SLAC Magnetic Measurements Date: 01-18-1996 Time: 12:42:00 Magnet Name (Serial #): 885 Bar Code Number: 885 Project: PEP II High Energy Ring Quadrupoles Test Stand: IR8, Q1 Measurement Coil: # 2 Operator: dan Run Number: 1 Comment: none 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: 01-18-1996 Time: 13:29:48 Magnet Name: 885 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 10.00708 +- 1.323728E-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 0.00004 0.00000 166.48 0.49 0.2484 0.0014 2 0.01485 0.00000 44.90 0.00 100.0000 0.0000 3 0.00002 0.00000 20.00 0.31 0.1597 0.0027 4 0.00000 0.00000 -22.48 0.98 0.0148 0.0028 5 0.00000 0.00000 10.89 1.17 0.0258 0.0023 6 0.00003 0.00000 14.95 0.07 0.2212 0.0016 7 0.00000 0.00000 -5.27 17.01 0.0035 0.0008 8 0.00000 0.00000 -18.18 2.71 0.0052 0.0010 9 0.00000 0.00000 6.49 6.02 0.0030 0.0013 10 0.00004 0.00000 -9.15 0.03 0.3002 0.0024 11 0.00000 0.00000 -6.62 8.22 0.0021 0.0005 12 0.00000 0.00000 -7.22 8.02 0.0046 0.0011 13 0.00000 0.00000 -3.28 3.11 0.0055 0.0027 14 0.00004 0.00000 -6.50 0.02 0.2617 0.0017 15 0.00000 0.00000 -5.31 2.26 0.0058 0.0005 16 0.00000 0.00000 6.76 1.24 0.0047 0.0011 The magnetic center is at X = -25.9 +- 0.9 microns Y = 107.9 +- 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: 01-18-1996 Time: 13:35:54 Magnet Name: 885 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 25.1194 +- 4.129201E-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 0.00009 0.00000 160.85 0.44 0.2555 0.0030 2 0.03487 0.00000 44.90 0.00 100.0000 0.0000 3 0.00004 0.00000 19.65 0.48 0.1113 0.0028 4 0.00001 0.00000 -28.34 1.33 0.0196 0.0022 5 0.00001 0.00000 8.91 0.55 0.0229 0.0028 6 0.00008 0.00000 14.95 0.10 0.2253 0.0016 7 0.00000 0.00000 7.78 15.17 0.0020 0.0006 8 0.00000 0.00000 -21.59 0.61 0.0118 0.0017 9 0.00000 0.00000 9.87 6.07 0.0030 0.0017 10 0.00010 0.00000 -9.18 0.04 0.2987 0.0015 11 0.00000 0.00000 0.74 11.45 0.0029 0.0007 12 0.00000 0.00000 -8.37 4.71 0.0043 0.0017 13 0.00000 0.00000 -4.42 1.93 0.0042 0.0016 14 0.00009 0.00000 -6.55 0.05 0.2586 0.0023 15 0.00000 0.00000 -4.93 2.67 0.0067 0.0013 16 0.00000 0.00000 -0.74 5.45 0.0044 0.0016 The magnetic center is at X = -37.4 +- 0.9 microns Y = 107.8 +- 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: 01-18-1996 Time: 13:42:05 Magnet Name: 885 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 50.10084 +- 1.078126E-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 0.00018 0.00000 159.22 0.29 0.2636 0.0013 2 0.06876 0.00002 44.90 0.00 100.0000 0.0000 3 0.00007 0.00000 19.08 0.37 0.0974 0.0015 4 0.00001 0.00000 -24.42 1.31 0.0179 0.0009 5 0.00001 0.00000 8.48 1.56 0.0218 0.0008 6 0.00015 0.00000 14.89 0.07 0.2228 0.0014 7 0.00000 0.00000 10.97 1.39 0.0045 0.0006 8 0.00000 0.00000 -18.57 1.28 0.0032 0.0005 9 0.00000 0.00000 3.45 5.21 0.0022 0.0013 10 0.00021 0.00000 -9.15 0.04 0.3011 0.0010 11 0.00000 0.00000 -7.16 12.12 0.0024 0.0006 12 0.00001 0.00000 -10.99 1.86 0.0077 0.0017 13 0.00000 0.00000 0.25 5.74 0.0038 0.0009 14 0.00018 0.00000 -6.54 0.05 0.2547 0.0006 15 0.00001 0.00000 -5.43 0.87 0.0117 0.0017 16 