SLAC Magnetic Measurements Date: 04-13-1995 Time: 06:17:11 Magnet Name (Serial #): 160 Bar Code Number: 250 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: 04-13-1995 Time: 07:04:24 Magnet Name: 160 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 10.00286 +- 4.685914E-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 -140.88 0.54 0.3123 0.0032 2 0.01490 0.00000 44.99 0.00 100.0000 0.0000 3 0.00001 0.00000 16.88 0.83 0.0987 0.0039 4 0.00001 0.00000 22.96 0.33 0.0541 0.0028 5 0.00000 0.00000 14.91 2.58 0.0116 0.0024 6 0.00003 0.00000 14.98 0.06 0.2090 0.0016 7 0.00000 0.00000 -12.37 21.78 0.0082 0.0009 8 0.00000 0.00000 13.83 2.03 0.0044 0.0014 9 0.00000 0.00000 0.25 1.96 0.0050 0.0019 10 0.00004 0.00000 -9.01 0.01 0.2973 0.0013 11 0.00000 0.00000 1.93 13.33 0.0022 0.0011 12 0.00000 0.00000 8.85 1.47 0.0037 0.0020 13 0.00000 0.00000 0.81 2.28 0.0074 0.0028 14 0.00004 0.00000 -6.46 0.02 0.2570 0.0013 15 0.00000 0.00000 -1.32 7.13 0.0043 0.0020 16 0.00000 0.00000 -2.60 1.11 0.0058 0.0029 The magnetic center is at X = 88.0 +- 1.4 microns Y = 108.2 +- 1.4 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: 04-13-1995 Time: 07:10:31 Magnet Name: 160 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 25.10461 +- 4.686996E-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 -140.68 0.75 0.2128 0.0005 2 0.03493 0.00000 44.99 0.00 100.0000 0.0000 3 0.00002 0.00000 36.05 0.69 0.0515 0.0036 4 0.00002 0.00000 24.55 0.28 0.0506 0.0026 5 0.00001 0.00000 7.77 2.23 0.0163 0.0019 6 0.00008 0.00000 15.02 0.13 0.2163 0.0012 7 0.00000 0.00000 -0.32 22.15 0.0025 0.0010 8 0.00000 0.00000 19.84 0.68 0.0109 0.0016 9 0.00000 0.00000 -0.30 4.57 0.0095 0.0037 10 0.00010 0.00000 -9.07 0.03 0.2979 0.0014 11 0.00000 0.00000 -9.82 2.36 0.0033 0.0004 12 0.00000 0.00000 4.72 3.01 0.0063 0.0018 13 0.00000 0.00000 0.60 2.76 0.0092 0.0022 14 0.00009 0.00000 -6.43 0.05 0.2564 0.0025 15 0.00000 0.00000 0.80 1.59 0.0046 0.0015 16 0.00000 0.00000 -6.79 3.77 0.0038 0.0007 The magnetic center is at X = 60.2 +- 1.0 microns Y = 73.5 +- 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: 04-13-1995 Time: 07:16:43 Magnet Name: 160 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 50.06848 +- 8.697865E-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 -149.58 0.93 0.1958 0.0012 2 0.06881 0.00001 44.99 0.00 100.0000 0.0000 3 0.00004 0.00000 40.12 1.12 0.0549 0.0022 4 0.00003 0.00000 22.58 0.57 0.0478 0.0026 5 0.00001 0.00000 6.11 2.74 0.0154 0.0021 6 0.00015 0.00000 14.95 0.08 0.2165 0.0009 7 0.00000 0.00000 15.33 6.27 0.0027 0.0014 8 0.00000 0.00000 10.89 0.66 0.0053 0.0006 9 0.00001 0.00000 -4.89 3.12 0.0077 0.0036 10 0.00021 0.00000 -9.00 0.02 0.3000 0.0015 11 0.00000 0.00000 -8.50 2.45 0.0023 0.0014 12 0.00000 0.00000 7.16 9.64 0.0020 0.0017 13 0.00001 0.00000 -3.04 1.49 0.0103 0.0034 14 0.00017 0.00000 -6.44 0.04 0.2525 0.0015 15 0.00000 0.00000 -0.68 5.67 0.0026 0.0014 16 0.00000 0.00000 -4.34 8.32 0.0065 0.0024 The magnetic center is at X = 44.3 +- 1.3 microns