SLAC Magnetic Measurements Date: 04-24-1995 Time: 08:51:09 Magnet Name (Serial #): 151 Bar Code Number: 378 Project: PEP II High Energy Ring Quadrupoles Test Stand: IR8, Q1 Measurement Coil: # 2 Operator: mkl 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: 04-24-1995 Time: 09:38:19 Magnet Name: 151 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 10.00159 +- 3.023407E-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 0.00000 0.00000 37.82 7.97 0.0260 0.0046 2 0.01490 0.00000 45.03 0.00 100.0000 0.0000 3 0.00001 0.00000 42.97 1.12 0.0830 0.0025 4 0.00000 0.00000 -30.62 1.56 0.0196 0.0027 5 0.00000 0.00000 17.16 2.29 0.0143 0.0033 6 0.00003 0.00000 15.20 0.14 0.2202 0.0006 7 0.00000 0.00000 -0.28 3.77 0.0029 0.0012 8 0.00000 0.00000 -7.99 2.07 0.0036 0.0010 9 0.00000 0.00000 -2.32 1.98 0.0059 0.0012 10 0.00004 0.00000 -9.03 0.02 0.3011 0.0007 11 0.00000 0.00000 -7.33 5.78 0.0028 0.0016 12 0.00000 0.00000 -10.10 1.39 0.0047 0.0024 13 0.00000 0.00000 -2.60 1.28 0.0071 0.0009 14 0.00004 0.00000 -6.39 0.02 0.2618 0.0012 15 0.00000 0.00000 -5.90 1.91 0.0065 0.0020 16 0.00000 0.00000 6.63 1.93 0.0048 0.0013 The magnetic center is at X = -7.1 +- 1.8 microns Y = -9.2 +- 1.9 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: 04-24-1995 Time: 09:44:24 Magnet Name: 151 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 25.10426 +- 5.190285E-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 134.30 1.49 0.1341 0.0052 2 0.03500 0.00001 45.02 0.00 100.0000 0.0000 3 0.00002 0.00000 38.46 1.13 0.0579 0.0034 4 0.00001 0.00000 -34.22 1.65 0.0242 0.0025 5 0.00000 0.00000 18.44 2.22 0.0134 0.0025 6 0.00008 0.00000 15.13 0.09 0.2215 0.0014 7 0.00000 0.00000 11.28 7.30 0.0022 0.0013 8 0.00000 0.00000 -20.14 0.38 0.0090 0.0010 9 0.00000 0.00000 -3.99 0.23 0.0064 0.0004 10 0.00011 0.00000 -9.02 0.03 0.3018 0.0012 11 0.00000 0.00000 -5.99 12.58 0.0026 0.0009 12 0.00000 0.00000 -1.99 1.99 0.0045 0.0025 13 0.00000 0.00000 -4.88 0.79 0.0071 0.0006 14 0.00009 0.00000 -6.39 0.02 0.2590 0.0008 15 0.00000 0.00000 -4.85 1.55 0.0077 0.0019 16 0.00000 0.00000 0.32 5.37 0.0041 0.0017 The magnetic center is at X = -42.9 +- 2.0 microns Y = 41.8 +- 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: 04-24-1995 Time: 09:50:35 Magnet Name: 151 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 50.06952 +- 5.747421E-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 132.85 0.93 0.1874 0.0045 2 0.06889 0.00001 45.03 0.00 100.0000 0.0000 3 0.00004 0.00000 36.80 0.94 0.0551 0.0035 4 0.00001 0.00000 -29.24 1.60 0.0213 0.0020 5 0.00001 0.00000 17.75 1.45 0.0131 0.0019 6 0.00015 0.00000 15.22 0.03 0.2210 0.0017 7 0.00000 0.00000 -2.35 12.02 0.0017 0.0006 8 0.00000 0.00000 -3.89 11.05 0.0028 0.0016 9 0.00000 0.00000 -2.65 1.07 0.0069 0.0012 10 0.00021 0.00000 -9.01 0.02 0.3017 0.0020 11 0.00000 0.00000 -2.81 9.75 0.0031 0.0022 12 0.00000 0.00000 -9.61 3.45 0.0029 0.0011 13 0.00000 0.00000 -1.42 3.05 0.0062 0.0021 14 0.00018 0.00000 -6.38 0.02 0.2572 0.0020 15 0.00001 0.00000 -5.60 1.58 0.0081 0.0025 16 0.00001 0.00000 