0.00001 0.00000 7.13 1.74 0.0083 0.0029 The magnetic center is at X = -41.8 +- 0.6 microns Y = 110.1 +- 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 ^ | N S --> x S N Date: 01-18-1996 Time: 13:48:21 Magnet Name: 885 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 100.1289 +- 1.266749E-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 0.00037 0.00000 156.87 0.36 0.2724 0.0012 2 0.13721 0.00002 44.90 0.00 100.0000 0.0000 3 0.00013 0.00000 19.04 0.43 0.0930 0.0001 4 0.00003 0.00000 -22.62 0.72 0.0183 0.0016 5 0.00003 0.00000 8.57 0.49 0.0222 0.0024 6 0.00031 0.00000 14.89 0.03 0.2256 0.0016 7 0.00000 0.00000 15.01 2.03 0.0033 0.0009 8 0.00001 0.00000 -7.36 16.43 0.0039 0.0008 9 0.00000 0.00000 7.14 5.58 0.0025 0.0008 10 0.00041 0.00000 -9.15 0.03 0.3017 0.0015 11 0.00000 0.00000 -11.12 1.12 0.0024 0.0009 12 0.00000 0.00000 -11.65 1.47 0.0034 0.0014 13 0.00001 0.00000 -1.26 3.78 0.0041 0.0013 14 0.00035 0.00000 -6.53 0.03 0.2563 0.0014 15 0.00001 0.00000 -6.02 1.08 0.0088 0.0026 16 0.00000 0.00000 3.71 4.87 0.0036 0.0001 The magnetic center is at X = -47.8 +- 0.7 microns Y = 111.9 +- 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 ^ | N S --> x S N Date: 01-18-1996 Time: 13:54:37 Magnet Name: 885 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 150.1789 +- 1.61754E-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 0.00054 0.00001 149.95 0.18 0.2616 0.0025 2 0.20539 0.00004 44.87 0.00 100.0000 0.0000 3 0.00019 0.00000 18.65 0.18 0.0925 0.0018 4 0.00004 0.00000 -20.13 1.64 0.0173 0.0023 5 0.00004 0.00000 8.44 1.06 0.0218 0.0022 6 0.00045 0.00000 14.88 0.09 0.2175 0.0016 7 0.00001 0.00000 12.92 3.43 0.0049 0.0014 8 0.00001 0.00000 -0.97 19.70 0.0034 0.0015 9 0.00001 0.00000 7.91 5.31 0.0041 0.0021 10 0.00063 0.00000 -9.18 0.03 0.3073 0.0016 11 0.00001 0.00000 -9.44 1.05 0.0025 0.0009 12 0.00002 0.00000 -12.54 0.83 0.0083 0.0018 13 0.00001 0.00000 -1.83 4.05 0.0046 0.0020 14 0.00052 0.00001 -6.55 0.02 0.2545 0.0025 15 0.00001 0.00001 -6.01 0.87 0.0053 0.0025 16 0.00001 0.00001 -0.02 9.07 0.0050 0.0032 The magnetic center is at X = -58.5 +- 0.6 microns Y = 101.2 +- 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: 01-18-1996 Time: 14:00:52 Magnet Name: 885 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 200.4586 +- 1.470416E-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 0.00071 0.00000 149.88 0.11 0.2615 0.0008 2 0.27303 0.00010 44.87 0.00 100.0000 0.0000 3 0.00025 0.00000 18.47 0.13 0.0926 0.0012 4 0.00006 0.00000 -33.08 1.46 0.0204 0.0007 5 0.00006 0.00000 8.29 1.06 0.0215 0.0016 6 0.00057 0.00001 14.86 0.06 0.2092 0.0027 7 0.00001 0.00000 17.45 4.04 0.0033 0.0012 8 0.00001 0.00000 -1.53 1.33 0.0054 0.0005 9 0.00001 0.00000 3.43 11.92 0.0019 0.0007 10 0.00084 0.00001 -9.18 0.01 0.3065 0.0018 11 0.00001 0.00000 -4.15 12.23 0.0031 0.0008 12 0.00002 0.00001 -6.58 12.28 0.0079 0.0031 13 0.00002 0.00000 -2.45 1.60 0.0064 0.0017 14 0.00071 0.00001 -6.52 0.03 0.2596 0.0028 15 0.00002 0.00001 -3.72 0.68 0.0077 0.0039 16 0.00002 0.00001 4.47 7.63 0.0058 0.0019 The magnetic center is at X = -58.6 +- 0.3 