SLAC Magnetic Measurements Date: 07-02-1998 Time: 12:41:22 Project: PEP2LER Magnet Type: SEXT Magnet Name (Serial #): 153 Measurement System: 2895 Operator: zw Run Number: 2 Comment: 60 A run Standardization Currents 3 cycles, 0 to 60 to 0 A Test Currents 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0 45.0 50.0 55.0 60.0 Harmonics Measurements Date: 07-02-1998 Time: 13:28:40 Magnet Name: 153 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 20.05205 +- 3.014181E-03 A Harmonics at Rcoil = .045002 m Main Harmonic N = 3 n BLn sigBLn THspole sigTH BLn/BLN sBLn/BLN (Tm) (Tm) (deg) (deg) (%) (%) --- ------------+------------ --------+-------- ---------+--------- 1 0.344748E-04 0.355137E-06 -128.16 0.79 0.82711 0.00852 2 0.818726E-04 0.665771E-06 85.90 0.08 1.96426 0.01598 3 0.416812E-02 0.705544E-06 -30.65 0.00 100.00000 0.02394 4 0.159097E-04 0.113140E-06 -19.94 2.06 0.38170 0.00272 5 0.494471E-05 0.571010E-06 14.34 0.60 0.11863 0.01370 6 0.149106E-05 0.295713E-06 -11.04 6.18 0.03577 0.00709 7 0.196927E-05 0.579567E-06 14.18 2.44 0.04725 0.01390 8 0.195046E-05 0.543206E-06 0.84 1.57 0.04679 0.01303 9 0.147314E-04 0.783562E-06 9.29 0.12 0.35343 0.01880 10 0.828113E-06 0.762662E-06 12.68 12.95 0.01987 0.01830 11 0.113112E-05 0.505126E-06 12.13 8.33 0.02714 0.01212 12 0.799244E-06 0.670409E-06 3.24 13.93 0.01918 0.01608 13 0.127524E-05 0.918668E-06 -7.32 3.89 0.03060 0.02204 14 0.123418E-05 0.833903E-06 -2.14 1.02 0.02961 0.02001 15 0.278787E-05 0.855883E-06 4.98 0.94 0.06689 0.02053 16 0.131391E-05 0.709200E-06 0.56 5.30 0.03152 0.01701 17 0.965031E-06 0.635427E-06 -4.70 6.39 0.02315 0.01524 18 0.820988E-06 0.577571E-06 9.65 5.35 0.01970 0.01386 19 0.839505E-06 0.789687E-06 -2.44 9.51 0.02014 0.01895 20 0.104333E-05 0.691446E-06 -0.72 4.50 0.02503 0.01659 21 0.113464E-05 0.912681E-06 -5.40 3.36 0.02722 0.02190 22 0.126332E-05 0.965482E-06 -3.07 2.89 0.03031 0.02316 23 0.146567E-05 0.618431E-06 3.90 4.22 0.03516 0.01484 24 0.137518E-05 0.496632E-06 0.28 3.09 0.03299 0.01192 25 0.117033E-05 0.619261E-06 4.89 14.40 0.02808 0.01486 26 0.139139E-05 0.729507E-06 4.38 1.17 0.03338 0.01750 27 0.137186E-05 0.491453E-06 5.51 2.06 0.03291 0.01179 28 0.116823E-05 0.581784E-06 0.32 1.53 0.02803 0.01396 29 0.115573E-05 0.874949E-06 -3.58 3.43 0.02773 0.02099 30 0.101999E-05 0.589434E-06 2.73 3.39 0.02447 0.01414 31 0.920933E-06 0.817577E-06 -5.72 2.98 0.02209 0.01962 32 0.108687E-05 0.100746E-05 2.51 2.18 0.02608 0.02417 33 0.847233E-06 0.747640E-06 3.41 5.35 0.02033 0.01794 34 0.879020E-06 0.666253E-06 2.40 2.01 0.02109 0.01598 35 0.929482E-06 0.935850E-06 2.22 2.02 0.02230 0.02245 36 0.880780E-06 0.771529E-06 -4.94 1.17 0.02113 0.01851 37 0.923755E-06 0.650345E-06 -4.35 1.04 0.02216 0.01560 38 0.937715E-06 0.840801E-06 -3.04 2.06 0.02250 0.02017 39 0.112462E-05 0.594387E-06 4.01 3.22 0.02698 0.01426 40 0.152863E-05 0.946449E-06 0.42 1.22 0.03667 0.02271 Date: 07-02-1998 Time: 14:06:09 Magnet Name: 153 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 40.0724 +- 4.105664E-03 A Harmonics at Rcoil = .045002 m Main Harmonic N = 3 n BLn sigBLn