Minimization of Aberrations in Beam Line Design

The aberrations present in a beam line represent the departure from the ideal first-order design. Such aberrations may be of second and higher order. Individual second-order terms may be represented by a matrix T. We derive a formalism for representing the net contribution of such terms to the beam dimensions. Corrective elements such as sextupoles or non-linearities in bending magnets may be employed. A method for minimizing the effects of second-order aberrations has been derived. This method has been incorporated into the program TRANSPORT. Higher-order effects may now arise from the coupling of second-order terms. A computer program TURTLE is used to evaluate such effects.