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AS SHOWN

AS SHOWN. PHYSICS AND MATHEMATICS OF MAGNETS ARE SIMPLE AND LINEAR EXCEPT IN FREE SPACE THE MAGNETISM IS VERY NON-LINEAR THERE ARE MANY COMPUTER PROGRAMS WHICH CAN CALCULATE AND SOLVE VECTOR AND SCALAR POTENTIAL POISSON — 2 DIMENSIONAL TOSCA – 3DIMENTIONAL OPERA 3D SOPRANO ETC

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AS SHOWN

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  1. AS SHOWN • PHYSICS AND MATHEMATICS OF MAGNETS ARE SIMPLE AND LINEAR • EXCEPT IN FREE SPACE THE MAGNETISM IS VERY NON-LINEAR • THERE ARE MANY COMPUTER PROGRAMS WHICH CAN CALCULATE AND SOLVE VECTOR AND SCALAR POTENTIAL • POISSON—2 DIMENSIONAL • TOSCA– 3DIMENTIONAL • OPERA 3D • SOPRANO ETC • THE CALCULATION IS ACCURATE TO 10-3 • DIFFERNTIAL CALCULATION IS ACCURATE TO FEW MORE ORDER OF MAGNITUDE • SO IN GENERAL MAGNET DESIGN START WITH EXISTING DESIGN AND SCALE, IMPROVE ETC

  2. CLASSES OF DIPOLES • SOLENOIDS • HELMHOLTZCOIL • WINDOW FRAME MAGNET • H-MAGNET • C-MAGNET • COS q MAGNET

  3. H MAGNET holds hc But good field region does not Extends to the conductor surface Or edge of the pole g w wc Following criterion generally holds for wide enough pole and large m

  4. Multipoles for a H magnet roughly can be expressed Edge shims The good field region can be extended by edge shims some times Called Rose shims Increase good field regeon by .5g for .01 And g for 0.001 d s

  5. H-MAGNET saturation H magnet pole field is higher than corresponding gap due to the field Spread beyond the pole Therefore onset of saturation is much lower field Empirical formula for the sextupole term is It can be rewritten in a form

  6. H MAGNET end effect Like window frame magnet similar but slightly different results were reported Compared with widowframe

  7. C-MAGNET SOMETIMES ONE HAS TO MAKE MAGNETS C SHAPED BECAUSE OF THE GEOMETRY OR SPACE RESTRICTIONS The field in c-magnets behaves like H-magnets except the 2-fold symmetry Does not exist Considerable amount of odd multipoles can exist

  8. C-MAGNET SOMETIMES ONE HAS TO MAKE MAGNETS C SHAPED BECAUSE OF THE GEOMETRY OR SPACE RESTRICTIONS The field in c-magnets behaves like H-magnets except the 2-fold symmetry Does not exist Considerable amount of odd multipoles can exist

  9. C-MAGNET cont. Again the good field region like H-magnet And shims can be used to extend the good field Will increase good field region by .5g for 0,01 and g for 0.001 The sextupole term can be expressed

  10. End effect is similar to a H-magnet They are slightly deferent from H-magnet but one may not put too much stock on to it because the numbers are based on just a few measurment Table shows a significant quadrupole and octupole term

  11. COSq MAGNET If one makes current around a ciecle with the current Density distribution cosq The magnetic field inside the current sheet is uniform and It is perfect dipole Since it is impractical to produce perfect cosq distribution Usually simulate the distribution with number of current Blocks It has been shown that n number of current blocks can Eliminate n number of multipoles. That is say 6 blocks may Eliminate b2 …b12

  12. SEPTUM MAGNET current SOMETIMES ONE WANT TO HAVE FIELD TO HAVE SHARP CUTOFF -----USE SEPTUM The septum thickness shall be as thin as Possible Whenever possible the septum should be pulsed In order to reduce duty factor -I I B=B0 B=0 It is perfect septum if the Usually and there is leakage field and the magnitude is empirically At the surface of the septum The leakage field will fall off as

  13. Small gap between septum conductor and return yoke increses the leakage field by Total leakage field would be In addition a cooling channels for the septum also contribute on fringe field The fringe field can be reduced somewhat by arranging cooling channel appropriately Another trick is to increase current in back leg conductor Very short pulse( <<time constant of Cu) septum I -I

  14. LAMBERTSON SEPTUM While a current septum divides field free region in the direction of magnetic field, a lambertson Septum divides region perpendicular to the field line B q Advantage; No restriction on duty factor ie can run CW Also can pulse by laminating the yoke

  15. COMBINED FUNCTION MAGNET • DIPOLE AND QUADRUPOLE CAN BE COMBINED BY OFFSETTING A QUADRUPOLE • ADVANTAGE IS TO REDUCE NUMBER OF MAGNET COMPONENTS AND BETTER PACKING FACTOR • DISADVANTAGE IS THE MAXIMUM DIPOLE FIELD IS LIMITED

  16. FAST RISING KICKER MAGNET • FAST RISING KICKER SHOULD BE ABLE TO RISE BETWEEN TWO SYNCHROTRON BUNCHES • RISE TIME <<1-6 SEC. • MAGNETIC STEEL LAMINATION IS NOT SUITABLE FOR THIS PERPOSE • FERRITE MATERIAL IS USED FOR THE CORE • USUALLY SATURATE AROUND 5 KG AND SOME EVEN LESS • THE CURIE TEMPERRATURE FOR THE FERRITS ARE ABOUT 100 TO 200OC SO CAREFUL NOT TO HEAT THE CORE • USUALLY CONSTRUCTED AS A WIDOWFRAME OR C MAGNET

