SLAC Magnetic Measurements Date: 03-01-1995 Time: 10:23:47 Magnet Name (Serial #): 188 Bar Code Number: 485 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: 03-01-1995 Time: 11:10:53 Magnet Name: 188 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 10.00096 +- 6.770137E-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 168.69 0.60 0.1913 0.0016 2 0.01482 0.00000 51.37 0.00 100.0000 0.0000 3 0.00001 0.00000 33.59 0.64 0.0924 0.0018 4 0.00000 0.00000 -22.52 3.46 0.0100 0.0016 5 0.00000 0.00000 20.34 1.51 0.0187 0.0016 6 0.00003 0.00000 21.52 0.01 0.2212 0.0013 7 0.00000 0.00000 17.12 4.82 0.0051 0.0033 8 0.00000 0.00000 -0.49 13.88 0.0023 0.0007 9 0.00000 0.00000 3.40 0.48 0.0085 0.0021 10 0.00004 0.00000 -2.60 0.03 0.2998 0.0010 11 0.00000 0.00000 -13.27 1.75 0.0038 0.0014 12 0.00000 0.00000 2.92 4.23 0.0044 0.0014 13 0.00000 0.00000 2.81 0.90 0.0124 0.0022 14 0.00004 0.00000 -0.01 0.02 0.2579 0.0017 15 0.00000 0.00000 6.12 1.29 0.0065 0.0029 16 0.00000 0.00000 0.19 9.76 0.0032 0.0015 The magnetic center is at X = -16.7 +- 0.9 microns Y = 83.8 +- 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: 03-01-1995 Time: 11:16:58 Magnet Name: 188 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 25.10155 +- 5.305404E-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 0.00010 0.00000 154.95 0.75 0.2854 0.0049 2 0.03490 0.00000 51.36 0.00 100.0000 0.0000 3 0.00003 0.00000 33.11 0.47 0.0905 0.0019 4 0.00001 0.00000 -29.61 1.46 0.0186 0.0021 5 0.00001 0.00000 20.56 1.50 0.0192 0.0015 6 0.00008 0.00000 21.44 0.08 0.2226 0.0005 7 0.00000 0.00000 22.56 1.12 0.0046 0.0009 8 0.00000 0.00000 -15.53 0.31 0.0075 0.0015 9 0.00000 0.00000 3.25 0.62 0.0086 0.0013 10 0.00010 0.00000 -2.61 0.05 0.2996 0.0008 11 0.00000 0.00000 -8.60 3.07 0.0028 0.0015 12 0.00000 0.00000 5.42 1.97 0.0058 0.0018 13 0.00000 0.00000 2.01 0.67 0.0126 0.0012 14 0.00009 0.00000 -0.01 0.03 0.2567 0.0026 15 0.00000 0.00000 6.83 1.54 0.0097 0.0024 16 0.00000 0.00000 4.85 2.21 0.0046 0.0017 The magnetic center is at X = -54.0 +- 1.8 microns Y = 115.5 +- 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: 03-01-1995 Time: 11:23:08 Magnet Name: 188 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 50.06255 +- 2.179141E-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 0.00021 0.00000 153.51 0.29 0.3105 0.0038 2 0.06876 0.00001 51.36 0.00 100.0000 0.0000 3 0.00006 0.00000 33.10 0.62 0.0821 0.0031 4 0.00001 0.00000 -26.46 1.47 0.0162 0.0011 5 0.00001 0.00000 20.42 1.50 0.0171 0.0021 6 0.00015 0.00000 21.45 0.03 0.2242 0.0010 7 0.00000 0.00000 9.64 20.08 0.0039 0.0017 8 0.00000 0.00000 -3.57 11.48 0.0018 0.0012 9 0.00000 0.00000 3.91 0.89 0.0071 0.0015 10 0.00021 0.00000 -2.61 0.02 0.3013 0.0012 11 0.00000 0.00000 -3.48 10.46 0.0013 0.0004 12 0.00000 0.00000 5.43 6.38 0.0029 0.0016 13 0.00001 0.00000 2.99 0.55 0.0133 0.0013 14 0.00018 0.00000 -0.03 0.05 0.2551 0.0017 15 0.00001 0.00000 7.36 1.83 0.0084 0.0017 16 0.00000 0.00000 -2.34 7.82 0.0054 0.0015 The magnetic center is