THspole sigTH BLn/BLN sBLn/BLN (Tm) (Tm) (deg) (deg) (%) (%) --- ------------+------------ --------+-------- ---------+--------- 1 0.227813E-04 0.720676E-07 -151.13 1.31 0.27656 0.00087 2 0.163470E-03 0.392516E-06 86.54 0.10 1.98450 0.00477 3 0.823736E-02 0.352968E-06 -30.65 0.00 100.00000 0.00606 4 0.317267E-04 0.496784E-06 -18.52 0.50 0.38516 0.00603 5 0.104234E-04 0.701737E-06 12.89 0.33 0.12654 0.00852 6 0.282868E-05 0.929113E-07 -17.18 1.89 0.03434 0.00113 7 0.271634E-05 0.823648E-06 13.63 4.36 0.03298 0.01000 8 0.430943E-05 0.383278E-06 -0.58 0.45 0.05232 0.00465 9 0.291918E-04 0.625690E-06 9.41 0.12 0.35438 0.00760 10 0.140147E-05 0.665032E-06 -3.77 4.80 0.01701 0.00807 11 0.137982E-05 0.399216E-06 8.64 3.97 0.01675 0.00485 12 0.125891E-05 0.459014E-06 9.09 3.15 0.01528 0.00557 13 0.118128E-05 0.869029E-06 -7.19 3.76 0.01434 0.01055 14 0.166882E-05 0.673692E-06 -3.08 1.20 0.02026 0.00818 15 0.578493E-05 0.646044E-06 6.01 0.50 0.07023 0.00784 16 0.127869E-05 0.223335E-06 5.02 4.17 0.01552 0.00271 17 0.135828E-05 0.235176E-06 -1.24 8.65 0.01649 0.00285 18 0.181415E-05 0.388064E-06 0.19 2.40 0.02202 0.00471 19 0.178462E-05 0.672779E-06 -8.69 2.40 0.02166 0.00817 20 0.166084E-05 0.835109E-06 2.98 8.03 0.02016 0.01014 21 0.190245E-05 0.474355E-06 -1.30 3.74 0.02310 0.00576 22 0.203107E-05 0.587929E-06 -7.70 3.70 0.02466 0.00714 23 0.224200E-05 0.525679E-06 -7.19 8.61 0.02722 0.00638 24 0.268796E-05 0.701675E-06 4.67 1.73 0.03263 0.00852 25 0.221491E-05 0.102411E-05 -3.97 2.74 0.02689 0.01243 26 0.232553E-05 0.805628E-06 -2.55 2.98 0.02823 0.00978 27 0.325874E-05 0.413928E-06 -4.84 2.78 0.03956 0.00503 28 0.228054E-05 0.813515E-06 5.46 2.09 0.02769 0.00988 29 0.233948E-05 0.321854E-06 1.89 2.15 0.02840 0.00391 30 0.132170E-05 0.396540E-06 -1.30 2.54 0.01605 0.00481 31 0.184424E-05 0.108271E-05 -3.01 5.47 0.02239 0.01314 32 0.147186E-05 0.877022E-06 -4.56 2.03 0.01787 0.01065 33 0.140232E-05 0.371874E-06 -1.62 3.21 0.01702 0.00451 34 0.112540E-05 0.327790E-06 -0.95 2.32 0.01366 0.00398 35 0.112637E-05 0.495599E-06 -4.37 0.86 0.01367 0.00602 36 0.105664E-05 0.501832E-06 0.53 1.74 0.01283 0.00609 37 0.139722E-05 0.733331E-06 3.38 2.74 0.01696 0.00890 38 0.147140E-05 0.361325E-06 -2.64 2.18 0.01786 0.00439 39 0.168305E-05 0.606611E-06 -3.18 1.25 0.02043 0.00736 40 0.252713E-05 0.480463E-06 -0.06 9.00 0.03068 0.00583 Date: 07-02-1998 Time: 14:42:17 Magnet Name: 153 Run Number: 2 FIELD HARMONICS Magnet Current, Imag = 60.15343 +- 1.957305E-03 A Harmonics at Rcoil = .045002 m Main Harmonic N = 3 n BLn sigBLn THspole sigTH BLn/BLN sBLn/BLN (Tm) (Tm) (deg) (deg) (%) (%) --- ------------+------------ --------+-------- ---------+--------- 1 0.199875E-04 0.752355E-07 161.28 0.09 0.16179 0.00061 2 0.248856E-03 0.130354E-06 86.82 0.01 2.01440 0.00106 3 0.123539E-01 0.193096E-06 -30.65 0.00 100.00000 0.00221 4 0.473769E-04 0.316760E-06 -19.08 0.08 0.38350 0.00256 5 0.166583E-04 0.343449E-06 12.95 0.24 0.13484 0.00278 6 0.435696E-05 0.301062E-06 -15.60 0.89 0.03527 0.00244 7 0.413309E-05 0.112435E-05 12.89 3.11 0.03346 0.00910 8 0.557959E-05 0.442415E-06 -0.46 0.54 0.04516 0.00358 9 0.434530E-04 0.238385E-06 9.32 0.05 0.35174 0.00193 10 0.128589E-05 0.240605E-06 -3.21 0.92 0.01041 0.00195 11 0.143163E-05 0.298167E-06 13.27 2.57 0.01159 0.00241 12 0.164360E-05 0.462730E-06 -11.28 6.44 0.01330 0.00375 13 0.102627E-05 0.458630E-06 -9.47 19.94 0.00831 0.00371 14 0.190550E-05 0.307165E-06 -2.29 0.38 0.01542 0.00249 15 0.890577E-05 0.402889E-06 5.68 0.17 0.07209 0.00326 16 0.951159E-06 0.362644E-06 0.20 2.33 0.00770 0.00294 17 0.839517E-06 0.343245E-06 2.27 5.26 0.00680 0.00278 18 0.144661E-05 0.610676E-06 -1.70 0.52 0.01171 0.00494 19 0.127665E-05 0.206767E-06 -7.73 2.70 0.01033 0.00167 20 0.164001E-05 0.683870E-06 7.31 2.42 0.01328 0.00554 21 0.293831E-05 0.644606E-06 -0.01 4.11 0.02378 0.00522 22 0.193429E-05 0.510166E-06 7.59 5.85 0.01566 0.00413 23 0.289208E-05 0.513614E-06 -6.65 3.66 0.02341 0.00416 24 0.295706E-05 0.101538E-05 5.08 0.71 0.02394 0.00822 25 0.178310E-05 0.480284E-06 -3.03 4.66 0.01443 0.00389 26 0.266317E-05 0.319976E-06 -5.26 0.83 0.02156 0.00259 27 0.384851E-05 0.507780E-06 -5.52 1.37 0.03115 0.00411 28 0.265951E-05 0.535292E-06 2.99 4.36 0.02153 0.00433 29 0.369452E-05 0.637007E-06 1.22 1.31 0.02991 0.00516 30 0.206077E-05 0.587664E-06 -1.74 7.18 0.01668 0.00476 31 0.108420E-05 0.225707E-06 -2.85 2.96 0.00878 0.00183 32 0.126427E-05 0.540451E-06 1.80 6.44 0.01023 0.00437 33 0.129175E-05 0.193003E-06 3.18 1.57 0.01046 0.00156 34 0.122057E-05 0.651416E-06 -0.27 2.32 0.00988 0.00527 35 0.970993E-06 0.261929E-06 2.50 4.49 0.00786 0.00212 36 0.105870E-05 0.141571E-06 0.56 2.22 0.00857 0.00115 37 0.835084E-06 0.340344E-06 -2.80 0.85 0.00676 0.00275 38 0.260928E-05 0.545726E-06 -2.26 1.51 0.02112 0.00442 39 0.206386E-05 0.262618E-06 -3.32 4.37 0.01671 0.00213 40 0.352985E-05 0.478706E-06 -0.16 2.85 0.02857 0.00387 SUMMARY OF THE CALCULATIONS AND CONVENTIONS USED Calculation Of SL: V3 = Nturns * velocity * B3 * L = Nturns * Rcoil * ang_freq * 1/2 * SL * Rcoil^2 = Nturns * Rcoil^3 * ang_freq * 1/2 * SL SL = 2 * V3 / (Nturns * Rcoil^3 * ang_freq) For a double coil (for coil bowing correction), SL = ( (1 / Nturns * Rcoil^3)1 + (1 / Nturns * Rcoil^3)2 ) * (2 * V3 / ang_freq) Let CoilConst = ( (1 / Nturns * Rcoil^3)1 + (1 / Nturns * Rcoil^3)2 ) SL = CoilConst * 2 * V3 / 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 / BL3 = Vn / V3 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 Sextupole Center: In the sextupole's frame, Bx' = S * x' * y' By' = 1/2 * S * (x'^2 - y'^2). In the coil's frame (unprimed frame) the magnetic center is at (x0, y0). In the coil's frame, Bx = S * (x - x0) * (y - y0) By = 1/2 * S * [(x - x0)^2 - (y - y0)^2]. The magnetic center can be found in terms of the measured quadrupole field. Compare Br and Btheta on the x-axis to Bxquad = -S * (x0 * y + y0 * x) Byquad = -S * (x0 * x - y0 * y). Evaluate at x = Rcoil, y = 0 and compare to Br(theta = 0) = Bx, Btheta(theta = 0) = By. In terms of the measured integrated strengths, this gives Xcenter = x0 = - (1/(SL * Rcoil)) * BL2 * sin(2 * THspole2) Ycenter = y0 = - (1/(SL * Rcoil)) * BL2 * cos(2 * THspole2)