Y = 75.4 +- 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: 04-13-1995 Time: 07:22:59 Magnet Name: 160 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 100.0647 +- 7.144491E-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 0.00027 0.00000 -156.67 0.54 0.1993 0.0019 2 0.13727 0.00003 44.99 0.00 100.0000 0.0000 3 0.00007 0.00000 39.57 0.99 0.0540 0.0016 4 0.00006 0.00000 22.75 0.75 0.0469 0.0018 5 0.00002 0.00000 5.79 1.49 0.0156 0.0022 6 0.00030 0.00000 14.98 0.10 0.2170 0.0010 7 0.00000 0.00000 20.73 3.07 0.0031 0.0006 8 0.00001 0.00000 12.23 0.96 0.0053 0.0004 9 0.00001 0.00000 -3.27 3.37 0.0070 0.0027 10 0.00041 0.00000 -9.00 0.03 0.3015 0.0008 11 0.00000 0.00000 1.78 12.57 0.0019 0.0005 12 0.00001 0.00000 7.45 2.56 0.0039 0.0009 13 0.00001 0.00001 -1.40 7.70 0.0074 0.0049 14 0.00035 0.00000 -6.43 0.04 0.2533 0.0036 15 0.00001 0.00000 -2.78 3.43 0.0071 0.0023 16 0.00001 0.00000 2.56 4.55 0.0038 0.0019 The magnetic center is at X = 35.3 +- 0.8 microns Y = 81.8 +- 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: 04-13-1995 Time: 07:29:15 Magnet Name: 160 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 150.0806 +- 9.404602E-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 0.00037 0.00000 -156.80 0.73 0.1820 0.0018 2 0.20549 0.00001 44.97 0.00 100.0000 0.0000 3 0.00011 0.00001 40.26 0.32 0.0557 0.0028 4 0.00009 0.00000 22.30 0.61 0.0447 0.0021 5 0.00003 0.00001 4.69 2.11 0.0136 0.0030 6 0.00043 0.00000 14.93 0.09 0.2071 0.0014 7 0.00001 0.00000 11.83 16.37 0.0029 0.0011 8 0.00001 0.00000 11.90 1.18 0.0047 0.0013 9 0.00002 0.00001 -2.29 3.13 0.0078 0.0031 10 0.00063 0.00000 -9.02 0.01 0.3051 0.0010 11 0.00000 0.00000 -4.67 10.54 0.0023 0.0014 12 0.00001 0.00001 5.51 9.87 0.0051 0.0025 13 0.00002 0.00001 3.79 4.37 0.0080 0.0043 14 0.00052 0.00001 -6.46 0.02 0.2526 0.0026 15 0.00001 0.00000 -3.06 2.16 0.0034 0.0019 16 0.00001 0.00000 1.18 7.58 0.0042 0.0012 The magnetic center is at X = 32.0 +- 1.0 microns Y = 74.7 +- 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: 04-13-1995 Time: 07:35:30 Magnet Name: 160 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 200.3268 +- 4.984278E-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 0.00049 0.00001 -159.28 0.41 0.1810 0.0030 2 0.27316 0.00007 44.97 0.00 100.0000 0.0000 3 0.00016 0.00000 39.18 1.21 0.0571 0.0013 4 0.00013 0.00000 27.89 0.78 0.0460 0.0008 5 0.00004 0.00001 5.95 2.79 0.0139 0.0019 6 0.00055 0.00000 14.96 0.06 0.1998 0.0012 7 0.00001 0.00000 12.84 15.85 0.0019 0.0014 8 0.00002 0.00000 3.39 0.51 0.0083 0.0013 9 0.00002 0.00001 1.03 4.01 0.0066 0.0037 10 0.00084 0.00000 -9.03 0.04 0.3057 0.0013 11 0.00001 0.00000 -5.10 11.66 0.0030 0.0008 12 0.00002 0.00001 7.28 3.05 0.0058 0.0024 13 0.00003 0.00002 3.22 3.77 0.0093 0.0062 14 0.00069 0.00000 -6.47 0.03 0.2539 0.0001 15 0.00001 0.00001 3.33 5.42 0.0049 0.0022 16 0.00002 0.00000 -3.51 7.91 0.0064 0.0008 The magnetic center is at X = 28.6 +- 0.7 microns Y = 75.6 +- 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: 