SLAC Magnetic Measurements Date: 04-27-1995 Time: 11:50:11 Magnet Name (Serial #): 124 Bar Code Number: 398 Project: PEP II High Energy Ring Quadrupoles Test Stand: IR8, Q1 Measurement Coil: # 2 Operator: janitor 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: 12:37:19 Magnet Name: 124 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 10.00918 +- 2.857787E-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 0.00005 0.00000 -92.37 0.67 0.3044 0.0013 2 0.01487 0.00000 45.10 0.00 100.0000 0.0000 3 0.00001 0.00000 53.93 0.77 0.0473 0.0029 4 0.00000 0.00000 29.31 3.50 0.0143 0.0045 5 0.00000 0.00000 -10.14 8.07 0.0035 0.0028 6 0.00003 0.00000 15.46 0.10 0.2208 0.0060 7 0.00000 0.00000 14.57 4.02 0.0061 0.0014 8 0.00000 0.00000 9.80 14.93 0.0022 0.0008 9 0.00000 0.00000 6.88 1.28 0.0032 0.0008 10 0.00004 0.00000 -8.90 0.03 0.2982 0.0009 11 0.00000 0.00000 -4.47 6.90 0.0023 0.0009 12 0.00000 0.00000 13.71 1.66 0.0049 0.0028 13 0.00000 0.00000 -0.56 3.65 0.0058 0.0039 14 0.00004 0.00000 -6.33 0.01 0.2567 0.0015 15 0.00000 0.00000 -1.84 2.08 0.0065 0.0021 16 0.00000 0.00000 3.79 4.93 0.0044 0.0011 The magnetic center is at X = 135.9 +- 0.6 microns Y = 5.6 +- 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 ^ | N S --> x S N Date: 04-27-1995 Time: 12:43:26 Magnet Name: 124 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 25.11613 +- 3.276631E-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 0.00006 0.00000 -136.27 1.58 0.1651 0.0054 2 0.03496 0.00001 45.10 0.00 100.0000 0.0000 3 0.00002 0.00000 36.27 1.71 0.0604 0.0024 4 0.00001 0.00000 37.86 1.99 0.0188 0.0034 5 0.00000 0.00000 5.87 8.55 0.0056 0.0017 6 0.00008 0.00000 15.29 0.07 0.2260 0.0012 7 0.00000 0.00000 12.73 5.71 0.0041 0.0014 8 0.00000 0.00000 10.92 18.90 0.0104 0.0015 9 0.00000 0.00000 6.62 1.12 0.0035 0.0006 10 0.00010 0.00000 -8.87 0.04 0.2987 0.0014 11 0.00000 0.00000 -0.96 8.93 0.0025 0.0010 12 0.00000 0.00000 2.98 2.26 0.0060 0.0024 13 0.00000 0.00000 0.88 4.32 0.0067 0.0023 14 0.00009 0.00000 -6.32 0.02 0.2541 0.0024 15 0.00000 0.00000 -2.29 2.76 0.0065 0.0029 16 0.00000 0.00000 2.83 6.14 0.0064 0.0034 The magnetic center is at X = 51.0 +- 2.2 microns Y = 53.3 +- 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: 12:49:37 Magnet Name: 124 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 50.08066 +- 3.838892E-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 0.00011 0.00000 -160.58 1.15 0.1599 0.0041 2 0.06884 0.00002 45.10 0.00 100.0000 0.0000 3 0.00005 0.00000 33.70 1.40 0.0666 0.0036 4 0.00001 0.00000 33.97 2.71 0.0123 0.0022 5 0.00000 0.00000 9.01 11.51 0.0056 0.0022 6 0.00016 0.00000 15.27 0.02 0.2271 0.0018 7 0.00000 0.00000 13.43 8.37 0.0032 0.0006 8 0.00000 0.00000 7.31 16.01 0.0036 0.0013 9 0.00000 0.00000 6.09 0.66 0.0043 0.0015 10 0.00021 0.00000 -8.91 0.01 0.3004 0.0019 11 0.00000 0.00000 0.94 1.70 0.0024 0.0012 12 0.00000 0.00000 -12.25 2.26 0.0038 0.0016 13 0.00001 0.00000 0.24 1.96 0.0100 0.0011 14 0.00017 0.00000 -6.34 0.03 0.2504 0.0012 15 0.00000 0.00000 -0.62 2.72 0.0062 