Rome University La Sapienza, Roma
ENEA C. R. Frascati, Frascati (Roma)
Methods employing integration techniques of Lie algebraic nature have been successfully employed in the past to develop charged beam transport codes, for different types of accelerators. These methods have been so far applied to the transverse motion dynamics, while the longitudinal part has been treated using standard tracking codes. In this contribution we extend the simplectic technique to the analysis of longitudinal and coupled longitudinal and transverse motion in charged beam transport with the inclusion of the non linear dynamics due to the wake field effects. We use the method to model different types of instabilities due to high current. We consider in particular the case of coherent synchrotron instabilities and its implication in the design and performances of high current accelerators. We discuss either single pass and recirculated devices. As to this last case, we also include the effect due to quantum noise and damping.
MSU, East Lansing, Michigan
The code COSY INFINITY supports rigorous computations with numerical verification based on Taylor models, a tool developed by us that can be viewed as an extension of the differential algebraic methods that also determines rigorous Taylor remainder bounds. Such verified computation techniques can be utilized for global optimization tasks, resulting in a guarantee that the true optimum over a given domain is found. The method of Taylor models has a high order scaling property, suppressing the problem of over-estimation that is a common problem of reliable computational methods. We have applied the method to some of typical optimization tasks in accelerator physics such as lattice design parameter optimizations and the Lyapunov function based long-term stability estimates for storage rings. The implementation of Taylor models in COSY INFINITY has inherited all the advantageous features of the implementation of differential algebras in the code, resulting in very efficient execution. COSY-GO, the Taylor model based rigorous global optimizer of COSY INFINITY, can run either on a single processor or in a multi processor mode based on MPI. We present various results of optimization problems run on more than 2,000 processors at NERSC operated by the US Department of Energy. Specifically, we discuss rigorous long-term stability estimates of the Tevatron, as well as high-dimensional rigorous design optimization of RIA fragment separators.
GSI, Darmstadt
National Taras Shevchenko University of Kyiv, The Faculty of Physics, Kyiv