microns Y = 101.0 +- 0.4 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: 01-18-1996 Time: 14:07:08 Magnet Name: 885 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 250.5901 +- 1.151862E-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 0.00085 0.00001 149.10 0.15 0.2512 0.0015 2 0.33770 0.00005 44.87 0.00 100.0000 0.0000 3 0.00029 0.00000 18.81 0.39 0.0870 0.0009 4 0.00005 0.00001 -28.91 2.56 0.0154 0.0029 5 0.00008 0.00001 8.48 0.74 0.0241 0.0024 6 0.00063 0.00000 14.95 0.13 0.1871 0.0008 7 0.00001 0.00000 11.24 3.01 0.0043 0.0010 8 0.00003 0.00000 -21.25 0.89 0.0088 0.0009 9 0.00001 0.00000 4.00 8.87 0.0030 0.0011 10 0.00106 0.00000 -9.19 0.03 0.3129 0.0006 11 0.00001 0.00000 -9.96 1.77 0.0029 0.0005 12 0.00002 0.00001 -5.58 1.71 0.0069 0.0023 13 0.00001 0.00000 -3.33 2.95 0.0037 0.0011 14 0.00086 0.00001 -6.54 0.03 0.2551 0.0024 15 0.00003 0.00001 -4.72 0.42 0.0100 0.0026 16 0.00002 0.00002 3.89 8.11 0.0063 0.0049 The magnetic center is at X = -57.6 +- 0.4 microns Y = 96.3 +- 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: 01-18-1996 Time: 14:13:25 Magnet Name: 885 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 300.6024 +- 1.889073E-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 0.00095 0.00001 142.01 0.42 0.2449 0.0027 2 0.38917 0.00008 44.87 0.00 100.0000 0.0000 3 0.00036 0.00001 22.79 0.36 0.0930 0.0015 4 0.00006 0.00001 -23.79 2.58 0.0152 0.0023 5 0.00010 0.00001 7.96 0.39 0.0249 0.0020 6 0.00053 0.00001 14.94 0.08 0.1357 0.0021 7 0.00001 0.00001 16.51 2.78 0.0034 0.0022 8 0.00004 0.00000 -11.02 18.59 0.0097 0.0002 9 0.00001 0.00000 -8.07 7.66 0.0024 0.0011 10 0.00125 0.00001 -9.17 0.02 0.3213 0.0017 11 0.00001 0.00001 -10.20 2.39 0.0030 0.0014 12 0.00003 0.00001 -11.14 1.77 0.0065 0.0016 13 0.00002 0.00001 0.04 3.91 0.0050 0.0022 14 0.00100 0.00000 -6.50 0.03 0.2569 0.0012 15 0.00003 0.00001 -6.68 2.28 0.0079 0.0013 16 0.00002 0.00001 2.66 2.63 0.0055 0.0028 The magnetic center is at X = -67.3 +- 1.0 microns Y = 86.2 +- 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: 01-18-1996 Time: 14:19:41 Magnet Name: 885 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 350.6333 +- 1.987805E-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 0.00101 0.00001 138.48 0.34 0.2384 0.0019 2 0.42519 0.00006 44.87 0.00 100.0000 0.0000 3 0.00040 0.00001 24.05 0.52 0.0944 0.0014 4 0.00006 0.00001 -24.45 2.59 0.0138 0.0020 5 0.00011 0.00001 8.22 0.36 0.0250 0.0013 6 0.00035 0.00000 14.87 0.29 0.0813 0.0004 7 0.00002 0.00001 10.08 7.36 0.0041 0.0021 8 0.00003 0.00000 -9.90 18.26 0.0064 0.0009 9 0.00001 0.00000 1.45 7.51 0.0024 0.0011 10 0.00141 0.00000 -9.16 0.01 0.3318 0.0011 11 0.00001 0.00000 -9.76 5.41 0.0024 0.0009 12 0.00002 0.00000 -10.12 0.49 0.0056 0.0004 13 0.00002 0.00001 -3.00 0.96 0.0057 0.0024 14 0.00108 0.00001 -6.54 0.04 0.2546 0.0014 15 0.00003 0.00000 -4.32 1.15 0.0070 0.0011 16 0.00004 0.00001 3.31 1.29 0.0083 0.0035 The magnetic center is at X = -70.6 +- 0.7 microns Y = 79.7 +- 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 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)