Analytic formulas for the rapid evaluation of the orbit response matrix and chromatic functions from lattice parameters in circular accelerators

Measurements and analysis of orbit response matrix have been providing for decades a formidable tool in the detection of linear lattice imperfections and their correction. Basically all storage- ring-based synchrotron light sources across the world make routinely use of this technique in their daily operation, reaching in some cases a correction of linear optics down to 1% beta beating and 0.1% coupling. During the design phase of a new storage ring it is also applied in simulations for the evaluation of magnetic and mechanical tolerances. However, this technique is known for its intrinsic slowness compared to other methods based on turn-by-turn beam position data, both in the measurement and in the data analysis. In this paper analytic formulas are derived and discussed that shall greatly speed up this second part. The mathematical formalism based on the Lie algebra and the resonance driving terms is extended to the off-momentum regime and explicit analytic formulas for the evaluation of chromatic functions from lattice parameters are also derived. The robustness of these formulas, which are linear in the magnet strengths, is tested with different lattice configurations

Holographic Algorithm with Matchgates Is Universal for Planar #\#CSP Over Boolean Domain

We prove a complexity classification theorem that classifies all counting constraint satisfaction problems ($\#$CSP) over Boolean variables into exactly three categories: (1) Polynomial-time tractable; (2) $\#$P-hard for general instances, but solvable in polynomial-time over planar graphs; and (3) $\#$P-hard over planar graphs. The classification applies to all sets of local, not necessarily symmetric, constraint functions on Boolean variables that take complex values. It is shown that Valiant's holographic algorithm with matchgates is a universal strategy for all problems in category (2).Comment: 94 page

Measurement of Resonance driving terms in the ATF Damping Ring

The measurement of resonance driving terms in the Damping Ring of the Accelerator Test Facility in KEK could help finding possible machine imperfections and even to optimize single particle stability through the minimization of non-linearities. The first experimental attempts of this enterprise are reported in this note

Hyperdeterminants as integrable discrete systems

We give the basic definitions and some theoretical results about hyperdeterminants, introduced by A. Cayley in 1845. We prove integrability (understood as 4d-consistency) of a nonlinear difference equation defined by the 2x2x2-hyperdeterminant. This result gives rise to the following hypothesis: the difference equations defined by hyperdeterminants of any size are integrable. We show that this hypothesis already fails in the case of the 2x2x2x2-hyperdeterminant.Comment: Standard LaTeX, 11 pages. v2: corrected a small misprint in the abstrac

First β-beating measurement and optics analysis for the CERN Large Hadron Collider

Proton beams were successfully steered through the entire ring of the CERN Large Hadron Collider (LHC) on September the 10th of 2008. A reasonable lifetime was achieved for the counterclockwise beam, namely beam 2, after the radiofrequency capture of the particle bunch was established. This provided the unique opportunity of acquiring turn-by-turn betatron oscillations for a maximum of 90 turns right at injection. Transverse coupling was not corrected and chromaticity was estimated to be large. Despite this largely constrained scenario, reliable optics measurements have been accomplished. These measurements together with the application of new algorithms for the reconstruction of optics errors have led to the identification of a dominant error source