Cryomodule Quad Doublet Solutions – M Church 9/12/07 1 NML Cryomodule Quad Doublet Lattice Solutions  Question  Are quadrupoles required as part of the cryomodule package?  Assumptions  29E-6 normalized emittance (blowup by CSR in chicane)  Injector kinetic energy = 46 MeV  6 cryomodules: 1 st = TTF no quads; 2 nd = TTF with quad doublet; 3 rd – 6 th = ILC with quad doublet  TTF-like quad doublets: 20 T/m, L=0.15 m  Physical aperture = ±17.5mm  Applied condition  Require minimum aperture of ±8 beam sigmas through cryomodules

Cryomodule Quad Doublet Solutions – M Church 9/12/07 2 Allowed Initial Lattice Parameters: 31 MV/m, no quads For initial lattice parameters outside this region, the beam size violates the aperture requirement somewhere within the 6 cryomodules.

Cryomodule Quad Doublet Solutions – M Church 9/12/07 3 Quad Doublet Solution: 31 MV/m CM2 quads: 6.8 T/m CM3 quads: 3.1 T/m CM4 quads: 4.3 T/m CM5 quads: 5.9 T/m CM6 quads: 7.6 T/m

Cryomodule Quad Doublet Solutions – M Church 9/12/07 4 Allowed Initial Lattice Parameters: 16 MV/m, no quads For initial lattice parameters outside this region, the beam size violates the aperture requirement somewhere within the 6 cryomodules.

Cryomodule Quad Doublet Solutions – M Church 9/12/07 5 Quad Doublet Solution: 16 MV/m CM2 quads: 1.3 T/m CM3 quads: 1.2 T/m CM4 quads: 1.8 T/m CM5 quads: 2.4 T/m CM6 quads: 3.2 T/m

Cryomodule Quad Doublet Solutions – M Church 9/12/07 6 Summary Quadrupole doublets are required in most of the cryomodules to compensate RF focusing Quadrupole focusing strength of 20 T/m x.15 m is adequate; half that is probably adequate Initial lattice functions at entrance of 1 st cryomodule is a constraint on injector design