0.0024 16 0.00000 0.00000 -4.51 5.16 0.0047 0.0013 The magnetic center is at X = 23.7 +- 1.5 microns Y = 67.3 +- 1.8 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: 04-27-1995 Time: 12:55:54 Magnet Name: 124 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 100.0759 +- 1.19286E-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 0.00022 0.00001 -168.32 1.27 0.1566 0.0047 2 0.13734 0.00004 45.10 0.00 100.0000 0.0000 3 0.00009 0.00001 34.62 1.17 0.0669 0.0044 4 0.00002 0.00000 35.49 3.42 0.0117 0.0029 5 0.00001 0.00000 13.12 4.84 0.0066 0.0007 6 0.00031 0.00000 15.26 0.07 0.2273 0.0019 7 0.00000 0.00000 3.18 13.53 0.0028 0.0004 8 0.00000 0.00000 -1.59 16.96 0.0036 0.0010 9 0.00001 0.00000 5.02 1.54 0.0049 0.0009 10 0.00041 0.00000 -8.91 0.04 0.3013 0.0023 11 0.00000 0.00000 -4.26 5.09 0.0023 0.0008 12 0.00000 0.00000 9.62 2.83 0.0030 0.0006 13 0.00001 0.00001 -0.92 2.26 0.0097 0.0042 14 0.00035 0.00000 -6.36 0.04 0.2544 0.0013 15 0.00001 0.00000 -2.02 3.21 0.0064 0.0028 16 0.00001 0.00000 3.17 2.06 0.0050 0.0020 The magnetic center is at X = 14.2 +- 1.6 microns Y = 68.5 +- 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: 13:02:09 Magnet Name: 124 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 150.0928 +- 1.626368E-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 0.00030 0.00001 -172.91 1.37 0.1454 0.0072 2 0.20553 0.00002 45.08 0.00 100.0000 0.0000 3 0.00014 0.00001 35.43 1.76 0.0659 0.0035 4 0.00002 0.00000 34.32 5.57 0.0109 0.0024 5 0.00001 0.00001 9.15 4.93 0.0060 0.0029 6 0.00045 0.00000 15.27 0.04 0.2177 0.0018 7 0.00001 0.00000 1.16 18.68 0.0029 0.0008 8 0.00001 0.00000 3.70 13.94 0.0031 0.0008 9 0.00001 0.00000 7.04 1.78 0.0043 0.0020 10 0.00062 0.00000 -8.95 0.02 0.3019 0.0015 11 0.00001 0.00000 -3.29 5.71 0.0029 0.0014 12 0.00002 0.00000 13.76 1.11 0.0083 0.0008 13 0.00002 0.00000 0.26 1.17 0.0109 0.0022 14 0.00053 0.00000 -6.37 0.02 0.2562 0.0012 15 0.00001 0.00000 -4.20 4.74 0.0044 0.0015 16 0.00002 0.00001 7.68 2.34 0.0079 0.0026 The magnetic center is at X = 8.0 +- 1.6 microns Y = 64.4 +- 3.2 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: 13:08:25 Magnet Name: 124 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 200.3504 +- 6.345712E-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 0.00040 0.00001 -87.61 154.39 0.1458 0.0054 2 0.27325 0.00005 45.08 0.00 100.0000 0.0000 3 0.00019 0.00001 34.23 1.28 0.0680 0.0040 4 0.00007 0.00000 40.96 0.97 0.0242 0.0008 5 0.00002 0.00000 12.97 0.89 0.0085 0.0018 6 0.00058 0.00000 15.24 0.08 0.2105 0.0013 7 0.00001 0.00000 -3.96 18.21 0.0019 0.0008 8 0.00002 0.00001 0.41 1.64 0.0062 0.0020 9 0.00001 0.00000 6.26 1.72 0.0043 0.0016 10 0.00084 0.00001 -8.91 0.02 0.3083 0.0019 11 0.00000 0.00000 7.26 6.70 0.0018 0.0004 12 0.00001 0.00000 -0.06 9.16 0.0030 0.0007 13 0.00002 0.00000 0.96 2.39 0.0062 0.0018 14 0.00069 0.00000 -6.38 0.01 0.2539 0.0013 15 0.00001 0.00001 -2.72 1.37 0.0054 0.0035 16 0.00001 0.00001 -3.05 7.81 0.0054 0.0025 The magnetic center is at X = 65.1 +- 7.7 microns Y = -2.7 +- 175.4 