SLAC Magnetic Measurements Date: 04-12-1995 Time: 06:32:11 Magnet Name (Serial #): 195 Bar Code Number: 497 Project: PEP II High Energy Ring Quadrupoles Test Stand: IR8, Q1 Measurement Coil: # 2 Operator: mkl 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: 04-12-1995 Time: 07:19:24 Magnet Name: 195 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 10.00243 +- 4.185468E-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 -98.73 0.58 0.4974 0.0027 2 0.01481 0.00000 44.95 0.00 100.0000 0.0000 3 0.00001 0.00000 -47.01 2.15 0.0491 0.0033 4 0.00001 0.00000 37.88 0.61 0.0454 0.0009 5 0.00000 0.00000 21.62 0.78 0.0295 0.0010 6 0.00003 0.00000 15.04 0.04 0.2183 0.0034 7 0.00000 0.00000 15.45 1.35 0.0057 0.0022 8 0.00000 0.00000 -0.16 21.43 0.0051 0.0014 9 0.00000 0.00000 7.79 2.45 0.0084 0.0010 10 0.00004 0.00000 -9.02 0.02 0.2978 0.0019 11 0.00000 0.00000 -6.44 10.61 0.0018 0.0006 12 0.00000 0.00000 11.51 1.74 0.0050 0.0029 13 0.00000 0.00000 1.16 1.11 0.0121 0.0016 14 0.00004 0.00000 -6.41 0.04 0.2568 0.0003 15 0.00000 0.00000 -2.75 1.30 0.0079 0.0022 16 0.00000 0.00000 8.33 1.19 0.0068 0.0029 The magnetic center is at X = 219.6 +- 1.2 microns Y = 33.7 +- 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: 04-12-1995 Time: 07:25:30 Magnet Name: 195 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 25.10505 +- 5.196834E-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 0.00013 0.00000 -101.41 0.56 0.3791 0.0014 2 0.03491 0.00001 44.95 0.00 100.0000 0.0000 3 0.00002 0.00000 -53.55 0.14 0.0714 0.0039 4 0.00002 0.00000 38.28 0.37 0.0493 0.0026 5 0.00001 0.00000 21.20 0.62 0.0275 0.0023 6 0.00008 0.00000 14.98 0.08 0.2205 0.0009 7 0.00000 0.00000 12.17 2.16 0.0050 0.0006 8 0.00000 0.00000 -0.14 21.95 0.0143 0.0010 9 0.00000 0.00000 7.74 1.36 0.0055 0.0010 10 0.00010 0.00000 -9.02 0.02 0.3005 0.0010 11 0.00000 0.00000 -5.17 11.98 0.0021 0.0005 12 0.00000 0.00000 -2.03 2.23 0.0068 0.0009 13 0.00000 0.00000 3.75 1.45 0.0095 0.0043 14 0.00009 0.00000 -6.50 0.04 0.2562 0.0030 15 0.00000 0.00000 -2.87 0.87 0.0097 0.0041 16 0.00000 0.00000 -1.22 9.10 0.0040 0.0016 The magnetic center is at X = 166.0 +- 0.7 microns Y = 33.5 +- 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: 04-12-1995 Time: 07:31:42 Magnet Name: 195 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 50.06796 +- 5.996572E-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 0.00024 0.00000 -104.88 0.79 0.3453 0.0007 2 0.06881 0.00002 44.95 0.00 100.0000 0.0000 3 0.00005 0.00000 -54.02 0.35 0.0759 0.0032 4 0.00003 0.00000 37.54 0.81 0.0440 0.0019 5 0.00002 0.00000 21.51 0.50 0.0264 0.0028 6 0.00015 0.00000 14.93 0.07 0.2203 0.0021 7 0.00000 0.00000 10.63 1.85 0.0046 0.0014 8 0.00000 0.00000 -0.82 21.07 0.0056 0.0007 9 0.00000 0.00000 8.84 0.37 0.0071 0.0026 10 0.00021 0.00000 -9.04 0.02 0.3002 0.0016 11 0.00000 0.00000 6.52 8.51 0.0017 0.0011 12 0.00000 0.00000 6.31 10.77 0.0032 0.0011 13 0.00001 0.00000 3.12 1.85 0.0084 0.0006 14 0.00017 0.00000 -6.50 0.02 0.2542 0.0009 15 0.00001 0.00000 -2.46 1.38 0.0102 0.0024 16 0.00000 