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Magnets’ interactions with beam.

Magnets’ interactions with beam. Neil Marks, DLS/CCLRC, Daresbury Laboratory, Warrington WA4 4AD, U.K. Tel: (44) (0)1925 603191 Fax: (44) (0)1925 603192. Dipoles. Dipoles can be:. Parallel ended dipole. Sector dipole. These dipoles have different focusing effect on the beam;

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Magnets’ interactions with beam.

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  1. Magnets’ interactions with beam. Neil Marks, DLS/CCLRC, Daresbury Laboratory, Warrington WA4 4AD, U.K. Tel: (44) (0)1925 603191 Fax: (44) (0)1925 603192

  2. Dipoles • Dipoles can be: Parallel ended dipole. Sector dipole These dipoles have different focusing effect on the beam; (the curved nature is to save material and has no effect on beam focusing).

  3. B B beam End focusing effects • Sector dipoles focus horizontally : The end field in a parallel ended dipole focuses vertically : Off the vertical centre line, the field component normal to the beam direction produces a vertical focusing force.

  4. Upright quadrupole field. • Beam that is radially • focused is vertically • defocused.

  5. Skew quadrupole field. • Beam that has radial displacement (but no vertical) is deflected vertically; • horizontally central beam with vertical displacement is deflected radially; • so skew quadrupole couples horizontal and vertical betatron oscillations.

  6. -C +C +C -C -C +C By x Sextupole field. • off-momentum particles are incorrectly focused in quadrupoles (eg, high momentum particles with greater rigidity are under-focused), so betatron oscillation frequencies are modified - chromaticity; • but off momentum particles circulate with a radial displacement (high momentum particles at larger x); • so positive sextupole field corrects this effect – can reduce chromaticity to 0; • we shall also see that the first ‘allowed’ error harmonic in a dipole is sextupole field – resulting negative chromaticity requires correction.

  7. Octupole field • Effect? • By  x3 • Octupole field induces ‘Landau damping’ : • introduces tune-spread as a function of betatron amplitude; • de-coheres betatron oscillations; • reduces couplings.

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