7.63 2.79 0.0076 0.0021 The magnetic center is at X = -61.4 +- 1.7 microns Y = 56.9 +- 1.7 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: 04-24-1995 Time: 09:56:51 Magnet Name: 151 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 100.0678 +- 1.650931E-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 0.00029 0.00001 131.99 0.74 0.2103 0.0043 2 0.13742 0.00003 45.03 0.00 100.0000 0.0000 3 0.00007 0.00001 36.53 1.06 0.0538 0.0040 4 0.00003 0.00000 -29.72 0.96 0.0210 0.0021 5 0.00002 0.00000 19.45 1.61 0.0116 0.0025 6 0.00030 0.00000 15.16 0.06 0.2214 0.0013 7 0.00000 0.00000 1.22 13.02 0.0016 0.0007 8 0.00001 0.00000 -7.40 2.60 0.0043 0.0014 9 0.00001 0.00000 -3.98 0.96 0.0066 0.0007 10 0.00042 0.00000 -9.01 0.01 0.3044 0.0005 11 0.00001 0.00000 -10.27 2.49 0.0053 0.0015 12 0.00000 0.00000 -7.64 4.65 0.0029 0.0018 13 0.00001 0.00000 -2.62 1.55 0.0072 0.0008 14 0.00036 0.00000 -6.40 0.02 0.2594 0.0026 15 0.00001 0.00000 -5.41 2.11 0.0087 0.0034 16 0.00000 0.00000 2.80 8.05 0.0036 0.0017 The magnetic center is at X = -69.8 +- 1.6 microns Y = 62.8 +- 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: 04-24-1995 Time: 10:03:05 Magnet Name: 151 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 150.0859 +- 4.775538E-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 0.00001 134.09 1.15 0.2193 0.0061 2 0.20571 0.00004 45.00 0.00 100.0000 0.0000 3 0.00010 0.00000 35.58 1.56 0.0492 0.0021 4 0.00004 0.00000 -27.91 0.96 0.0208 0.0018 5 0.00002 0.00000 17.77 0.72 0.0113 0.0004 6 0.00044 0.00000 15.11 0.07 0.2123 0.0011 7 0.00000 0.00000 -4.68 11.04 0.0022 0.0007 8 0.00001 0.00000 -8.55 0.43 0.0033 0.0009 9 0.00001 0.00000 -5.50 0.54 0.0072 0.0013 10 0.00063 0.00000 -9.04 0.01 0.3059 0.0009 11 0.00001 0.00000 -11.69 1.41 0.0035 0.0003 12 0.00001 0.00000 -6.22 10.82 0.0040 0.0015 13 0.00001 0.00000 -1.83 1.66 0.0057 0.0010 14 0.00053 0.00001 -6.46 0.03 0.2567 0.0035 15 0.00002 0.00000 -4.94 1.30 0.0083 0.0018 16 0.00001 0.00000 8.84 1.61 0.0065 0.0014 The magnetic center is at X = -70.4 +- 2.4 microns Y = 68.2 +- 2.4 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: 04-24-1995 Time: 10:09:20 Magnet Name: 151 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 200.3359 +- 4.645794E-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 138.55 0.52 0.2274 0.0059 2 0.27334 0.00003 45.00 0.00 100.0000 0.0000 3 0.00012 0.00001 32.00 2.38 0.0434 0.0033 4 0.00009 0.00001 -34.59 1.12 0.0315 0.0019 5 0.00003 0.00001 20.96 3.22 0.0101 0.0027 6 0.00056 0.00000 15.20 0.03 0.2052 0.0011 7 0.00001 0.00000 6.18 12.99 0.0019 0.0006 8 0.00003 0.00000 -1.71 1.29 0.0093 0.0007 9 0.00002 0.00000 -2.72 1.09 0.0062 0.0007 10 0.00084 0.00000 -9.02 0.02 0.3088 0.0014 11 0.00001 0.00000 -7.67 2.36 0.0037 0.0015 12 0.00001 0.00000 -6.71 4.05 0.0038 0.0016 13 0.00002 0.00000 -2.58 0.96 0.0072 0.0013 14 0.00070 0.00000 -6.41 0.03 0.2579 0.0009 15 0.00002 0.00001 -5.60 1.18 0.0077 0.0020 16 0.00002 0.00001 2.99 7.40 0.0065 0.0030 The magnetic center is at X = -67.2 +- 1.9 microns Y = 76.1 +- 