0.00000 3.83 8.55 0.0068 0.0030 The magnetic center is at X = 149.1 +- 0.6 microns Y = 39.6 +- 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: 04-12-1995 Time: 07:37:59 Magnet Name: 195 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 100.0647 +- 6.386628E-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 -108.01 0.63 0.3311 0.0028 2 0.13728 0.00002 44.95 0.00 100.0000 0.0000 3 0.00010 0.00001 -53.56 0.24 0.0752 0.0053 4 0.00006 0.00000 37.62 0.44 0.0446 0.0022 5 0.00003 0.00000 21.22 0.89 0.0250 0.0016 6 0.00030 0.00000 14.99 0.08 0.2211 0.0015 7 0.00000 0.00000 10.50 2.24 0.0036 0.0010 8 0.00001 0.00000 19.56 1.15 0.0045 0.0009 9 0.00001 0.00000 8.37 0.83 0.0053 0.0012 10 0.00041 0.00000 -9.03 0.03 0.3022 0.0015 11 0.00000 0.00000 0.55 10.84 0.0020 0.0004 12 0.00000 0.00000 4.52 10.96 0.0028 0.0008 13 0.00001 0.00000 3.04 0.74 0.0069 0.0010 14 0.00035 0.00000 -6.48 0.03 0.2525 0.0016 15 0.00001 0.00000 -2.06 1.64 0.0091 0.0016 16 0.00001 0.00000 3.13 8.50 0.0053 0.0034 The magnetic center is at X = 140.6 +- 1.3 microns Y = 45.7 +- 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: 04-12-1995 Time: 07:44:15 Magnet Name: 195 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 150.0803 +- 5.012808E-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 0.00067 0.00000 -109.26 0.82 0.3272 0.0020 2 0.20542 0.00003 44.93 0.00 100.0000 0.0000 3 0.00015 0.00000 -53.38 0.63 0.0744 0.0022 4 0.00009 0.00000 37.53 0.26 0.0434 0.0016 5 0.00005 0.00000 20.91 1.54 0.0260 0.0012 6 0.00044 0.00000 15.00 0.10 0.2118 0.0009 7 0.00001 0.00000 10.27 2.24 0.0039 0.0014 8 0.00001 0.00000 20.18 1.77 0.0038 0.0005 9 0.00001 0.00000 8.50 0.50 0.0063 0.0011 10 0.00063 0.00000 -9.05 0.03 0.3080 0.0004 11 0.00001 0.00000 10.03 2.87 0.0027 0.0017 12 0.00001 0.00001 -5.66 9.20 0.0061 0.0026 13 0.00002 0.00001 5.01 2.19 0.0081 0.0027 14 0.00052 0.00001 -6.50 0.04 0.2525 0.0025 15 0.00002 0.00001 -2.39 0.72 0.0104 0.0035 16 0.00001 0.00000 5.17 4.40 0.0034 0.0007 The magnetic center is at X = 137.9 +- 1.1 microns Y = 48.2 +- 2.0 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: 04-12-1995 Time: 07:50:30 Magnet Name: 195 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 200.3288 +- 8.424524E-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 0.00088 0.00000 -109.43 0.85 0.3229 0.0018 2 0.27315 0.00005 44.93 0.00 100.0000 0.0000 3 0.00021 0.00001 -53.60 0.76 0.0773 0.0029 4 0.00015 0.00000 40.25 0.21 0.0562 0.0015 5 0.00007 0.00001 21.37 0.42 0.0249 0.0023 6 0.00056 0.00001 14.96 0.04 0.2039 0.0023 7 0.00001 0.00000 8.95 1.33 0.0040 0.0004 8 0.00001 0.00000 1.40 0.63 0.0042 0.0006 9 0.00002 0.00001 7.28 1.25 0.0061 0.0019 10 0.00084 0.00000 -9.06 0.02 0.3077 0.0010 11 0.00001 0.00000 -5.55 11.01 0.0028 0.0017 12 0.00001 0.00000 -5.14 10.23 0.0050 0.0014 13 0.00002 0.00001 3.48 1.98 0.0082 0.0020 14 0.00070 0.00001 -6.51 0.05 0.2556 0.0041 15 0.00003 0.00001 -3.64 1.83 0.0103 0.0038 16 0.00003 0.00000 10.65 0.50 0.0095 0.0011 The magnetic center is at X = 136.0 +- 1.0 microns Y = 48.0 +- 2.0 