Long-term stability of the Tevatron by verified global optimization

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