SLAC Magnetic Measurements Date: 01-16-1997 Time: 14:02:04 Project: SLC Magnet Type: QUAD Magnet Name (Serial #): 434 Bar Code Number: Test Stand: 1 Measurement System: COIL Operator: tss Run Number: 2 Comment: 2 buttons run to 140 amps. Standardization Currents 4 cycles, 2 to 140 to 2 A Test Currents 5.0 25.0 50.0 75.0 100.0 110.0 120.0 125.0 130.0 140.0 130.0 125.0 120.0 110.0 100.0 75.0 50.0 25.0 5.0 Harmonics Measurements Date: 01-16-1997 Time: 14:31:50 Magnet Name: 434 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 125.1608 +- 6.852347E-04 A Harmonics at Rcoil = .0189973 m Nmain = 2 n BLn sigBLn THspole sigTH BLn/BLN sBLn/BLN (Tm) (Tm) (deg) (deg) (%) (%) --- --------+-------- --------+-------- --------+-------- 1 0.00020 0.00000 -60.25 0.09 0.3881 0.0006 2 0.05126 0.00000 44.23 0.00 100.0000 0.0084 3 0.00003 0.00000 29.84 50.55 0.0493 0.0017 4 0.00001 0.00000 -29.72 1.61 0.0213 0.0025 5 0.00004 0.00000 -16.04 0.37 0.0779 0.0011 6 0.00003 0.00000 -5.82 0.30 0.0605 0.0045 7 0.00003 0.00000 17.57 0.76 0.0592 0.0034 8 0.00002 0.00000 9.10 3.82 0.0374 0.0044 9 0.00002 0.00001 10.62 2.22 0.0302 0.0141 10 0.00017 0.00000 -10.23 0.03 0.3264 0.0045 11 0.00000 0.00000 2.74 1.67 0.0091 0.0037 12 0.00000 0.00000 -12.19 1.57 0.0029 0.0008 13 0.00000 0.00000 -7.18 0.39 0.0091 0.0011 14 0.00001 0.00000 -7.11 0.12 0.0202 0.0019 15 0.00000 0.00000 2.11 9.56 0.0024 0.0004 16 0.00000 0.00000 7.45 0.37 0.0031 0.0006 The magnetic center is at X = 64.0 +- 0.1 microns Y = -36.6 +- 0.1 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: 01-16-1997 Time: 14:39:04 Magnet Name: 434 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 140.181 +- 2.501348E-03 A Harmonics at Rcoil = .0189973 m Nmain = 2 n BLn sigBLn THspole sigTH BLn/BLN sBLn/BLN (Tm) (Tm) (deg) (deg) (%) (%) --- --------+-------- --------+-------- --------+-------- 1 0.00022 0.00001 -59.58 1.06 0.3768 0.0092 2 0.05730 0.00002 44.22 0.00 100.0000 0.0399 3 0.00002 0.00000 47.11 12.76 0.0357 0.0038 4 0.00002 0.00000 -32.06 1.74 0.0321 0.0040 5 0.00004 0.00000 -14.38 0.37 0.0781 0.0035 6 0.00004 0.00000 -4.95 0.49 0.0701 0.0042 7 0.00005 0.00000 21.32 0.63 0.0923 0.0087 8 0.00003 0.00000 -7.63 1.61 0.0596 0.0025 9 0.00002 0.00001 15.82 1.61 0.0400 0.0095 10 0.00018 0.00000 -10.07 0.08 0.3143 0.0033 11 0.00000 0.00000 3.13 1.65 0.0084 0.0034 12 0.00000 0.00000 -5.29 4.97 0.0019 0.0007 13 0.00001 0.00000 -7.78 0.58 0.0088 0.0006 14 0.00001 0.00000 -7.30 0.20 0.0217 0.0013 15 0.00000 0.00000 -4.66 3.68 0.0020 0.0011 16 0.00000 0.00000 10.03 0.82 0.0029 0.0004 The magnetic center is at X = 61.7 +- 1.7 microns Y = -36.2 +- 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: 01-16-1997 Time: 14:46:17 Magnet Name: 434 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 125.1263 +- 4.470021E-02 A Harmonics at Rcoil = .0189973 m Nmain = 2 n BLn sigBLn THspole sigTH BLn/BLN sBLn/BLN (Tm) (Tm) (deg) (deg) (%) (%) --- --------+-------- --------+-------- --------+-------- 1 0.00019 0.00000 -63.61 0.09 0.3738 0.0007 2 0.05155 0.00000 44.20 0.00 100.0000 0.0124 3 0.00001 0.00000 40.65 1.06 0.0226 0.0024 4 0.00001 0.00000 -29.80 2.40 0.0275 0.0010 5 0.00003 0.00000 -14.20 0.19 0.0657 0.0013 6 0.00003 0.00000 -8.63 0.80 0.0527 0.0057 7 0.00003 0.00001 16.27 0.13 0.0581 0.0114 8 0.00002 0.00000 -1.22 19.50 0.0323 0.0048 9 0.00006 0.00001 10.90 1.09 0.1090 0.0130 10 0.00017 0.00000 -9.93 0.02 0.3305 0.0009 11 0.00000 0.00000 0.75 2.23 0.0095 0.0028 12 0.00000 0.00000 1.12 10.35 0.0023 0.0015 13 0.00000 0.00000 -7.96 0.74 0.0088 0.0014 14 0.00001 0.00000 -7.20 0.23 0.0226 0.0006 15 0.00000 0.00000 -4.29 1.49 0.0010 0.0005 16 0.00000 0.00000 7.36 1.06 0.0040 0.0007 The magnetic center is at X = 63.6 +- 0.1 microns Y = -31.6 +- 0.1 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) For a double coil (for coil bowing correction), GL = ( (Nturns * Rcoil^2)1 + (Nturns * Rcoil^2)2 )^-1 * (V2 / ang_freq) Let CoilConst = ( (Nturns * Rcoil^2)1 + (Nturns * Rcoil^2)2 )^-1 GL = CoilConst * V2 / 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)