Long-Term Stability of the Tevatron by Verified Global Optimization
AbstractThe tools used to compute high order transfer maps based on differential algebraic
(DA) methods have recently been augmented by methods that also allow a rigorous
computation of an interval bound for the remainder. In this paper we will show how
such methods can also be used to determine rigorous bounds for the global extrema
of functions in an efficient way. The method is used for the bounding of normal form
defect functions, which allows rigorous stability estimates for repetitive particle
accelerators. However, the method is also applicable to general lattice design problems
and can enhance the commonly used local optimization with heuristic successive
starting point modification.
The global optimization approach studied rests on the
ability of the method to suppress the so-called dependency problem common to
validated computations, as well as effective polynomial bounding techniques. We
review the linear dominated bounder (LDB) and the quadratic fast bounder (QFB)
and study their performance for various example problems in global optimization.
We observe that the method is superior to other global optimization approaches and
can prove stability times similar to what is desired, without any need for expensive
long-term tracking and in a fully rigorous way.
M. Berz, K. Makino, Y.-K. Kim, Nuclear Instruments and Methods A558 (2006) 1-10
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