Towards a general solution to the linear Heisenberg problem

The construction of a complete set of stationary states of the linear Heisenberg system with periodic boundary conditions (rings) has been a topic of intensive research for many decades. Many eminent theoreticians have made their contribution to this joint eort, but we should mention in the rst place the epoch-making work of Bethe 1 and Hulthen. 5 Their work is the basis of many papers on this topic that have appeared during the past 70 years. We do no have the intention to give a complete survey of all this work but we will try to indicate that especially an asymptotic approach starting from the Hypothesis of Strings gives the prospect of a general and complete solution of the Heisenberg chain

First Experiments on Stochastic Cooling of Heavy Ion Beams at the ESR

At the experimental storage ring ESR of GSI, one half of the foreseen pick-up and kicker tanks are installed, the rest will follow in 1998. First experimental tests of the stochastic precooling system have been performed since April 1997. Longitudinal Palmer cooling was successfully demonstrated. E-folding cooling times of 8.6 seconds were determined with carbon beams. No significant dependence of the cooling time on the number of particles was observed during these first tests. This may be explained by a low signal to noise ratio of the signals obtained from the pick-ups in the present configuration. With heavy ions in higher charge states faster cooling times are expected. The experiments are an important step towards the realization of experiments with radioactive fragments, e.g. in order to measure nuclear masses or half-lives of stripped exotic ions

Generalised Shastry-Sutherland Models in three and higher dimensions

We construct Heisenberg anti-ferromagnetic models in arbitrary dimensions that have isotropic valence bond crystals (VBC) as their exact ground states. The d=2 model is the Shastry-Sutherland model. In the 3-d case we show that it is possible to have a lattice structure, analogous to that of SrCu_2(BO_3)_2, where the stronger bonds are associated with shorter bond lengths. A dimer mean field theory becomes exact at d -> infinity and a systematic 1/d expansion can be developed about it. We study the Neel-VBC transition at large d and find that the transition is first order in even but second order in odd dimensions.Comment: Published version; slightly expande

Comparison between Laboratory Measurements, Simulations and Analytical Predictions of the Resistive Wall Transverse Beam Impedance at low frequencies

The prediction of the resistive wall transverse beam impedance at the first unstable betatron line (8 kHz) of the CERN Large Hadron Collider (LHC) is of paramount importance for understanding and controlling the related coupled-bunch instability. Until now only novel analytical formulas were available at this frequency. Recently, laboratory measurements and numerical simulations were performed to crosscheck the analytical predictions. The experimental results based on the measurement of the variation of a probe coil inductance in the presence of i) sample graphite plates, ii) stand-alone LHC collimator jaws and iii) a full LHC collimator assembly are presented in detail. The measurement results are compared to both analytical theories and simulations. In addition, the consequences for the understanding of the LHC impedance are discussed

Bench measurements of the Low Frequency Transverse Impedance of the CERN LHC Beam Vacuum Interconnects with RF Contacts

The low frequency longitudinal and transverse impedances of the CERN Large Hadron Collider (LHC) have to be specifically minimized to prevent the onset of coherent instabilities. The LHC beam vacuum interconnects were designed as Plug In Modules (PIMs) with RF contacts to reduce their coupling impedances, but the resulting contact resistance is a concern, as this effect is difficult to estimate. High sensitivity measurements of the transverse impedance of a PIM at low frequency using a coil probe are presented. In particular, the increase of the transverse impedance of the PIM when it is elongated to its operating position is discussed in detail. Finally, the issue of non-conforming contact resistance is also addressed

Impedance Studies for the Phase 2 LHC Collimators

The LHC phase 2 collimation project aims at gaining a factor ten in cleaning efficiency, robustness and impedance reduction. From the impedance point of view, several ideas emerged during the last year, such as using dielectric collimators, slots or rods in copper plates, or Litz wires. The purpose of this paper is to discuss the possible choices, showing analytical estimates, electromagnetic simulations performed using Maxwell, HFSS and GdFidL, and preliminary bench measurements. The corresponding complex tune shifts are computed for the different cases and compared on the stability diagram defined by the settings of the Landau octupoles available in the LHC at 7 TeV