SLAC Magnetic Measurements Date: 04-27-1995 Time: 06:33:58 Magnet Name (Serial #): 125 Bar Code Number: 470 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: 04-27-1995 Time: 07:21:11 Magnet Name: 125 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 10.00157 +- 3.165218E-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 -88.19 2.27 0.1349 0.0036 2 0.01489 0.00000 45.02 0.00 100.0000 0.0000 3 0.00001 0.00000 -39.57 0.63 0.0678 0.0054 4 0.00001 0.00000 22.15 0.66 0.0788 0.0046 5 0.00000 0.00000 2.69 3.68 0.0198 0.0023 6 0.00003 0.00000 14.87 0.45 0.2128 0.0036 7 0.00000 0.00000 9.19 3.10 0.0085 0.0010 8 0.00000 0.00000 8.03 16.00 0.0052 0.0024 9 0.00000 0.00000 -7.74 0.35 0.0077 0.0014 10 0.00004 0.00000 -8.99 0.04 0.3012 0.0020 11 0.00000 0.00000 2.58 3.79 0.0030 0.0009 12 0.00000 0.00000 10.91 0.62 0.0088 0.0020 13 0.00000 0.00000 0.91 2.70 0.0140 0.0044 14 0.00004 0.00000 -6.36 0.02 0.2535 0.0008 15 0.00000 0.00000 -7.37 1.36 0.0112 0.0065 16 0.00000 0.00000 3.93 8.67 0.0048 0.0014 The magnetic center is at X = 60.2 +- 1.6 microns Y = -1.9 +- 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: 04-27-1995 Time: 07:27:16 Magnet Name: 125 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 25.10515 +- 6.675053E-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 144.79 0.73 0.2029 0.0028 2 0.03494 0.00001 45.01 0.00 100.0000 0.0000 3 0.00001 0.00000 18.18 1.61 0.0264 0.0023 4 0.00003 0.00000 23.11 0.64 0.0817 0.0037 5 0.00001 0.00000 4.39 1.60 0.0204 0.0033 6 0.00007 0.00000 14.81 0.21 0.2088 0.0022 7 0.00000 0.00000 -10.15 17.12 0.0040 0.0006 8 0.00001 0.00000 20.86 0.68 0.0150 0.0040 9 0.00000 0.00000 -7.85 1.12 0.0090 0.0010 10 0.00011 0.00000 -8.94 0.02 0.3010 0.0023 11 0.00000 0.00000 0.63 4.79 0.0048 0.0012 12 0.00000 0.00000 6.09 4.94 0.0086 0.0033 13 0.00000 0.00000 -2.30 1.30 0.0135 0.0039 14 0.00009 0.00000 -6.41 0.04 0.2531 0.0036 15 0.00000 0.00000 -1.27 4.05 0.0070 0.0025 16 0.00000 0.00000 -2.56 6.87 0.0077 0.0026 The magnetic center is at X = -52.2 +- 1.2 microns Y = 74.0 +- 1.2 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: 04-27-1995 Time: 07:33:29 Magnet Name: 125 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 50.06955 +- 2.815779E-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 0.00018 0.00000 142.18 0.75 0.2623 0.0025 2 0.06875 0.00002 45.02 0.00 100.0000 0.0000 3 0.00002 0.00000 15.79 2.50 0.0315 0.0040 4 0.00005 0.00000 21.93 0.17 0.0791 0.0031 5 0.00001 0.00000 4.42 1.13 0.0186 0.0030 6 0.00014 0.00000 14.90 0.04 0.2103 0.0020 7 0.00000 0.00000 -24.10 1.14 0.0036 0.0016 8 0.00000 0.00000 16.92 4.97 0.0036 0.0010 9 0.00001 0.00000 -6.91 1.28 0.0093 0.0010 10 0.00021 0.00000 -8.96 0.02 0.3048 0.0011 11 0.00000 0.00000 -5.10 3.74 0.0025 0.0012 12 0.00000 0.00000 7.93 2.63 0.0046 0.0015 13 0.00001 0.00000 -1.96 0.61 0.0209 0.0052 14 0.00017 0.00000 -6.39 0.07 0.2526 0.0026 15 0.00000 0.00000 1.89 8.04 0.0047 0.0022 16 0.00000 0.00000 -3.31 6.94 0.0060 0.0020 The magnetic center is at X = -71.8 +- 1.4 microns