at X = -61.9 +- 1.0 microns Y = 124.1 +- 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: 03-01-1995 Time: 11:29:22 Magnet Name: 188 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 100.0539 +- 2.269024E-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 0.00045 0.00000 152.47 0.48 0.3246 0.0016 2 0.13722 0.00002 51.36 0.00 100.0000 0.0000 3 0.00011 0.00001 33.92 0.63 0.0796 0.0039 4 0.00002 0.00000 -26.66 1.25 0.0172 0.0009 5 0.00002 0.00000 20.63 1.47 0.0176 0.0015 6 0.00031 0.00000 21.53 0.05 0.2229 0.0008 7 0.00001 0.00000 20.42 2.63 0.0044 0.0012 8 0.00000 0.00000 -0.78 8.31 0.0021 0.0013 9 0.00001 0.00000 2.82 0.92 0.0077 0.0013 10 0.00041 0.00000 -2.60 0.03 0.3012 0.0010 11 0.00000 0.00000 -8.51 7.00 0.0015 0.0005 12 0.00001 0.00000 -1.14 1.99 0.0042 0.0020 13 0.00002 0.00000 1.95 0.59 0.0147 0.0009 14 0.00035 0.00000 -0.04 0.01 0.2547 0.0014 15 0.00002 0.00000 6.63 0.79 0.0126 0.0032 16 0.00001 0.00000 -2.15 2.95 0.0042 0.0017 The magnetic center is at X = -67.0 +- 1.1 microns Y = 128.6 +- 0.9 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: 03-01-1995 Time: 11:35:36 Magnet Name: 188 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 150.064 +- 4.262231E-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 0.00068 0.00001 150.00 0.19 0.3317 0.0033 2 0.20535 0.00005 51.34 0.00 100.0000 0.0000 3 0.00016 0.00001 34.43 0.73 0.0778 0.0036 4 0.00004 0.00000 -25.10 2.53 0.0173 0.0021 5 0.00003 0.00000 22.28 1.91 0.0161 0.0011 6 0.00044 0.00000 21.47 0.11 0.2147 0.0011 7 0.00001 0.00000 19.06 3.31 0.0034 0.0008 8 0.00000 0.00000 9.71 8.26 0.0022 0.0006 9 0.00002 0.00000 2.16 1.14 0.0091 0.0010 10 0.00063 0.00000 -2.63 0.06 0.3054 0.0014 11 0.00001 0.00000 -11.47 3.10 0.0028 0.0013 12 0.00001 0.00000 0.98 7.55 0.0039 0.0022 13 0.00003 0.00000 2.31 0.14 0.0142 0.0024 14 0.00052 0.00000 -0.05 0.02 0.2542 0.0015 15 0.00002 0.00000 5.14 1.07 0.0093 0.0016 16 0.00001 0.00000 -6.84 1.33 0.0048 0.0007 The magnetic center is at X = -74.1 +- 0.8 microns Y = 128.3 +- 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: 03-01-1995 Time: 11:41:50 Magnet Name: 188 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 200.3059 +- 1.029092E-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 0.00091 0.00001 150.58 0.39 0.3347 0.0019 2 0.27302 0.00004 51.34 0.00 100.0000 0.0000 3 0.00021 0.00001 34.31 0.27 0.0764 0.0054 4 0.00008 0.00001 -31.53 0.85 0.0285 0.0027 5 0.00004 0.00000 21.66 0.77 0.0163 0.0009 6 0.00056 0.00001 21.58 0.07 0.2068 0.0021 7 0.00001 0.00001 18.26 1.35 0.0043 0.0021 8 0.00002 0.00000 5.91 1.48 0.0070 0.0010 9 0.00002 0.00000 2.15 1.55 0.0079 0.0004 10 0.00084 0.00000 -2.64 0.03 0.3060 0.0014 11 0.00001 0.00000 4.17 7.38 0.0024 0.0007 12 0.00001 0.00000 -4.81 4.39 0.0037 0.0017 13 0.00004 0.00000 2.53 0.45 0.0137 0.0018 14 0.00069 0.00000 -0.02 0.05 0.2541 0.0017 15 0.00002 0.00001 2.41 7.32 0.0059 0.0031 16 0.00002 0.00001 -6.04 0.67 0.0079 0.0019 The magnetic center is at X = -73.4 +- 1.0 microns Y = 130.2 +- 0.9 