SLAC Magnetic Measurements Date: 04-21-1995 Time: 06:48:13 Magnet Name (Serial #): 123 Bar Code Number: 466 Project: PEP II High Energy Ring Quadrupoles Test Stand: IR8, Q1 Measurement Coil: # 2 Operator: bmd Run Number: 3 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: 04-21-1995 Time: 07:35:30 Magnet Name: 123 Run Number: 3 FIELD HARMONICS Magnet Current, Imag = 10.00109 +- 3.494045E-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 0.00001 0.00000 26.65 3.55 0.0480 0.0030 2 0.01487 0.00000 45.01 0.00 100.0000 0.0000 3 0.00001 0.00000 23.54 0.75 0.0573 0.0028 4 0.00001 0.00000 19.34 1.53 0.0421 0.0036 5 0.00000 0.00000 7.39 0.88 0.0265 0.0038 6 0.00003 0.00000 15.28 0.14 0.2214 0.0028 7 0.00000 0.00000 7.04 2.11 0.0107 0.0016 8 0.00000 0.00000 10.52 2.57 0.0055 0.0007 9 0.00000 0.00000 -0.72 6.99 0.0020 0.0012 10 0.00004 0.00000 -8.98 0.02 0.2999 0.0010 11 0.00000 0.00000 -10.77 2.14 0.0025 0.0011 12 0.00000 0.00000 4.53 11.00 0.0037 0.0020 13 0.00000 0.00000 -2.93 0.38 0.0096 0.0042 14 0.00004 0.00000 -6.39 0.02 0.2591 0.0024 15 0.00000 0.00000 -3.87 9.16 0.0122 0.0018 16 0.00000 0.00000 1.21 7.25 0.0042 0.0022 The magnetic center is at X = -9.6 +- 1.3 microns Y = -19.1 +- 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: 04-21-1995 Time: 07:41:36 Magnet Name: 123 Run Number: 3 FIELD HARMONICS Magnet Current, Imag = 25.1031 +- 3.909576E-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 101.19 0.94 0.1917 0.0021 2 0.03493 0.00001 45.01 0.00 100.0000 0.0000 3 0.00003 0.00000 24.34 0.47 0.0957 0.0024 4 0.00001 0.00000 21.12 0.74 0.0400 0.0025 5 0.00001 0.00000 9.31 0.31 0.0271 0.0013 6 0.00008 0.00000 15.18 0.08 0.2248 0.0021 7 0.00000 0.00000 6.61 1.61 0.0079 0.0016 8 0.00000 0.00000 18.56 0.40 0.0099 0.0015 9 0.00000 0.00000 -3.12 3.78 0.0024 0.0007 10 0.00010 0.00000 -8.97 0.02 0.3003 0.0016 11 0.00000 0.00000 -2.00 10.43 0.0022 0.0015 12 0.00000 0.00000 1.23 2.48 0.0063 0.0017 13 0.00000 0.00000 -2.57 1.37 0.0111 0.0018 14 0.00009 0.00000 -6.41 0.02 0.2566 0.0014 15 0.00000 0.00000 -4.88 9.51 0.0107 0.0029 16 0.00000 0.00000 -2.97 3.93 0.0061 0.0016 The magnetic center is at X = -84.0 +- 1.0 microns Y = 16.6 +- 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: 04-21-1995 Time: 07:47:48 Magnet Name: 123 Run Number: 3 FIELD HARMONICS Magnet Current, Imag = 50.06723 +- 6.239596E-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 0.00017 0.00000 106.13 0.35 0.2448 0.0032 2 0.06881 0.00002 45.01 0.00 100.0000 0.0000 3 0.00007 0.00000 23.85 0.31 0.1001 0.0031 4 0.00003 0.00000 18.04 0.90 0.0408 0.0021 5 0.00002 0.00000 9.35 0.79 0.0278 0.0021 6 0.00015 0.00000 15.19 0.05 0.2237 0.0012 7 0.00000 0.00000 5.17 1.33 0.0060 0.0011 8 0.00000 0.00000 10.74 1.75 0.0054 0.0007 9 0.00000 0.00000 -3.33 1.41 0.0041 0.0019 10 0.00021 0.00000 -9.00 0.01 0.3016 0.0012 11 0.00000 0.00000 -12.54 2.60 0.0022 0.0005 12 0.00000 0.00000 8.63 3.45 0.0040 0.0012 13 0.00001 0.00000 -3.89 2.39 0.0092 0.0022 14 0.00017 0.00000 -6.43 0.03 0.2536 0.0018 15 0.00001 0.00000 -8.07 2.75 0.0094 0.0039 16 0.00000 