Arbitrary Order Description of Arbitrary Particle Optical Systems
AbstractThe differential algebraic approach for the design and analysis of particle optical systems
and accelerators is presented. It allows the computation of transfer maps to arbitrary
orders for arbitrary arrangements of electromagnetic fields, including the dependence
on system parameters. The resulting maps can be cast into different forms. In the case of
a Hamiltonian system, they can be used to determine the generating function or Eikonal
representation. Also various factored Lie operator representations can be determined
directly. These representations for Hamiltonian systems cannot be determined with any
other method beyond relatively low orders.
In the case of repetitive systems, a combination of the power seres representation and the
Lie operator representation allows a nonlinear change of variables such that the motion is
very simple and its long term behaviour can be studied very efficiently. Furthermore, it is
now possible to compute quantities relevant to the study of circular machines like tune
shifts and chromaticities much more efficiently. Besides these aspects, the ability to
compute maps depending on parameters provides analytical insight into the system. In
addition, this approach allows very efficient optimization, to the extent that in many
cases it is almost completely analytic.
M. Berz, Nuclear Instruments and Methods A298 (1990) 426-440
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