0.00001 0.00000 -5.29 11.37 0.0022 0.0012 10 0.00083 0.00000 -9.06 0.01 0.3051 0.0016 11 0.00001 0.00000 5.55 2.27 0.0019 0.0008 12 0.00001 0.00000 2.21 9.40 0.0048 0.0016 13 0.00001 0.00001 -0.44 8.44 0.0053 0.0026 14 0.00070 0.00000 -6.40 0.03 0.2570 0.0014 15 0.00003 0.00001 -4.68 1.12 0.0123 0.0029 16 0.00002 0.00001 -1.39 8.66 0.0080 0.0026 The magnetic center is at X = -24.2 +- 0.6 microns Y = 56.6 +- 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: 04-12-1995 Time: 13:35:27 Magnet Name: 153 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 250.4419 +- 8.934539E-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 0.00050 0.00001 157.39 0.76 0.1485 0.0032 2 0.33790 0.00003 44.97 0.00 100.0000 0.0000 3 0.00010 0.00000 20.10 1.11 0.0293 0.0014 4 0.00011 0.00001 28.40 0.44 0.0330 0.0028 5 0.00006 0.00001 14.56 1.27 0.0175 0.0023 6 0.00058 0.00000 15.07 0.02 0.1713 0.0011 7 0.00003 0.00000 13.87 0.50 0.0085 0.0004 8 0.00001 0.00000 14.93 1.51 0.0041 0.0007 9 0.00001 0.00000 4.03 9.62 0.0019 0.0011 10 0.00104 0.00001 -9.07 0.02 0.3069 0.0016 11 0.00001 0.00000 4.74 2.87 0.0025 0.0012 12 0.00002 0.00000 2.66 3.66 0.0056 0.0014 13 0.00003 0.00001 -4.03 5.48 0.0085 0.0019 14 0.00086 0.00001 -6.40 0.05 0.2549 0.0018 15 0.00004 0.00001 -3.59 1.77 0.0109 0.0037 16 0.00003 0.00001 9.61 1.44 0.0080 0.0018 The magnetic center is at X = -25.5 +- 1.0 microns Y = 61.2 +- 1.4 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: 04-12-1995 Time: 13:41:43 Magnet Name: 153 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 300.4268 +- 6.794874E-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 157.38 0.81 0.1352 0.0018 2 0.38967 0.00004 44.97 0.00 100.0000 0.0000 3 0.00009 0.00001 21.30 0.75 0.0231 0.0030 4 0.00011 0.00001 25.43 1.30 0.0289 0.0017 5 0.00006 0.00001 12.50 1.05 0.0158 0.0020 6 0.00047 0.00000 15.02 0.16 0.1194 0.0007 7 0.00003 0.00000 11.75 1.10 0.0074 0.0008 8 0.00002 0.00000 17.33 2.07 0.0051 0.0007 9 0.00001 0.00001 -4.50 6.60 0.0031 0.0017 10 0.00124 0.00001 -9.06 0.04 0.3172 0.0029 11 0.00001 0.00000 1.76 4.03 0.0024 0.0005 12 0.00001 0.00001 6.37 3.30 0.0032 0.0013 13 0.00003 0.00001 -0.03 5.22 0.0065 0.0036 14 0.00100 0.00000 -6.39 0.03 0.2576 0.0013 15 0.00004 0.00003 -5.38 1.46 0.0093 0.0065 16 0.00001 0.00001 5.22 2.87 0.0037 0.0031 The magnetic center is at X = -23.2 +- 0.8 microns Y = 55.7 +- 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: 04-12-1995 Time: 13:47:59 Magnet Name: 153 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 350.434 +- 1.208627E-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 0.00050 0.00001 153.14 0.46 0.1180 0.0034 2 0.42592 0.00007 44.97 0.00 100.0000 0.0000 3 0.00010 0.00001 28.01 1.29 0.0239 0.0030 4 0.00012 0.00001 26.55 1.15 0.0272 0.0019 5 0.00007 0.00001 12.23 1.53 0.0168 0.0022 6 0.00026 0.00000 15.16 0.29 0.0612 0.0010 7 0.00003 0.00001 11.32 1.04 0.0073 0.0012 8 0.00002 0.00000 12.91 2.12 0.0037 0.0006 9 0.00000 0.00000 -0.23 9.49 0.0010 0.0009 10 0.00139 0.00000 -9.06 0.03 0.3270 0.0006 11 0.00002 0.00001 0.70 4.26 0.0037 0.0015 12 0.00002 0.00001 0.62 12.03 0.0045 0.0012 13 0.00003 0.00002 -1.74 2.33 0.0073 0.0036 14 0.00108 0.00001 -6.38 0.01 0.2530 0.0026 15 0.00005 0.00000 -5.39 1.56 0.0109 0.0011 16 0.00003 0.00001 2.75 1.97 0.0075 0.0030 The magnetic center is at X = -23.8 +- 0.8 microns Y = 47.0 +- 1.4 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 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)