Y = 92.5 +- 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: 04-27-1995 Time: 07:39:46 Magnet Name: 125 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 100.068 +- 2.031626E-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 0.00040 0.00001 140.96 0.76 0.2938 0.0065 2 0.13712 0.00002 45.02 0.00 100.0000 0.0000 3 0.00005 0.00001 14.92 1.89 0.0364 0.0056 4 0.00011 0.00000 21.91 0.33 0.0799 0.0023 5 0.00002 0.00000 6.52 1.57 0.0167 0.0024 6 0.00029 0.00000 14.81 0.05 0.2120 0.0013 7 0.00001 0.00000 -20.82 2.61 0.0048 0.0003 8 0.00001 0.00000 18.15 1.95 0.0050 0.0025 9 0.00001 0.00000 -7.88 1.81 0.0093 0.0018 10 0.00042 0.00000 -8.98 0.04 0.3056 0.0019 11 0.00000 0.00000 1.92 5.37 0.0025 0.0009 12 0.00001 0.00000 9.25 1.94 0.0090 0.0022 13 0.00002 0.00001 -5.47 4.72 0.0143 0.0048 14 0.00035 0.00000 -6.43 0.03 0.2539 0.0026 15 0.00002 0.00001 -4.84 3.13 0.0123 0.0079 16 0.00001 0.00000 -0.74 5.94 0.0101 0.0030 The magnetic center is at X = -82.6 +- 2.3 microns Y = 101.9 +- 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: 04-27-1995 Time: 07:46:01 Magnet Name: 125 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 150.0872 +- 9.896475E-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 0.00064 0.00001 140.14 0.80 0.3120 0.0058 2 0.20526 0.00005 44.99 0.00 100.0000 0.0000 3 0.00009 0.00001 14.53 1.91 0.0415 0.0042 4 0.00016 0.00000 21.49 0.15 0.0775 0.0012 5 0.00004 0.00001 6.80 3.03 0.0183 0.0037 6 0.00042 0.00000 14.75 0.06 0.2034 0.0014 7 0.00001 0.00000 -22.74 1.38 0.0050 0.0016 8 0.00001 0.00000 14.22 3.12 0.0046 0.0010 9 0.00002 0.00001 -6.88 0.71 0.0095 0.0028 10 0.00063 0.00000 -9.01 0.04 0.3054 0.0022 11 0.00001 0.00000 -8.06 6.11 0.0025 0.0008 12 0.00002 0.00000 5.24 11.22 0.0095 0.0012 13 0.00003 0.00002 -3.46 2.28 0.0137 0.0089 14 0.00052 0.00000 -6.46 0.01 0.2549 0.0016 15 0.00002 0.00001 0.97 6.64 0.0106 0.0047 16 0.00001 0.00000 3.10 3.36 0.0037 0.0006 The magnetic center is at X = -89.3 +- 2.2 microns Y = 107.0 +- 2.3 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: 04-27-1995 Time: 07:52:17 Magnet Name: 125 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 200.3373 +- 7.673138E-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 0.00089 0.00001 138.83 0.76 0.3260 0.0053 2 0.27278 0.00008 44.99 0.00 100.0000 0.0000 3 0.00014 0.00002 15.33 1.64 0.0502 0.0057 4 0.00021 0.00001 24.07 0.54 0.0769 0.0023 5 0.00005 0.00000 6.99 1.42 0.0183 0.0016 6 0.00054 0.00000 14.77 0.07 0.1970 0.0010 7 0.00001 0.00000 -8.65 17.57 0.0037 0.0017 8 0.00001 0.00000 3.71 3.49 0.0049 0.0007 9 0.00003 0.00000 -7.84 0.63 0.0102 0.0008 10 0.00085 0.00000 -9.02 0.04 0.3101 0.0014 11 0.00001 0.00000 -2.95 6.35 0.0028 0.0009 12 0.00002 0.00000 9.02 1.21 0.0067 0.0017 13 0.00003 0.00001 -2.22 0.88 0.0126 0.0044 14 0.00070 0.00000 -6.40 0.03 0.2571 0.0011 15 0.00002 0.00001 -4.44 2.87 0.0068 0.0019 16 0.00002 0.00000 -1.59 8.07 0.0067 0.0010 The magnetic center is at X = -95.9 +- 2.1 microns Y = 109.6 +- 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: 