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Injection through iron and fringe field

This text discusses the transportation of a muon beam through a beam line to a storage ring, specifically focusing on the alignment of the ring and beam line, trajectory displacement, and compensating for fringe fields. It also explores the use of a larger aperture inflector and the propagation of Twiss parameters through iron and other components.

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Injection through iron and fringe field

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  1. Injection through iron and fringe field D. Rubin January 15, 2014 D. Rubin

  2. Transport through M5 beam line to storage ring • Align ring/beam-line so that • Muon trajectory is centered in inflector (narrowest aperture), nominally tangent to storage ring and displaced 68mm + 9=77mm radially outward at inflector exit. Where x_i = 9mm (inflector half aperture) • What about a new inflector with a larger aperture (x_n)? Then the trajectory at the end of M5 line should be displaced D = x_n - x_i further outward. (D ~ 2 cm) • Meanwhile, fringe fields steer beam near upstream end of inflector, thus requiring some compensating angle (with respect to tangent line) at end of M5 line. • (To determine the initial angle and offset that will place the trajectory at the center of a new larger aperture inflector, requires a more expansive field map.) • Fringe field focusing • Vertical field increases from 0 to 1.5T along trajectory through gap => horizontal defocus – with equivalent 1 m long quadrupole with k ~ 0.35 m-2 • Difficult to compensate D. Rubin

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  4. B D. Rubin

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  8. Larger aperture inflector Existing inflector D. Rubin

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  10. Gradient due to fringe from main dipole dBy / dr = 1.45T / 40cm = 3.625 T/m => k = 0.35 m-2 Path length through the fringe L ~ 1. Equivalent to the strongest quadrupole in the M5 line B D. Rubin

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  12. bx= 8.0 m by = 20.0 m h = 4m { At inflector exit For best match into ring K(Q27) = 0.774 m-2 D. Rubin

  13. Questions? How can we place the ring with respect to the M5 line, to accommodate the existing as well as a larger aperture inflector? Do the final focus quadrupoles have sufficient aperture to clear a muon beam where both b and h are large? Do the final focus quadrupoles have sufficient gradient? (Is if possible to place Q27 even closer to the iron?) D. Rubin

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  16. How do twiss parameters propagate through iron, cryostat, inflector into ring D. Rubin

  17. What are the fields along the route of injected beam ? From P. Debevec2012 D. Rubin

  18. Width of backleg =544mm Width of gap = 1394-544 = 850 mm Distance from edge of iron to ideal orbit = 280mm Width of pole = 2 x 280mm From center of gap to backleg iron = 850-280=570mm Radius of central orbit = 7.112 m Field starts to fall off linearly 18cm from center of pole This is 570-180mm =390mm Then the gradient G = Bmax/.39 = 1.4 T/.39m = 3.58 T/m Inflector is 1.7m long. Tan (theta) = 1.7/(7.112 + 0.077) Radius of upstream end of inflector = 7.189 - sqrt(7.189^2+1.7^2)=0.198 So the inflector goes from 77mm to 198+77mm =275mm from center of pole D. Rubin

  19. Radial beam motion • Beam exits yoke • Beam through outer coil • Beam through Inflector • Beam kicked onto orbit B D. Rubin

  20. Inflector Geometry ~1.7 m m central orbit D. Rubin

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