04-13-1995 Time: 07:41:47 Magnet Name: 160 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 250.4298 +- 8.209313E-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 -163.63 0.36 0.1785 0.0019 2 0.33810 0.00004 44.97 0.00 100.0000 0.0000 3 0.00021 0.00001 38.11 0.82 0.0606 0.0018 4 0.00014 0.00001 25.96 0.84 0.0412 0.0025 5 0.00005 0.00001 6.90 1.67 0.0137 0.0019 6 0.00060 0.00001 15.02 0.05 0.1766 0.0015 7 0.00001 0.00000 9.75 19.74 0.0021 0.0008 8 0.00002 0.00000 17.01 0.42 0.0059 0.0008 9 0.00003 0.00000 -0.90 1.88 0.0074 0.0009 10 0.00104 0.00000 -9.04 0.01 0.3089 0.0011 11 0.00001 0.00000 -4.01 10.76 0.0033 0.0013 12 0.00002 0.00000 2.81 0.95 0.0074 0.0005 13 0.00003 0.00001 -0.24 1.48 0.0098 0.0027 14 0.00086 0.00001 -6.47 0.01 0.2537 0.0022 15 0.00002 0.00000 -0.49 7.40 0.0051 0.0011 16 0.00002 0.00000 -1.54 8.45 0.0052 0.0014 The magnetic center is at X = 22.5 +- 0.5 microns Y = 76.5 +- 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: 04-13-1995 Time: 07:48:03 Magnet Name: 160 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 300.4194 +- 5.469802E-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 0.00078 0.00001 -169.50 0.62 0.2006 0.0014 2 0.39033 0.00011 44.97 0.00 100.0000 0.0000 3 0.00025 0.00001 33.85 0.24 0.0640 0.0026 4 0.00015 0.00000 24.27 0.63 0.0384 0.0011 5 0.00006 0.00001 7.12 1.75 0.0152 0.0032 6 0.00048 0.00001 14.93 0.04 0.1240 0.0020 7 0.00001 0.00000 -9.19 20.04 0.0030 0.0005 8 0.00003 0.00000 19.41 0.61 0.0079 0.0011 9 0.00001 0.00001 3.79 2.05 0.0037 0.0015 10 0.00125 0.00001 -9.03 0.04 0.3196 0.0021 11 0.00001 0.00001 -3.53 11.60 0.0032 0.0015 12 0.00002 0.00000 3.21 4.69 0.0059 0.0011 13 0.00003 0.00001 1.55 1.58 0.0068 0.0025 14 0.00099 0.00001 -6.46 0.02 0.2538 0.0014 15 0.00002 0.00001 2.99 5.83 0.0050 0.0020 16 0.00003 0.00001 1.15 1.93 0.0068 0.0034 The magnetic center is at X = 16.3 +- 1.0 microns Y = 88.1 +- 0.6 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: 04-13-1995 Time: 07:54:19 Magnet Name: 160 Run Number: 1 FIELD HARMONICS Magnet Current, Imag = 350.4258 +- 1.47845E-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 0.00092 0.00002 -171.61 0.33 0.2147 0.0036 2 0.42684 0.00008 44.96 0.00 100.0000 0.0000 3 0.00028 0.00001 31.30 0.85 0.0655 0.0021 4 0.00016 0.00001 24.63 0.64 0.0374 0.0020 5 0.00006 0.00001 6.44 2.35 0.0137 0.0033 6 0.00028 0.00001 14.88 0.15 0.0663 0.0012 7 0.00001 0.00000 -8.79 18.81 0.0026 0.0010 8 0.00003 0.00000 16.64 0.68 0.0066 0.0011 9 0.00003 0.00001 0.15 1.40 0.0062 0.0013 10 0.00141 0.00001 -9.02 0.01 0.3293 0.0013 11 0.00001 0.00000 -6.14 5.83 0.0023 0.0011 12 0.00002 0.00001 -0.00 4.89 0.0037 0.0015 13 0.00004 0.00001 0.73 0.88 0.0084 0.0024 14 0.00106 0.00001 -6.49 0.03 0.2485 0.0016 15 0.00001 0.00000 1.81 5.71 0.0034 0.0007 16 0.00004 0.00001 -0.88 0.92 0.0092 0.0027 The magnetic center is at X = 14.0 +- 0.6 microns Y = 94.9 +- 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 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)