  17. Magnet rise time L=Lmagnet+Lstray About 0.5 to 1 mH Not practical to reduce inductance less than 1mH In general construct single turn

  18. - PS + When installed in a synchrotron the magnetic core Should be cut at the neutral point and install a Conductor strip to block circulating RF from the Beam current No such problem for C-magnets

  19. + PS - PS Use two power supplies to reduce magnet’s Inductive load to half per power supply

  20. MANUFACTURING CONSIDERATION • ECONOMIC • MANUFACTURING COST • OPERATING COST • ACCURACY AND REPEATABILITY • SPECTROMETR • TRANSPORT MAGNET • SYNCHROTRON MAGNET • RAPID CYCLING FREQURNCY • SOLID CORE • LAMINATED CORE • SOLID HOLLOW CONDUCTER • STRANDED CONDUCTOR

  21. SPECTROMETER DIPOLE IN GENERAL REQUIRE UNIFORM FIELD THROUGHOUT THE APERTURE 10-4 OR BETTER --WINDOWFRAME MAGNET --CAN BE COMPACT AND SHIMABLE TO VERY HIGH FIELD BY SHAPING THE POLES SOLID CORE 1006 OR 1010 STEEL DEPENDS ON HIGHEST FIELD REQUIRED SOLID HOLLW CONDUCTOR

  22. TRANSPOT DIPOLE Reasonable accuracy for this purpose is ~10-3 Higher multipole content can be relaxed because unlike synchrotronthe beam goes through once Generally constructed with solid core, however, depending on the number of magnet a laminated core may be used Parallel or wedged ends? manufacturing consideration vertical horizontal focusing reqirement

  23. Wedge Horizontal focusing No focusing vertical Parallel No focusing horizontal Vertical focusing

  24. STORAGE RING DIPOLES • SOLID CORE MAY BE USED --- SNS • NEEDED TO BE SHIMMED • OVER 10-3 DIFFERENCE MAGNET TO MAGNET ALTHOUGH, MACHINED BY A CNC MACHINE, THERE WERE ENOUGH ERROR ALL STEELS WERE FROM SAME HEAT FROM A MILL THERE WERE ENOUGH DIFFERENCE BETWEEN TOP AND BOTTOM PART OF A LADDLE MAY CONTAIN ODD HARMONICS THE MAGNETS WERE SHIMMED ACCORDING TO THE MEASUREMENT POISSON OR OPERA ARE NOT ACCURATE ENOUGH IN TEIR PERMIABILITY TABEL HOWEVER DIFFERENTAL CALCULATION IS FEW ORDER OF MAGNITUDE BETTER

  25. LAMINATED CORE • ACCURACY OF INDIVIDUAL MAGNETDEPENDS ON THAT OF CUTTING DIE • HARD TO SHIM INDIVIDUAL MAGNET • PRODUCE CONSISTENT MAGNET—COOKIE CUTTER • VERY EFFECTIVE TO ELIMINATE UMALLOWED MULTIPOLES • CONSISTENT LOW FIELD CHARACTERISTICS • EDDY CURRENT • USING LAMINATION THICKNESS DEPENDS ON REPETITION RATE • MAY USE 1006 OR EVEN 1010 STEEL FOR LOW REP RATE • GENERALLY USE Si STEEL(TRANSFORMER STEEL)FOR A HIGHER REP. RATE

  26. SYNCHROTRON DIPOLE • ALL DIPOLES SHOULD BE AS IDENTICAL AS POSSIBLE • FROM LOW INJECTION FIELD TO HIGH FIELD • UNIFORMITY OF STEEL • RANDOMIZE STEEL LAMINATION PLATES • SYMMETRY IS IMPORTANT • ELIMINATE UNALLOWED ODD HARMONICS • PUNCHING DIE USUALLY IS NOT ACCURATE AND SYMMETRIC ENOUGH • THICKNESS OF STEEL COIL MAY NOT BE UNFORM • WHEN STACKING THE LAMINATIONS, NEED TO FLIP THE LAMINATIONS TO EVEN • ASYMMETRY • THICKNESS

  27. HALF OF THE ROLL SHOULD BE PUNCHED FROM THE OTHER SIDE ON THE BACK OF THE LAMINATION SHOULD HAVE IDENTIFYING NOTCHES SHOULD BE INCLUDED—FROM WHICH COIL, REVERSE ETC PROPER RANDOMIZATION COULD BE CHECKED BY LOOKING AT THE NOTCHES

  28. RAPID CYCLING MAGNET AND VACUUM CHAMBER In synchrotron the vacuum chambers function not only is to contain the vacuum but also work as the shield for the circulating RF and forming co-axial current So it should have reasonable conductivity Need reasonable thickness to withstand vacuum pressure There are two problems for synchrotron due to the vacuum chamber Eddy current created multipole field Heat generated by eddy current

  29. Case where one can withstand the heat Like the AGS booster the repetition rate is low enough ~10Hz and dB/dt~10T/sec stainless steel or inconnel Chamber can be used However there still is the multipole problem mainly sextupole Case of flat conducting plate chamber I I x sextupole constant

  30. If one can add a current block counteracting this dB/dt Related sextupole Voltage generated by dB/dt Current driven by pole winding The eddy current generated sextupole is compensated for any rate of magnetic field rise

  31. CERAMIC VACUUM CHAMBER Expensive and difficult to maintain In side surface should be coated with conductive material to prevent electron accumulation Should form a conductive cage to support counter beam RF current to flow ISIS conductive wire cage inside the chamber JPARC conductive strips outside the chamber The wire spacing should be less than the wave-length of relevant micro-wave---GHz??

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