SLAC Magnetic Measurements Date: 03-02-1995 Time: 14:01:19 Magnet Name (Serial #): 197 Bar Code Number: 602 Project: PEP II High Energy Ring Quadrupoles Test Stand: IR8, Q1 Measurement Coil: # 2 Operator: bmd 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: 03-02-1995 Time: 14:49:01 Magnet Name: 197 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 10.00435 +- 2.610038E-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 0.00009 0.00000 3.69 0.16 0.5850 0.0038 2 0.01487 0.00000 -46.02 0.00 100.0000 0.0000 3 0.00001 0.00000 42.04 0.31 0.0616 0.0029 4 0.00000 0.00000 19.61 1.00 0.0221 0.0021 5 0.00000 0.00000 -6.29 2.36 0.0057 0.0024 6 0.00003 0.00000 -15.80 0.09 0.2220 0.0020 7 0.00000 0.00000 -11.90 0.79 0.0100 0.0010 8 0.00000 0.00000 16.66 1.48 0.0042 0.0008 9 0.00000 0.00000 8.01 15.84 0.0084 0.0008 10 0.00004 0.00000 7.95 0.01 0.2970 0.0014 11 0.00000 0.00000 9.00 3.16 0.0037 0.0004 12 0.00000 0.00000 2.72 5.81 0.0041 0.0019 13 0.00000 0.00000 12.52 0.69 0.0147 0.0021 14 0.00004 0.00000 5.42 0.06 0.2583 0.0033 15 0.00000 0.00000 -7.72 3.26 0.0066 0.0027 16 0.00000 0.00000 -7.94 1.22 0.0051 0.0011 The magnetic center is at X = 16.8 +- 0.7 microns Y = 260.8 +- 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 ^ | S N --> x N S Date: 03-02-1995 Time: 14:55:05 Magnet Name: 197 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 25.1068 +- 3.187641E-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 -3.20 0.33 0.4770 0.0040 2 0.03493 0.00000 -46.02 0.00 100.0000 0.0000 3 0.00002 0.00000 -35.53 1.42 0.0539 0.0023 4 0.00001 0.00000 22.73 1.67 0.0245 0.0025 5 0.00000 0.00000 -15.93 0.51 0.0116 0.0012 6 0.00008 0.00000 -15.72 0.08 0.2247 0.0013 7 0.00000 0.00000 -12.04 3.83 0.0042 0.0007 8 0.00000 0.00000 19.95 0.88 0.0101 0.0010 9 0.00000 0.00000 16.82 0.94 0.0110 0.0009 10 0.00010 0.00000 7.97 0.01 0.2997 0.0012 11 0.00000 0.00000 -2.05 11.11 0.0021 0.0005 12 0.00000 0.00000 1.55 0.60 0.0063 0.0020 13 0.00001 0.00000 11.96 0.53 0.0147 0.0023 14 0.00009 0.00000 5.41 0.03 0.2592 0.0011 15 0.00000 0.00000 -4.80 8.84 0.0072 0.0014 16 0.00000 0.00000 -0.50 1.35 0.0070 0.0031 The magnetic center is at X = -11.9 +- 1.2 microns Y = 212.7 +- 1.8 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 ^ | S N --> x N S Date: 03-02-1995 Time: 15:01:15 Magnet Name: 197 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 50.0668 +- 6.863964E-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 0.00031 0.00000 -3.74 0.31 0.4454 0.0030 2 0.06880 0.00001 -46.02 0.00 100.0000 0.0000 3 0.00005 0.00000 -32.71 0.54 0.0748 0.0035 4 0.00002 0.00000 20.16 1.10 0.0278 0.0026 5 0.00001 0.00000 -16.71 1.55 0.0142 0.0009 6 0.00016 0.00000 -15.82 0.03 0.2259 0.0016 7 0.00000 0.00000 -8.67 4.49 0.0033 0.0020 8 0.00000 0.00000 14.12 4.49 0.0045 0.0013 9 0.00001 0.00000 17.93 0.50 0.0097 0.0009 10 0.00021 0.00000 7.94 0.04 0.3027 0.0016 11 0.00000 0.00000 -2.10 6.55 0.0011 0.0007 12 0.00000 0.00000 4.80 10.55 0.0037 0.0011 13 0.00001 0.00000 11.85 0.49 0.0135 0.0017 14 0.00018 0.00000 5.38 0.03 0.2577 0.0012 15 0.00000 0.00000 -0.11 10.09 0.0041 0.0009 16 0.00000 0.00000 -7.13 