Symplectic Scaling of Transfer Maps including Fringe Fields
AbstractA new method is introduced that provides an accurate and fast approximation
of high-order maps of fringe fields and other fields that change with the
independent variable. While the effects of main fields of optical elements
can be determined very efficiently with DA methods via exponentiation of the
respective propagator, the computation of high-order maps of non-stationary
fields in general requires time-consuming DA integration. The method of
symplectic scaling presented in this paper provides a very fast
approximation of such maps by relating an arbitrary map to that of a
specific previously computed map. This is achieved by a combination of
geometric scaling and a canonically perturbative treatment of a strength
The method is useful for detailed analysis of nonlinear motion, which in
many cases is strongly influenced or even dominated by the presence of
fringe fields. The use of the symplectic scaling method typically speeds up
the computation of fringe field effects by around two orders of magnitude
and thus approaches speeds similar to that of the main field calculation.
The method has been implemented in the code COSY INFINITY; several examples
from various subfields of beam physics are given to illustrate accuracy and
speed of the method.
G. Hoffstätter, M. Berz, Physical Review E
54,5 (1996) 5664-5672
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