Design of a Fifth-Order Achromat
AbstractA repetitive system free of all aberrations up to the
fifth order was designed based on a recently developed analytical theory that, in principle,
allows the design of such achromats to an arbitrary order.
It serves as an example to show that complete correction
of aberrations is possible beyound order three, which is the highest order
Instead of repetition of identical cells, which is widely used
in achromat design based on normal form theory, we utilize cells which are
obtained from the the original ones through mirror imaging about the
$x$-$y$ plane, which corresponds to a reversion. In our design, the second half of
the ring is the reversion of the first one, and two turns make a
fifth-order achromat. A possible application of repetitive high-order achromats being
time-of-flight spectroscopy, the resulting ring was analyzed with
respect to dynamic aperture and energy resolution using maps of orders nine and higher.
W. Wan, M. Berz, Nuclear Instruments and Methods A423, 1 (1999) 1-6
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