1.27 0.0043 0.0029 The magnetic center is at X = -13.0 +- 1.1 microns Y = 198.5 +- 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 ^ | S N --> x N S Date: 03-02-1995 Time: 15:07:30 Magnet Name: 197 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 100.0562 +- 7.110395E-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 0.00060 0.00001 -2.03 0.28 0.4340 0.0036 2 0.13728 0.00002 -46.02 0.00 100.0000 0.0000 3 0.00011 0.00000 -32.33 1.21 0.0788 0.0011 4 0.00004 0.00000 20.10 0.63 0.0303 0.0015 5 0.00002 0.00000 -15.12 2.02 0.0140 0.0020 6 0.00031 0.00000 -15.87 0.04 0.2266 0.0007 7 0.00000 0.00000 -2.94 4.94 0.0031 0.0009 8 0.00001 0.00000 13.38 1.69 0.0046 0.0008 9 0.00001 0.00000 18.20 0.85 0.0093 0.0011 10 0.00042 0.00000 7.98 0.04 0.3028 0.0010 11 0.00000 0.00000 3.95 8.98 0.0022 0.0010 12 0.00001 0.00000 7.98 4.13 0.0038 0.0016 13 0.00002 0.00000 11.67 0.46 0.0142 0.0012 14 0.00036 0.00000 5.45 0.05 0.2588 0.0010 15 0.00001 0.00000 -0.30 8.60 0.0044 0.0022 16 0.00001 0.00000 -0.97 6.47 0.0082 0.0028 The magnetic center is at X = -6.9 +- 1.0 microns Y = 193.7 +- 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 ^ | S N --> x N S Date: 03-02-1995 Time: 15:13:44 Magnet Name: 197 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 150.0668 +- 1.10784E-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 0.00086 0.00001 -1.34 0.31 0.4196 0.0028 2 0.20549 0.00001 -46.05 0.00 100.0000 0.0000 3 0.00016 0.00001 -30.73 0.68 0.0770 0.0034 4 0.00006 0.00000 20.05 0.66 0.0307 0.0014 5 0.00003 0.00001 -17.03 2.67 0.0126 0.0029 6 0.00045 0.00000 -15.88 0.08 0.2186 0.0020 7 0.00000 0.00000 0.16 14.96 0.0017 0.0005 8 0.00001 0.00000 16.50 1.73 0.0037 0.0014 9 0.00002 0.00000 16.70 0.75 0.0107 0.0010 10 0.00062 0.00000 7.96 0.04 0.3033 0.0014 11 0.00001 0.00000 7.17 3.59 0.0024 0.0012 12 0.00001 0.00001 -4.53 11.09 0.0052 0.0038 13 0.00003 0.00000 11.35 0.46 0.0156 0.0022 14 0.00053 0.00001 5.39 0.05 0.2564 0.0034 15 0.00001 0.00000 -5.14 9.17 0.0054 0.0024 16 0.00001 0.00000 0.37 6.36 0.0042 0.0022 The magnetic center is at X = -4.4 +- 1.0 microns Y = 187.4 +- 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 ^ | S N --> x N S Date: 03-02-1995 Time: 15:19:58 Magnet Name: 197 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 200.31 +- 3.56873E-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 0.00109 0.00001 -3.10 0.41 0.4006 0.0034 2 0.27315 0.00002 -46.05 0.00 100.0000 0.0000 3 0.00023 0.00001 -29.14 0.58 0.0830 0.0033 4 0.00008 0.00000 26.73 0.96 0.0306 0.0006 5 0.00003 0.00000 -16.73 2.41 0.0108 0.0013 6 0.00058 0.00001 -15.86 0.08 0.2122 0.0018 7 0.00001 0.00000 5.04 13.80 0.0019 0.0007 8 0.00002 0.00000 4.64 0.41 0.0070 0.0009 9 0.00003 0.00000 16.59 0.86 0.0105 0.0008 10 0.00084 0.00001 7.95 0.03 0.3070 0.0023 11 0.00001 0.00000 9.78 3.39 0.0035 0.0005 12 0.00001 0.00000 6.72 3.03 0.0042 0.0010 13 0.00004 0.00000 11.02 0.68 0.0128 0.0010 14 0.00070 0.00000 5.38 0.07 0.2564 0.0011 15 0.00001 0.00001 3.92 7.44 0.0039 0.0019 16 0.00002 0.00001 -0.45 9.68 0.0074 0.0042 The magnetic center is at X = -9.7 +- 1.3 microns Y = 178.7 +- 