Beam transfer lines

After making some distinctions between transfer lines and circular machines, certain problems, typical of the type met by a transfer line designer, are discussed. The topics chosen include: steering, measurement of emittance and mismatch, setting tolerances for magnet alignment and excitation, emittance dilution due to mismatches and scattering in thin windows and lastly emittance-exchange insertions. 1 . DISTINCTIONS BETWEEN TRANSFER LINES AND PERIODIC CIRCULAR MACHINES Transmission of the position-velocity vector of a particle through a section of a transfer line, or circular machine, can be simply represented by a 2 x 2 matrix (Fig. 1). Fig. 1 Transmission through a section of lattice (y represents either transverse coordinate) y2 ′ y2     = C S ′ C ′ S     y1 ′ y1     = M1→2 y1 ′ y1     . (1) The transfer matrix M1→2 can be found by multiplying together the transfer matrices for the individual elements in the appropriate order. The individual matrices have the form, My = cos (or cosh) φ s φ sin (or sinh) φ − φ s sin (or − sinh) φ cos (or cosh) φ 