0.00000 -3.54 7.38 0.0038 0.0026 The magnetic center is at X = -105.1 +- 1.4 microns Y = 30.4 +- 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: 04-21-1995 Time: 07:54:04 Magnet Name: 123 Run Number: 3 FIELD HARMONICS Magnet Current, Imag = 100.0642 +- 2.937317E-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 0.00037 0.00001 106.20 1.38 0.2695 0.0047 2 0.13726 0.00002 45.01 0.00 100.0000 0.0000 3 0.00014 0.00001 25.01 0.86 0.1010 0.0045 4 0.00005 0.00000 18.73 0.86 0.0387 0.0017 5 0.00004 0.00000 10.05 0.64 0.0268 0.0015 6 0.00031 0.00000 15.18 0.04 0.2244 0.0013 7 0.00001 0.00000 5.78 2.06 0.0048 0.0011 8 0.00001 0.00000 10.98 0.31 0.0047 0.0011 9 0.00000 0.00000 -0.75 2.47 0.0036 0.0006 10 0.00042 0.00000 -8.97 0.03 0.3027 0.0017 11 0.00000 0.00000 -8.16 5.78 0.0016 0.0004 12 0.00000 0.00000 1.74 6.59 0.0030 0.0019 13 0.00001 0.00000 -2.00 2.34 0.0109 0.0026 14 0.00035 0.00000 -6.43 0.02 0.2552 0.0015 15 0.00001 0.00001 -3.56 8.88 0.0106 0.0051 16 0.00001 0.00000 -2.30 4.02 0.0064 0.0025 The magnetic center is at X = -115.6 +- 2.2 microns Y = 33.6 +- 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 Date: 04-21-1995 Time: 08:00:19 Magnet Name: 123 Run Number: 3 FIELD HARMONICS Magnet Current, Imag = 150.0815 +- 1.645192E-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 0.00057 0.00001 107.87 1.23 0.2756 0.0045 2 0.20550 0.00003 44.99 0.00 100.0000 0.0000 3 0.00021 0.00001 24.32 0.89 0.1010 0.0031 4 0.00008 0.00000 16.60 1.06 0.0373 0.0023 5 0.00005 0.00000 9.63 1.40 0.0259 0.0004 6 0.00044 0.00000 15.15 0.04 0.2145 0.0005 7 0.00001 0.00000 4.08 0.98 0.0060 0.0009 8 0.00001 0.00000 8.24 2.06 0.0060 0.0015 9 0.00000 0.00000 5.32 7.85 0.0014 0.0007 10 0.00062 0.00000 -8.99 0.03 0.3027 0.0014 11 0.00000 0.00000 -5.15 5.63 0.0017 0.0007 12 0.00001 0.00000 6.02 11.33 0.0050 0.0006 13 0.00002 0.00000 -1.04 1.15 0.0100 0.0017 14 0.00052 0.00000 -6.44 0.01 0.2536 0.0024 15 0.00002 0.00000 -9.43 0.90 0.0101 0.0018 16 0.00001 0.00000 -1.11 8.66 0.0066 0.0018 The magnetic center is at X = -117.2 +- 2.1 microns Y = 37.8 +- 2.6 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: 04-21-1995 Time: 08:06:35 Magnet Name: 123 Run Number: 3 FIELD HARMONICS Magnet Current, Imag = 200.3289 +- 1.233298E-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 0.00077 0.00001 108.28 1.03 0.2827 0.0039 2 0.27315 0.00005 44.99 0.00 100.0000 0.0000 3 0.00028 0.00001 24.23 1.12 0.1031 0.0038 4 0.00009 0.00000 23.50 0.51 0.0314 0.0009 5 0.00007 0.00001 10.36 0.77 0.0257 0.0026 6 0.00057 0.00000 15.16 0.09 0.2086 0.0014 7 0.00001 0.00000 4.08 1.37 0.0054 0.0004 8 0.00003 0.00000 3.50 0.88 0.0110 0.0006 9 0.00001 0.00000 -1.98 3.24 0.0024 0.0010 10 0.00084 0.00001 -9.00 0.02 0.3078 0.0019 11 0.00001 0.00000 3.96 8.02 0.0022 0.0009 12 0.00001 0.00000 0.49 8.99 0.0026 0.0011 13 0.00002 0.00000 -2.89 1.40 0.0081 0.0009 14 0.00070 0.00000 -6.43 0.03 0.2559 0.0012 15 0.00003 0.00001 -8.74 0.24 0.0113 0.0032 16 0.00001 0.00001 -1.02 6.86 0.0051 0.0025 The magnetic center is at X = -119.9 +- 1.8 microns Y = 39.6 +- 