TUSCI1
MSU, East Lansing, Michigan, USA
FZJ, Jülich, Germany
St. Petersburg State University, St. Petersburg, Russia
MSU, East Lansing, Michigan, USA
THSCI1
MSU, East Lansing, Michigan, USA
A common task in the design and analysis of an accelerator is the study of the transfer map of the system. Of particular interest is the estimation of the region of stability of a given system. Typically, this is done using symplectic particle tracking and visual analysis of the resulting Poincare maps for signatures of chaoticity and island structures near high-period fixed points. We describe a method to compute rigorous enclosures of all periodic points of a given order in a given map based on Taylor Model methods. We then apply this algorithm to a real world transfer map of the Tevatron accelerator to rigorously identify islands and resonances in its transfer map. This mathematically rigorous method to locate resonances in the transfer map automatically yields all regions where resonances up to a certain order appear. The island structure exhibited by the map in those regions is then studied further by computing the invariant manifolds associated with the hyperbolic periodic points of the map. This manifold structure can provide further insight into the dynamics of the map, including the emergence of chaotic motion at the appearance of crossings of the manifolds.
THADC2
MSU, East Lansing, Michigan, USA
Recent interest electric dipole moments of hadrons and light nuclei necessitates the design of storage ring designs relying on electrostatic elements for deflection and focusing. Since the effects of interest are exceedingly small and difficult to extract from the dynamics, unusually high precision in the understanding of the linear and nonlinear optics is required. This leads to the need of precise treatment of a various effects that are often of subdued importance, including the detailed shape of fringe fields and their influence on steering, spin flip devices, and rf cavities out of synch with the frequency of the ring. In all studies, it is important to perform symplectic tracking for the full spin-orbit dynamics. At the same time it is necessary to preserve the particle’s energy during transversal of electric potentials, errors in which are similarly detrimental as errors in symplecticity. Unfortunately it is known that schemes to preserve symplecticity do not simultaneously preserve energy and vice versa. We present some hybrid approaches based on high-order maps that minimize the violations of either invariant while minimally impacting spin-orbit motion.
THADC3
MSU, East Lansing, Michigan, USA
Fermilab, Batavia, USA
FFAGs are being considered for various new classes of accelerators, including proton drivers for muon colliders and neutrino factories, for accelerator driven subcritical reactors, and for medical applications. Their key advantages are compactness, CW operation and large acceptance. However, due to the complicated field arrangements, beam dynamics simulations are challenging for conventional simulation codes. Among various levels of sophistication of dealing with beam elements, one of the most advanced modes of the code COSY INFINITY computes the 3D field distributions along the trajectory of the particles, not only at the point of interest but also in the neighborhood with functional dependencies, using DA PDE solvers based on Differential Algebraic techniques. The scheme allows the code developer and user to describe rather complicated field arrangements with rather limited effort. Of particular advantage is the seamless integration with map-based symplectic tracking schemes. The methods are illustrated in design studies of FFAGs for various different machine types, including both conventional strong focusing and continuously varying combined function setups.