SLAC Magnetic Measurements Date: 04-17-1995 Time: 09:23:26 Magnet Name (Serial #): 116 Bar Code Number: 421 Project: PEP II High Energy Ring Quadrupoles Test Stand: IR8, Q1 Measurement Coil: # 2 Operator: bmd 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: 04-17-1995 Time: 10:10:36 Magnet Name: 116 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 9.999611 +- 5.224599E-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 0.00003 0.00000 -143.06 0.49 0.1959 0.0019 2 0.01490 0.00000 45.02 0.00 100.0000 0.0000 3 0.00001 0.00000 26.75 0.36 0.0561 0.0012 4 0.00000 0.00000 -21.01 1.34 0.0254 0.0017 5 0.00000 0.00000 16.64 1.69 0.0186 0.0030 6 0.00003 0.00000 15.27 0.06 0.2157 0.0002 7 0.00000 0.00000 12.31 0.75 0.0088 0.0011 8 0.00000 0.00000 -5.60 15.06 0.0015 0.0006 9 0.00000 0.00000 -2.97 1.99 0.0072 0.0013 10 0.00004 0.00000 -9.03 0.02 0.3009 0.0012 11 0.00000 0.00000 -4.06 10.67 0.0031 0.0024 12 0.00000 0.00000 -6.22 3.93 0.0041 0.0020 13 0.00000 0.00000 -4.39 0.83 0.0061 0.0025 14 0.00004 0.00000 -6.42 0.02 0.2576 0.0015 15 0.00000 0.00000 -3.52 1.37 0.0080 0.0021 16 0.00000 0.00000 -3.04 7.83 0.0022 0.0016 The magnetic center is at X = 52.6 +- 0.8 microns Y = 69.9 +- 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: 04-17-1995 Time: 10:16:42 Magnet Name: 116 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 25.10119 +- 7.688354E-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 176.36 0.43 0.1908 0.0028 2 0.03496 0.00000 45.02 0.00 100.0000 0.0000 3 0.00003 0.00000 32.32 0.58 0.0726 0.0022 4 0.00001 0.00000 -24.37 1.08 0.0298 0.0026 5 0.00001 0.00000 16.44 1.40 0.0176 0.0027 6 0.00008 0.00000 15.21 0.05 0.2241 0.0015 7 0.00000 0.00000 9.23 0.64 0.0072 0.0006 8 0.00000 0.00000 -21.24 0.73 0.0100 0.0012 9 0.00000 0.00000 -0.33 0.89 0.0081 0.0003 10 0.00010 0.00000 -9.00 0.04 0.2993 0.0023 11 0.00000 0.00000 -11.40 0.42 0.0038 0.0010 12 0.00000 0.00000 -2.72 1.97 0.0063 0.0032 13 0.00000 0.00000 -2.98 0.70 0.0070 0.0018 14 0.00009 0.00000 -6.39 0.03 0.2555 0.0018 15 0.00000 0.00000 -5.12 1.29 0.0075 0.0043 16 0.00000 0.00000 3.10 7.65 0.0043 0.0011 The magnetic center is at X = -5.4 +- 0.6 microns Y = 85.0 +- 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: 04-17-1995 Time: 10:22:54 Magnet Name: 116 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 50.0661 +- 4.882365E-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 0.00015 0.00000 165.77 0.41 0.2193 0.0030 2 0.06885 0.00001 45.02 0.00 100.0000 0.0000 3 0.00005 0.00000 32.90 0.86 0.0766 0.0023 4 0.00002 0.00000 -22.02 0.89 0.0310 0.0021 5 0.00001 0.00000 16.96 1.49 0.0187 0.0026 6 0.00015 0.00000 15.22 0.06 0.2229 0.0023 7 0.00000 0.00000 10.81 1.41 0.0065 0.0011 8 0.00000 0.00000 -12.40 3.28 0.0023 0.0005 9 0.00000 0.00000 -2.91 1.09 0.0066 0.0011 10 0.00021 0.00000 -8.98 0.04 0.3013 0.0009 11 0.00000 0.00000 -11.07 2.69 0.0037 0.0006 12 0.00000 0.00000 -6.87 3.44 0.0023 0.0014 13 0.00000 0.00000 -4.14 1.11 0.0056 0.0012 14 0.00017 0.00000 -6.41 0.01 0.2535 0.0018 15 0.00000 0.00000 -5.68 2.42 0.0063 0.0021 16 0.00000 