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: 04-21-1995 Time: 08:12:52 Magnet Name: 123 Run Number: 3 FIELD HARMONICS Magnet Current, Imag = 250.4305 +- 8.298523E-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 0.00091 0.00001 111.45 1.24 0.2693 0.0036 2 0.33826 0.00007 44.99 0.00 100.0000 0.0000 3 0.00033 0.00001 22.57 0.71 0.0969 0.0032 4 0.00010 0.00001 19.65 1.29 0.0289 0.0025 5 0.00009 0.00001 10.78 1.34 0.0257 0.0018 6 0.00063 0.00000 15.19 0.05 0.1866 0.0010 7 0.00002 0.00000 6.58 2.28 0.0049 0.0008 8 0.00002 0.00000 16.38 1.54 0.0054 0.0015 9 0.00001 0.00000 -1.91 10.62 0.0021 0.0010 10 0.00104 0.00000 -9.03 0.02 0.3089 0.0011 11 0.00001 0.00000 -0.67 12.10 0.0030 0.0007 12 0.00002 0.00001 2.84 0.94 0.0065 0.0017 13 0.00004 0.00002 -1.70 2.51 0.0105 0.0051 14 0.00086 0.00001 -6.46 0.03 0.2546 0.0017 15 0.00003 0.00001 -4.50 8.47 0.0096 0.0043 16 0.00003 0.00001 -8.33 1.78 0.0075 0.0023 The magnetic center is at X = -111.9 +- 1.8 microns Y = 44.0 +- 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: 04-21-1995 Time: 08:19:08 Magnet Name: 123 Run Number: 3 FIELD HARMONICS Magnet Current, Imag = 300.4218 +- 8.953412E-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 0.00084 0.00002 116.26 0.87 0.2147 0.0041 2 0.39021 0.00005 44.99 0.00 100.0000 0.0000 3 0.00026 0.00002 19.66 0.92 0.0672 0.0050 4 0.00010 0.00001 15.67 0.40 0.0256 0.0018 5 0.00010 0.00000 10.00 0.64 0.0253 0.0006 6 0.00052 0.00000 15.24 0.10 0.1334 0.0005 7 0.00002 0.00000 7.40 1.21 0.0062 0.0005 8 0.00003 0.00000 17.12 0.58 0.0073 0.0009 9 0.00001 0.00000 -1.49 1.91 0.0029 0.0010 10 0.00125 0.00000 -8.99 0.03 0.3204 0.0007 11 0.00001 0.00000 -9.76 7.73 0.0017 0.0009 12 0.00001 0.00001 -0.05 3.10 0.0026 0.0025 13 0.00005 0.00001 -2.50 1.36 0.0119 0.0020 14 0.00100 0.00001 -6.45 0.04 0.2573 0.0022 15 0.00004 0.00002 -4.60 9.15 0.0104 0.0047 16 0.00002 0.00001 -1.74 1.23 0.0054 0.0022 The magnetic center is at X = -86.0 +- 1.8 microns Y = 42.4 +- 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: 04-21-1995 Time: 08:25:24 Magnet Name: 123 Run Number: 3 FIELD HARMONICS Magnet Current, Imag = 350.4318 +- 7.908117E-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 0.00079 0.00002 119.37 2.49 0.1857 0.0040 2 0.42662 0.00007 44.98 0.00 100.0000 0.0000 3 0.00022 0.00002 17.41 2.37 0.0504 0.0041 4 0.00010 0.00001 14.97 0.76 0.0241 0.0019 5 0.00011 0.00000 9.67 0.75 0.0249 0.0009 6 0.00032 0.00001 15.53 0.20 0.0747 0.0012 7 0.00003 0.00000 8.70 1.31 0.0064 0.0007 8 0.00002 0.00000 16.17 2.48 0.0048 0.0012 9 0.00001 0.00000 -3.11 3.72 0.0030 0.0009 10 0.00140 0.00001 -9.00 0.02 0.3292 0.0015 11 0.00001 0.00000 -13.87 1.87 0.0028 0.0005 12 0.00002 0.00001 5.80 5.80 0.0038 0.0015 13 0.00004 0.00001 -6.75 2.89 0.0086 0.0031 14 0.00108 0.00001 -6.50 0.02 0.2534 0.0015 15 0.00004 0.00002 -4.80 5.70 0.0097 0.0036 16 0.00004 0.00001 0.56 0.71 0.0103 0.0027 The magnetic center is at X = -72.3 +- 2.3 microns Y = 40.7 +- 3.3 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 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)