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 ^ | S N --> x N S Date: 03-02-1995 Time: 15:26:13 Magnet Name: 197 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 250.4098 +- 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 0.00128 0.00001 -6.42 0.15 0.3801 0.0041 2 0.33806 0.00006 -46.05 0.00 100.0000 0.0000 3 0.00033 0.00001 -27.68 1.02 0.0962 0.0025 4 0.00010 0.00001 22.89 1.02 0.0286 0.0021 5 0.00004 0.00001 -17.97 0.53 0.0130 0.0018 6 0.00063 0.00001 -15.84 0.14 0.1851 0.0020 7 0.00001 0.00000 8.99 17.68 0.0028 0.0007 8 0.00003 0.00000 19.00 1.36 0.0086 0.0010 9 0.00003 0.00000 16.54 0.46 0.0100 0.0004 10 0.00106 0.00000 7.91 0.04 0.3123 0.0012 11 0.00001 0.00000 10.26 2.16 0.0021 0.0009 12 0.00003 0.00001 -1.41 1.76 0.0076 0.0032 13 0.00004 0.00001 12.11 0.37 0.0123 0.0022 14 0.00087 0.00001 5.40 0.05 0.2576 0.0019 15 0.00001 0.00000 -0.08 8.87 0.0035 0.0012 16 0.00001 0.00000 -3.43 7.59 0.0032 0.0009 The magnetic center is at X = -19.0 +- 0.5 microns Y = 168.7 +- 1.8 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 ^ | S N --> x N S Date: 03-02-1995 Time: 15:32:27 Magnet Name: 197 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 300.3904 +- 4.361452E-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 0.00138 0.00002 -1.77 0.27 0.3549 0.0042 2 0.39008 0.00005 -46.05 0.00 100.0000 0.0000 3 0.00032 0.00001 -23.90 0.61 0.0825 0.0029 4 0.00011 0.00001 21.51 1.66 0.0277 0.0022 5 0.00005 0.00001 -19.63 1.27 0.0122 0.0017 6 0.00052 0.00000 -15.61 0.12 0.1344 0.0011 7 0.00001 0.00001 11.84 8.79 0.0021 0.0017 8 0.00004 0.00001 18.78 0.39 0.0096 0.0023 9 0.00004 0.00001 16.11 0.56 0.0097 0.0017 10 0.00124 0.00000 7.94 0.03 0.3187 0.0006 11 0.00001 0.00000 9.69 3.57 0.0019 0.0010 12 0.00002 0.00001 -0.18 7.45 0.0054 0.0023 13 0.00006 0.00000 11.58 0.42 0.0153 0.0011 14 0.00100 0.00001 5.41 0.05 0.2559 0.0024 15 0.00003 0.00001 4.08 9.47 0.0072 0.0013 16 0.00003 0.00002 2.20 4.24 0.0065 0.0049 The magnetic center is at X = -4.9 +- 0.8 microns Y = 158.4 +- 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 ^ | S N --> x N S Date: 03-02-1995 Time: 15:38:41 Magnet Name: 197 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 350.3923 +- 1.044642E-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 0.00147 0.00002 2.11 0.32 0.3446 0.0053 2 0.42657 0.00008 -46.05 0.00 100.0000 0.0000 3 0.00032 0.00001 -21.94 0.96 0.0757 0.0016 4 0.00013 0.00001 21.92 1.11 0.0306 0.0025 5 0.00004 0.00001 -23.39 2.06 0.0092 0.0025 6 0.00034 0.00000 -15.45 0.05 0.0798 0.0006 7 0.00001 0.00000 15.19 3.15 0.0017 0.0001 8 0.00004 0.00001 17.83 1.27 0.0097 0.0016 9 0.00004 0.00000 17.19 0.60 0.0101 0.0011 10 0.00140 0.00001 7.93 0.02 0.3293 0.0018 11 0.00001 0.00000 3.99 4.72 0.0035 0.0009 12 0.00002 0.00001 8.64 2.68 0.0050 0.0020 13 0.00006 0.00001 11.93 0.32 0.0130 0.0012 14 0.00107 0.00001 5.38 0.01 0.2508 0.0031 15 0.00003 0.00001 4.63 7.31 0.0071 0.0016 16 0.00001 0.00000 2.07 3.24 0.0034 0.0008 The magnetic center is at X = 5.7 +- 0.9 microns Y = 153.8 +- 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 ^ | S N --> x N S 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)