0.00000 2.96 6.85 0.0065 0.0028 The magnetic center is at X = -24.1 +- 0.8 microns Y = 95.0 +- 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: 04-17-1995 Time: 10:29:09 Magnet Name: 116 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 100.0641 +- 8.009592E-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 0.00033 0.00000 162.62 0.28 0.2402 0.0016 2 0.13741 0.00001 45.02 0.00 100.0000 0.0000 3 0.00011 0.00000 32.21 0.43 0.0771 0.0015 4 0.00004 0.00000 -21.32 1.00 0.0323 0.0019 5 0.00003 0.00000 16.81 1.58 0.0201 0.0030 6 0.00031 0.00000 15.23 0.05 0.2231 0.0018 7 0.00001 0.00000 9.07 1.02 0.0061 0.0010 8 0.00000 0.00000 -6.43 8.09 0.0022 0.0009 9 0.00001 0.00000 -3.30 1.01 0.0076 0.0020 10 0.00042 0.00000 -8.99 0.01 0.3042 0.0012 11 0.00001 0.00000 -10.60 1.87 0.0050 0.0009 12 0.00001 0.00000 -9.16 1.72 0.0053 0.0015 13 0.00001 0.00000 -3.97 1.19 0.0065 0.0019 14 0.00035 0.00000 -6.40 0.03 0.2545 0.0009 15 0.00001 0.00000 -5.35 2.48 0.0085 0.0021 16 0.00001 0.00000 -0.58 9.32 0.0054 0.0022 The magnetic center is at X = -32.1 +- 0.5 microns Y = 102.4 +- 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: 04-17-1995 Time: 10:35:24 Magnet Name: 116 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 150.0814 +- 1.012269E-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 163.16 0.37 0.2440 0.0026 2 0.20559 0.00002 45.00 0.00 100.0000 0.0000 3 0.00016 0.00001 31.84 0.32 0.0763 0.0037 4 0.00007 0.00000 -21.13 1.42 0.0322 0.0020 5 0.00004 0.00001 16.03 1.21 0.0186 0.0025 6 0.00044 0.00001 15.21 0.06 0.2161 0.0027 7 0.00001 0.00000 9.46 0.60 0.0072 0.0008 8 0.00000 0.00000 -3.50 15.17 0.0019 0.0009 9 0.00001 0.00000 -2.61 1.66 0.0062 0.0018 10 0.00063 0.00000 -9.01 0.02 0.3073 0.0006 11 0.00001 0.00000 -8.88 2.10 0.0040 0.0017 12 0.00001 0.00000 -10.29 1.95 0.0067 0.0003 13 0.00001 0.00001 -2.62 1.77 0.0051 0.0032 14 0.00052 0.00001 -6.42 0.02 0.2535 0.0025 15 0.00002 0.00001 -4.16 0.92 0.0107 0.0030 16 0.00001 0.00000 9.17 1.10 0.0053 0.0012 The magnetic center is at X = -31.6 +- 0.7 microns Y = 104.3 +- 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: 04-17-1995 Time: 10:41:40 Magnet Name: 116 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 200.3297 +- 7.283575E-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 0.00066 0.00001 163.09 0.44 0.2428 0.0019 2 0.27319 0.00004 45.00 0.00 100.0000 0.0000 3 0.00021 0.00001 32.00 0.24 0.0762 0.0029 4 0.00009 0.00001 -28.01 1.22 0.0342 0.0021 5 0.00005 0.00001 17.66 1.09 0.0181 0.0035 6 0.00056 0.00000 15.21 0.04 0.2063 0.0016 7 0.00002 0.00000 10.40 0.53 0.0060 0.0008 8 0.00002 0.00000 -1.50 0.49 0.0077 0.0014 9 0.00002 0.00000 -2.16 1.14 0.0066 0.0010 10 0.00085 0.00000 -9.03 0.03 0.3097 0.0010 11 0.00001 0.00000 -10.09 0.65 0.0041 0.0012 12 0.00001 0.00000 -5.64 0.47 0.0051 0.0008 13 0.00002 0.00001 -2.52 1.50 0.0057 0.0023 14 0.00070 0.00000 -6.42 0.03 0.2555 0.0010 15 0.00002 0.00001 -4.64 0.85 0.0073 0.0019 16 0.00001 0.00000 -0.16 9.77 0.0054 0.0010 The magnetic center is at X = -31.6 +- 0.8 microns Y = 103.8 +- 