MAGNETS

1. MAGNETS

2. Dipole -I g I l Approximately 1 cm gap 1 kG requires 800 amp-turn Also ½ inch 1kG requires 1 kA This is true for infinite gap width but Use edge shimmes to control multipoles

3. Inductance Stored energy For rapid cycling machine try to keep B as low as possible

4. quadrupole Rule of thumb: 400 amp-turn for 10T/m and 1 cm radius Basic pole surface is hyperbola But shimmes to be added at ends

5. Inductance Distance from center to the coil face Cooling water formulae for power loss P Temperature rise Cooling water velocity Flow area Shape factor ( for a round holes Hydraulic diameter

6. Formulae continued For turbulent flow since For round pipe and take in meters alternately But many uses somewhat simpler formula and

7. Dipole design procedure use Poisson with the edge bump best 2-D design use 3-D edge chamfer (Rogowski contour) to minimize force on laminations and multi-pole(sexstupole) integral Quadrupole design procedure use Poisson to have 2D design best is start with known profile using edge profile to eliminate 12 pole and as much of 20 pole use edge chamfer to eliminate force and multipole integral Some times one has to build the multi-pole in the body to eliminate multi-pole integral

8. 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

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

10. B GOOD FIELD REGION SOLENOIDS

11. B GOOD FIELD REGION SOLENOIDS

12. ELECTRIC CURRENT AND MAGNETIC MATERIAL WITH INFINITE MU -I +I B .

13. ELECTRIC CURRENT AND MAGNETIC MATERIAL WITH INFINITE MU -I +I B .

14. ELECTRIC CURRENT AND MAGNETIC MATERIAL WITH INFINITE MU -I +I B .

15. B WINDOW FRAME MAGNET VERY UNIFORM FIELD MAINLY USED FOR A SPECTROMETER MAGNET FOR INFINITE m FIELD IS UNFORM UP TO THE COIL SURFACE

16. WIDOW FRAME MAGNET saturation effect t g w wc

19. Since there is two fold symmetry sextupole decapole Sextupole dominates the field non uniformity Computer study with Poisson show with good approximation Or can be expressed

20. WINDOWFRAME MAGNET end effect Also at the median plain Magnetic length can be expressed At lower field where there is no saturation effect and

24. 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

25. 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

26. d/g s/g

27. 0.01 0.001 SHIMED 0.001 0.01 Shimed

29. 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

32. H MAGNET end effect Like widow frame magnet similar but slightly different results were reported

34. 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

35. 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

39. 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

40. 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

42. 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

47. SEPTUM MAGNET current SOME TIMES 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

49. 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

50. 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