04-27-1995 Time: 07:58:34 Magnet Name: 125 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 250.441 +- 4.226574E-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 0.00111 0.00002 137.83 0.84 0.3302 0.0048 2 0.33763 0.00010 44.99 0.00 100.0000 0.0000 3 0.00017 0.00001 17.33 1.26 0.0494 0.0038 4 0.00025 0.00001 22.92 0.44 0.0752 0.0020 5 0.00006 0.00001 6.21 2.64 0.0164 0.0031 6 0.00060 0.00000 14.94 0.03 0.1778 0.0012 7 0.00001 0.00000 -17.99 1.52 0.0035 0.0012 8 0.00003 0.00000 18.42 0.78 0.0087 0.0008 9 0.00003 0.00000 -7.57 0.62 0.0100 0.0008 10 0.00104 0.00001 -8.96 0.02 0.3090 0.0016 11 0.00001 0.00000 5.80 2.33 0.0040 0.0005 12 0.00003 0.00001 3.72 1.75 0.0077 0.0016 13 0.00002 0.00002 -2.70 4.26 0.0055 0.0049 14 0.00085 0.00000 -6.42 0.04 0.2515 0.0015 15 0.00004 0.00001 -3.71 1.39 0.0114 0.0016 16 0.00003 0.00001 -9.01 1.10 0.0079 0.0036 The magnetic center is at X = -99.0 +- 2.1 microns Y = 109.3 +- 2.1 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: 04-27-1995 Time: 08:04:49 Magnet Name: 125 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 300.4318 +- 5.120228E-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 0.00124 0.00002 134.07 1.15 0.3193 0.0046 2 0.38961 0.00009 44.99 0.00 100.0000 0.0000 3 0.00019 0.00002 22.82 2.83 0.0490 0.0062 4 0.00028 0.00001 21.88 0.41 0.0727 0.0015 5 0.00007 0.00001 7.33 1.94 0.0173 0.0036 6 0.00050 0.00000 14.94 0.16 0.1278 0.0005 7 0.00001 0.00000 -20.42 2.04 0.0034 0.0010 8 0.00005 0.00000 21.11 0.39 0.0118 0.0011 9 0.00004 0.00000 -7.54 0.58 0.0102 0.0012 10 0.00126 0.00000 -8.98 0.01 0.3224 0.0012 11 0.00001 0.00000 1.93 9.43 0.0022 0.0006 12 0.00003 0.00001 6.50 2.50 0.0065 0.0025 13 0.00005 0.00001 -3.02 3.22 0.0139 0.0025 14 0.00099 0.00001 -6.42 0.02 0.2540 0.0026 15 0.00003 0.00001 -4.28 3.43 0.0076 0.0019 16 0.00003 0.00002 0.33 2.68 0.0089 0.0052 The magnetic center is at X = -102.5 +- 2.5 microns Y = 99.2 +- 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: 04-27-1995 Time: 08:11:05 Magnet Name: 125 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 350.4412 +- 2.497971E-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 0.00134 0.00002 130.58 0.86 0.3136 0.0049 2 0.42629 0.00005 44.99 0.00 100.0000 0.0000 3 0.00021 0.00001 28.62 1.31 0.0499 0.0019 4 0.00030 0.00001 21.75 0.45 0.0709 0.0025 5 0.00008 0.00001 6.77 1.87 0.0182 0.0018 6 0.00030 0.00001 15.04 0.29 0.0697 0.0014 7 0.00001 0.00000 -19.34 4.06 0.0032 0.0009 8 0.00003 0.00000 18.96 0.68 0.0077 0.0012 9 0.00004 0.00001 -7.06 0.95 0.0103 0.0015 10 0.00141 0.00000 -8.99 0.02 0.3298 0.0012 11 0.00002 0.00001 3.91 7.63 0.0044 0.0015 12 0.00003 0.00001 10.41 1.51 0.0065 0.0025 13 0.00006 0.00003 -3.12 1.75 0.0133 0.0080 14 0.00107 0.00001 -6.44 0.03 0.2509 0.0023 15 0.00003 0.00001 -4.16 3.98 0.0079 0.0033 16 0.00003 0.00002 1.57 1.92 0.0077 0.0051 The magnetic center is at X = -106.4 +- 2.1 microns Y = 91.1 +- 2.1 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 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)