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: 04-17-1995 Time: 10:47:57 Magnet Name: 116 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 250.4334 +- 8.13345E-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 0.00083 0.00001 162.45 0.12 0.2465 0.0018 2 0.33813 0.00007 45.00 0.00 100.0000 0.0000 3 0.00026 0.00000 31.30 0.32 0.0779 0.0013 4 0.00011 0.00001 -25.51 0.81 0.0328 0.0019 5 0.00007 0.00001 16.52 1.11 0.0194 0.0018 6 0.00062 0.00000 15.26 0.07 0.1833 0.0005 7 0.00002 0.00000 9.07 1.73 0.0051 0.0013 8 0.00002 0.00000 -20.27 0.87 0.0050 0.0002 9 0.00003 0.00000 -2.25 0.90 0.0080 0.0004 10 0.00105 0.00000 -9.04 0.01 0.3116 0.0010 11 0.00002 0.00001 -8.95 1.81 0.0056 0.0022 12 0.00003 0.00001 -0.64 0.84 0.0094 0.0024 13 0.00002 0.00000 -2.39 1.45 0.0050 0.0012 14 0.00086 0.00001 -6.44 0.02 0.2545 0.0015 15 0.00003 0.00001 -4.65 0.33 0.0096 0.0018 16 0.00002 0.00001 3.57 8.25 0.0064 0.0021 The magnetic center is at X = -33.2 +- 0.3 microns Y = 105.0 +- 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: 04-17-1995 Time: 10:54:13 Magnet Name: 116 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 300.4229 +- 2.091846E-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 0.00105 0.00001 158.16 0.22 0.2688 0.0015 2 0.39003 0.00002 45.00 0.00 100.0000 0.0000 3 0.00036 0.00001 29.47 0.17 0.0921 0.0025 4 0.00013 0.00001 -23.90 1.19 0.0327 0.0030 5 0.00006 0.00001 15.37 0.56 0.0165 0.0020 6 0.00051 0.00001 15.44 0.08 0.1302 0.0013 7 0.00002 0.00000 9.38 1.20 0.0047 0.0011 8 0.00002 0.00000 0.45 21.55 0.0060 0.0004 9 0.00003 0.00000 -2.30 0.74 0.0084 0.0006 10 0.00126 0.00000 -9.03 0.03 0.3233 0.0012 11 0.00002 0.00000 -12.33 1.50 0.0040 0.0006 12 0.00002 0.00000 -4.14 1.88 0.0060 0.0010 13 0.00002 0.00001 0.87 3.44 0.0045 0.0035 14 0.00100 0.00001 -6.42 0.01 0.2555 0.0018 15 0.00003 0.00001 -4.50 1.71 0.0073 0.0032 16 0.00001 0.00001 -0.63 1.31 0.0038 0.0021 The magnetic center is at X = -44.7 +- 0.5 microns Y = 111.4 +- 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: 04-17-1995 Time: 11:00:29 Magnet Name: 116 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 350.4296 +- 2.440166E-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 0.00117 0.00001 157.44 0.20 0.2733 0.0027 2 0.42658 0.00006 44.99 0.00 100.0000 0.0000 3 0.00041 0.00001 29.17 0.20 0.0966 0.0023 4 0.00013 0.00001 -24.92 0.95 0.0311 0.0021 5 0.00008 0.00001 16.03 1.19 0.0191 0.0015 6 0.00031 0.00001 15.71 0.24 0.0721 0.0012 7 0.00002 0.00001 9.50 1.69 0.0048 0.0012 8 0.00002 0.00000 -19.35 2.42 0.0048 0.0005 9 0.00003 0.00001 -2.46 0.77 0.0073 0.0018 10 0.00142 0.00001 -9.01 0.01 0.3333 0.0024 11 0.00001 0.00001 -10.24 3.76 0.0035 0.0013 12 0.00002 0.00000 -5.63 2.90 0.0036 0.0010 13 0.00002 0.00002 -4.28 2.62 0.0051 0.0036 14 0.00108 0.00001 -6.43 0.02 0.2527 0.0017 15 0.00004 0.00002 -3.41 2.20 0.0085 0.0048 16 0.00002 0.00000 2.32 4.11 0.0047 0.0010 The magnetic center is at X = -46.8 +- 0.6 microns Y = 112.7 +- 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 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)