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: 03-01-1995 Time: 11:48:05 Magnet Name: 188 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 250.4025 +- 3.014335E-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 0.00112 0.00001 153.57 0.61 0.3314 0.0035 2 0.33797 0.00007 51.34 0.00 100.0000 0.0000 3 0.00024 0.00001 33.10 0.47 0.0712 0.0023 4 0.00007 0.00001 -29.33 1.89 0.0221 0.0033 5 0.00006 0.00000 21.93 0.84 0.0164 0.0007 6 0.00061 0.00001 21.55 0.09 0.1817 0.0018 7 0.00001 0.00000 19.15 4.99 0.0037 0.0008 8 0.00002 0.00001 -16.97 1.24 0.0061 0.0025 9 0.00003 0.00000 1.56 0.70 0.0083 0.0011 10 0.00106 0.00001 -2.59 0.01 0.3134 0.0022 11 0.00001 0.00001 1.51 9.88 0.0028 0.0016 12 0.00004 0.00001 6.49 1.57 0.0110 0.0020 13 0.00005 0.00001 3.17 0.77 0.0145 0.0021 14 0.00087 0.00001 -0.08 0.03 0.2562 0.0038 15 0.00002 0.00001 7.53 2.33 0.0073 0.0024 16 0.00001 0.00001 2.50 5.57 0.0040 0.0026 The magnetic center is at X = -65.9 +- 1.6 microns Y = 132.6 +- 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: 03-01-1995 Time: 11:54:19 Magnet Name: 188 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 300.3855 +- 1.079175E-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 0.00140 0.00001 155.85 0.63 0.3581 0.0035 2 0.38991 0.00007 51.34 0.00 100.0000 0.0000 3 0.00030 0.00001 29.16 0.91 0.0762 0.0021 4 0.00007 0.00000 -27.92 1.42 0.0180 0.0010 5 0.00006 0.00001 22.96 1.44 0.0145 0.0018 6 0.00051 0.00000 21.61 0.06 0.1312 0.0005 7 0.00001 0.00000 11.05 19.17 0.0030 0.0011 8 0.00002 0.00000 -16.81 2.21 0.0044 0.0008 9 0.00004 0.00000 1.96 0.80 0.0091 0.0007 10 0.00125 0.00001 -2.65 0.04 0.3200 0.0015 11 0.00001 0.00000 -8.31 5.82 0.0029 0.0008 12 0.00002 0.00001 -1.28 4.50 0.0053 0.0025 13 0.00006 0.00001 2.91 0.46 0.0147 0.0013 14 0.00099 0.00000 -0.03 0.04 0.2543 0.0012 15 0.00003 0.00001 5.45 2.78 0.0083 0.0025 16 0.00003 0.00001 5.80 2.21 0.0064 0.0017 The magnetic center is at X = -65.4 +- 1.7 microns Y = 145.9 +- 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: 03-01-1995 Time: 12:00:34 Magnet Name: 188 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 350.3873 +- 7.086718E-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 0.00158 0.00001 157.09 0.35 0.3708 0.0026 2 0.42645 0.00008 51.33 0.00 100.0000 0.0000 3 0.00034 0.00000 27.42 1.24 0.0800 0.0009 4 0.00008 0.00001 -28.70 0.88 0.0195 0.0012 5 0.00006 0.00001 21.37 2.51 0.0151 0.0024 6 0.00032 0.00000 21.78 0.22 0.0751 0.0009 7 0.00001 0.00000 10.57 20.51 0.0022 0.0011 8 0.00002 0.00000 -15.62 1.79 0.0042 0.0008 9 0.00004 0.00000 2.94 0.58 0.0100 0.0009 10 0.00141 0.00001 -2.62 0.03 0.3304 0.0024 11 0.00000 0.00000 -0.14 10.79 0.0011 0.0004 12 0.00002 0.00000 0.25 5.48 0.0041 0.0007 13 0.00005 0.00000 2.14 0.88 0.0129 0.0011 14 0.00107 0.00002 -0.06 0.05 0.2508 0.0035 15 0.00005 0.00002 4.65 1.88 0.0111 0.0036 16 0.00002 0.00000 1.15 6.20 0.0054 0.0011 The magnetic center is at X = -64.5 +- 1.0 microns Y = 152.5 +- 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)