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: 13:14:41 Magnet Name: 124 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 250.4577 +- 3.553202E-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 0.00052 0.00002 -0.73 178.89 0.1526 0.0064 2 0.33813 0.00006 45.08 0.00 100.0000 0.0000 3 0.00024 0.00001 33.26 1.33 0.0699 0.0044 4 0.00006 0.00001 38.54 2.06 0.0171 0.0018 5 0.00002 0.00001 8.60 4.39 0.0072 0.0026 6 0.00063 0.00000 15.34 0.06 0.1875 0.0011 7 0.00001 0.00000 7.63 15.35 0.0021 0.0007 8 0.00002 0.00001 9.76 17.91 0.0071 0.0017 9 0.00001 0.00000 7.42 1.10 0.0032 0.0010 10 0.00105 0.00001 -8.89 0.02 0.3103 0.0020 11 0.00001 0.00000 -1.39 8.02 0.0020 0.0010 12 0.00002 0.00001 0.11 1.83 0.0063 0.0020 13 0.00003 0.00000 1.17 1.59 0.0100 0.0013 14 0.00085 0.00000 -6.36 0.05 0.2508 0.0008 15 0.00001 0.00001 -3.42 1.67 0.0039 0.0019 16 0.00002 0.00001 4.94 8.65 0.0069 0.0028 The magnetic center is at X = 0.9 +- 212.8 microns Y = -68.2 +- 4.0 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: 04-27-1995 Time: 13:20:57 Magnet Name: 124 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 300.4436 +- 9.281559E-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 0.00062 0.00002 -171.78 1.76 0.1602 0.0062 2 0.38996 0.00004 45.07 0.00 100.0000 0.0000 3 0.00021 0.00001 32.80 1.51 0.0539 0.0023 4 0.00005 0.00001 37.48 3.25 0.0128 0.0014 5 0.00003 0.00001 13.07 5.80 0.0077 0.0016 6 0.00053 0.00001 15.37 0.04 0.1372 0.0013 7 0.00001 0.00000 17.46 7.65 0.0013 0.0006 8 0.00004 0.00000 -10.56 18.93 0.0093 0.0005 9 0.00002 0.00000 6.98 2.05 0.0049 0.0011 10 0.00125 0.00000 -8.92 0.01 0.3215 0.0006 11 0.00001 0.00000 0.93 6.23 0.0027 0.0009 12 0.00002 0.00001 -6.10 2.39 0.0045 0.0026 13 0.00004 0.00001 1.01 1.37 0.0099 0.0031 14 0.00099 0.00000 -6.34 0.02 0.2538 0.0005 15 0.00002 0.00001 -2.43 5.54 0.0048 0.0023 16 0.00003 0.00000 3.69 0.66 0.0075 0.0009 The magnetic center is at X = 10.2 +- 2.2 microns Y = 70.8 +- 2.8 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: 04-27-1995 Time: 13:27:13 Magnet Name: 124 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 350.4539 +- 2.511218E-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 0.00003 -166.95 1.59 0.1668 0.0062 2 0.42619 0.00010 45.07 0.00 100.0000 0.0000 3 0.00020 0.00001 32.77 1.86 0.0461 0.0019 4 0.00005 0.00001 37.19 3.09 0.0126 0.0027 5 0.00004 0.00000 11.09 3.88 0.0090 0.0011 6 0.00033 0.00000 15.71 0.20 0.0782 0.0011 7 0.00001 0.00000 20.28 4.05 0.0022 0.0009 8 0.00003 0.00000 0.41 21.98 0.0068 0.0006 9 0.00002 0.00001 6.56 0.42 0.0054 0.0013 10 0.00141 0.00001 -8.92 0.01 0.3311 0.0012 11 0.00001 0.00000 2.49 8.66 0.0021 0.0009 12 0.00002 0.00001 -7.30 10.95 0.0044 0.0019 13 0.00002 0.00001 1.38 2.99 0.0055 0.0029 14 0.00108 0.00000 -6.36 0.03 0.2532 0.0007 15 0.00003 0.00001 -1.76 2.06 0.0073 0.0030 16 0.00004 0.00001 0.53 0.85 0.0089 0.0031 The magnetic center is at X = 16.8 +- 2.1 microns Y = 72.6 +- 2.8 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 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)