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: 04-12-1995 Time: 07:56:46 Magnet Name: 195 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 250.4327 +- 9.906174E-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 0.00107 0.00001 -110.74 0.84 0.3163 0.0024 2 0.33826 0.00007 44.93 0.00 100.0000 0.0000 3 0.00025 0.00001 -53.94 0.62 0.0742 0.0043 4 0.00017 0.00001 39.97 0.70 0.0491 0.0021 5 0.00009 0.00000 22.18 1.13 0.0255 0.0010 6 0.00062 0.00000 15.05 0.08 0.1824 0.0004 7 0.00001 0.00000 11.62 4.48 0.0040 0.0006 8 0.00003 0.00001 -0.16 21.72 0.0087 0.0017 9 0.00002 0.00001 8.05 0.42 0.0072 0.0021 10 0.00105 0.00000 -9.06 0.02 0.3098 0.0013 11 0.00000 0.00000 -11.53 2.06 0.0011 0.0004 12 0.00002 0.00001 -1.18 1.64 0.0062 0.0019 13 0.00004 0.00001 2.85 2.04 0.0114 0.0031 14 0.00085 0.00000 -6.49 0.05 0.2513 0.0011 15 0.00003 0.00001 -1.34 3.80 0.0094 0.0032 16 0.00003 0.00001 4.41 9.02 0.0092 0.0021 The magnetic center is at X = 132.1 +- 1.2 microns Y = 50.0 +- 2.0 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: 04-12-1995 Time: 08:03:02 Magnet Name: 195 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 300.4199 +- 3.642986E-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 0.00124 0.00001 -115.46 0.47 0.3179 0.0016 2 0.38999 0.00013 44.92 0.00 100.0000 0.0000 3 0.00024 0.00001 -53.53 0.44 0.0609 0.0035 4 0.00017 0.00001 39.84 0.69 0.0439 0.0017 5 0.00010 0.00001 22.48 0.47 0.0258 0.0019 6 0.00051 0.00001 15.11 0.08 0.1305 0.0015 7 0.00001 0.00000 10.69 1.73 0.0037 0.0007 8 0.00004 0.00000 10.86 18.70 0.0092 0.0010 9 0.00002 0.00001 6.41 2.58 0.0058 0.0014 10 0.00125 0.00001 -9.07 0.03 0.3204 0.0023 11 0.00000 0.00000 2.93 7.06 0.0009 0.0007 12 0.00001 0.00001 -9.37 4.36 0.0034 0.0018 13 0.00004 0.00001 4.71 1.76 0.0097 0.0024 14 0.00099 0.00000 -6.52 0.02 0.2544 0.0007 15 0.00003 0.00002 -4.52 2.44 0.0088 0.0045 16 0.00002 0.00000 -2.41 4.77 0.0045 0.0009 The magnetic center is at X = 128.2 +- 0.9 microns Y = 61.1 +- 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: 04-12-1995 Time: 08:09:18 Magnet Name: 195 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 350.4282 +- 2.002625E-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 0.00138 0.00001 -118.71 0.55 0.3228 0.0018 2 0.42644 0.00007 44.92 0.00 100.0000 0.0000 3 0.00022 0.00001 -52.99 1.25 0.0516 0.0024 4 0.00019 0.00001 40.67 0.60 0.0438 0.0018 5 0.00012 0.00001 21.63 1.00 0.0282 0.0014 6 0.00031 0.00000 15.07 0.27 0.0733 0.0007 7 0.00002 0.00000 13.23 3.37 0.0039 0.0005 8 0.00003 0.00001 1.10 21.21 0.0064 0.0012 9 0.00003 0.00000 6.16 1.27 0.0072 0.0007 10 0.00141 0.00001 -9.06 0.01 0.3303 0.0024 11 0.00000 0.00000 0.75 9.14 0.0011 0.0005 12 0.00002 0.00001 -4.45 10.02 0.0038 0.0017 13 0.00005 0.00001 3.95 1.71 0.0121 0.0035 14 0.00107 0.00001 -6.50 0.05 0.2500 0.0016 15 0.00004 0.00002 -4.58 2.23 0.0084 0.0045 16 0.00003 0.00001 1.61 3.23 0.0075 0.0013 The magnetic center is at X = 126.5 +- 1.0 microns Y = 69.3 +- 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 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)