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: 04-24-1995 Time: 10:15:36 Magnet Name: 151 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 250.4416 +- 6.840125E-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 0.00089 0.00002 147.35 1.02 0.2619 0.0051 2 0.33833 0.00005 45.00 0.00 100.0000 0.0000 3 0.00015 0.00002 19.67 1.78 0.0437 0.0050 4 0.00010 0.00001 -32.22 0.68 0.0295 0.0020 5 0.00004 0.00001 20.93 3.28 0.0109 0.0020 6 0.00062 0.00001 15.18 0.08 0.1819 0.0015 7 0.00001 0.00000 -9.20 16.77 0.0020 0.0006 8 0.00002 0.00000 -15.13 1.33 0.0051 0.0010 9 0.00003 0.00001 -2.81 1.05 0.0075 0.0018 10 0.00105 0.00000 -9.04 0.03 0.3113 0.0003 11 0.00001 0.00000 -9.48 1.40 0.0043 0.0007 12 0.00003 0.00001 -1.94 1.33 0.0085 0.0016 13 0.00002 0.00000 -2.85 1.12 0.0060 0.0010 14 0.00087 0.00000 -6.42 0.04 0.2560 0.0012 15 0.00002 0.00000 -4.25 0.71 0.0069 0.0014 16 0.00003 0.00001 4.72 8.86 0.0088 0.0022 The magnetic center is at X = -63.1 +- 2.1 microns Y = 98.5 +- 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: 04-24-1995 Time: 10:21:53 Magnet Name: 151 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 300.4309 +- 4.925541E-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 0.00131 0.00002 152.96 0.60 0.3354 0.0056 2 0.39001 0.00012 45.00 0.00 100.0000 0.0000 3 0.00031 0.00003 11.59 0.66 0.0786 0.0064 4 0.00010 0.00000 -30.52 1.64 0.0261 0.0010 5 0.00004 0.00001 24.04 1.74 0.0109 0.0015 6 0.00051 0.00001 15.29 0.14 0.1302 0.0017 7 0.00002 0.00000 -21.72 1.79 0.0040 0.0011 8 0.00002 0.00000 -17.51 1.14 0.0059 0.0010 9 0.00003 0.00000 -4.14 1.30 0.0076 0.0011 10 0.00126 0.00000 -9.02 0.00 0.3225 0.0007 11 0.00001 0.00000 -9.88 3.07 0.0034 0.0012 12 0.00002 0.00000 -3.45 1.43 0.0053 0.0003 13 0.00003 0.00000 -2.03 0.45 0.0084 0.0012 14 0.00101 0.00001 -6.39 0.02 0.2600 0.0018 15 0.00003 0.00000 -4.54 1.94 0.0073 0.0013 16 0.00002 0.00001 1.56 2.35 0.0049 0.0023 The magnetic center is at X = -68.1 +- 1.8 microns Y = 133.4 +- 2.4 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: 04-24-1995 Time: 10:28:10 Magnet Name: 151 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 350.4395 +- 1.175323E-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 0.00157 0.00003 155.01 0.50 0.3694 0.0063 2 0.42635 0.00008 45.00 0.00 100.0000 0.0000 3 0.00041 0.00003 9.89 0.67 0.0950 0.0061 4 0.00011 0.00001 -30.32 1.29 0.0266 0.0024 5 0.00006 0.00001 24.31 2.11 0.0132 0.0026 6 0.00031 0.00001 15.42 0.25 0.0734 0.0012 7 0.00002 0.00000 -11.98 21.34 0.0057 0.0009 8 0.00002 0.00000 -14.78 1.98 0.0040 0.0010 9 0.00004 0.00000 -2.86 0.69 0.0084 0.0008 10 0.00141 0.00000 -9.05 0.01 0.3318 0.0006 11 0.00001 0.00000 -7.72 4.85 0.0022 0.0011 12 0.00001 0.00001 -3.28 7.71 0.0025 0.0015 13 0.00003 0.00001 -5.54 1.08 0.0080 0.0022 14 0.00109 0.00001 -6.44 0.04 0.2551 0.0020 15 0.00003 0.00001 -2.96 1.04 0.0075 0.0022 16 0.00002 0.00001 2.39 2.40 0.0053 0.0029 The magnetic center is at X = -69.7 +- 1.8 microns Y = 149.5 +- 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 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)