Summary of the Mini BNL/LARP/CARE-HHH Workshop on Crab Cavities for the LHC (LHC-CC08)

The first mini-workshop on crab compensation for the LHC luminosity upgrade (LHC-CC08) was held February 24-25, 2008 at the Brookhaven National Laboratory. A total of 35 participants from 3 continents and 15 institutions from around the world participated to discuss the exciting prospect of a crab scheme for the LHC. If realized it will be the first demonstration in hadron colliders. The workshop is organized by joint collaboration of BNL, US-LARP and CARE-HHH. The enormous interest in the subject of crab cavities for the international linear collider and future light sources has resulted in a large international collaboration to exchange aspects of synergy and expertise. A central repository for this exchange of information documenting the latest design effort for LHC crab cavities is consolidated in a wiki page: https://twiki.cern.ch/twiki/bin/view/Main/LHCCrabCavities. The main goal of this workshop was to define a road-map for a prototype crab cavity to be installed in the LHC and to discuss the associated R&D and beam dynamics challenges. The diverse subject of implementing the crab scheme resulted in a scientific program with a wide range of subtopics which were divided into 8 sessions. Each session was given a list of fundamental questions to be addressed and used as a guideline to steer the discussions

R&D ERL: Photocathode Deposition and Transport System

The purpose of the photocathode deposition and transport system is to (1) produce a robust, high yield multialkali photocathode and (2) have a method of transporting the multialkali photocathode for insertion into a super conducting RF electron gun. This process is only successful if a sufficient quantum efficiency lifetime of the cathode, which is inserted in the SRF electron gun, is maintained. One important element in producing a multialkali photocathode is the strict vacuum requirements of 10{sup -11} torr to assure success in the production of longlived photocathodes that will not have their QE or lifetime depleted due to residual gas poisoning in a poor vacuum. A cutaway view of our third generation deposition system is shown in figure 1. There are certain design criteria and principles required. One must be able to install, remove, rejuvenate and replace a cathode without exposing the source or cathode to atmosphere. The system must allow one to deposit Cs, K, and Sb on a cathode tip surface at pressures in the 10{sup -10} to 10{sup -9} torr range. The cathode needs to be heated to as high as 850 C for cleaning and maintained at 130 C to 150 C during deposition. There should also be the capability for in-situ QE measurements. In addition the preparation of dispenser photocathodes must be accounted for, thus requiring an ion source for cathode cleaning. Finally the transport cart must be mobile and be able to negotiate the ERL facility labyrinth

Summary of the Mini BNL/LARP/CARE-HHH workshop on Crab Cavities for the LHC

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Beam-Breakup Instability Theory for Energy Recovery Linacs

Here we will derive the general theory of the beam-breakup instability in recirculating linear accelerators, in which the bunches do not have to be at the same RF phase during each recirculation turn. This is important for the description of energy recovery linacs (ERLs) where bunches are recirculated at a decelerating phase of the RF wave and for other recirculator arrangements where different RF phases are of an advantage. Furthermore it can be used for the analysis of phase errors of recirculated bunches. It is shown how the threshold current for a given linac can be computed and a remarkable agreement with tracking data is demonstrated. The general formulas are then analyzed for several analytically solvable cases, which show: (a) Why different higher order modes (HOM) in one cavity do not couple so that the most dangerous modes can be considered individually. (b) How different HOM frequencies have to be in order to consider them separately. (c) That no optics can cause the HOMs of two cavities to cancel. (d) How an optics can avoid the addition of the instabilities of two cavities. (e) How a HOM in a multiple-turn recirculator interferes with itself. Furthermore, a simple method to compute the orbit deviations produced by cavity misalignments has also been introduced. It is shown that the BBU instability always occurs before the orbit excursion becomes very large.Comment: 12 pages, 6 figure

Virasoro constraints in Drinfeld-Sokolov hierarchies

We describe a geometric theory of Virasoro constraints in generalized Drinfeld-Sokolov hierarchies. Solutions of Drinfeld-Sokolov hierarchies are succinctly described by giving a principal bundle on a complex curve together with the data of a Higgs field near infinity. String solutions for these hierarchies are defined as points having a big stabilizer under a certain Lie algebra action. We characterize principal bundles coming from string solutions as those possessing connections compatible with the Higgs field near infinity. We show that tau-functions of string solutions satisfy second-order differential equations generalizing the Virasoro constraints of 2d quantum gravity.Comment: 28 page

Coupled-Bunch Beam Breakup due to Resistive-Wall Wake

The coupled-bunch beam breakup problem excited by the resistive wall wake is formulated. An approximate analytic method of finding the asymptotic behavior of the transverse bunch displacement is developed and solved.Comment: 8 page

A categorification of Morelli's theorem

We prove a theorem relating torus-equivariant coherent sheaves on toric varieties to polyhedrally-constructible sheaves on a vector space. At the level of K-theory, the theorem recovers Morelli's description of the K-theory of a smooth projective toric variety. Specifically, let $X$ be a proper toric variety of dimension $n$ and let M_\bR = \mathrm{Lie}(T_\bR^\vee)\cong \bR^n be the Lie algebra of the compact dual (real) torus T_\bR^\vee\cong U(1)^n. Then there is a corresponding conical Lagrangian \Lambda \subset T^*M_\bR and an equivalence of triangulated dg categories \Perf_T(X) \cong \Sh_{cc}(M_\bR;\Lambda), where \Perf_T(X) is the triangulated dg category of perfect complexes of torus-equivariant coherent sheaves on $X$ and \Sh_{cc}(M_\bR;\Lambda) is the triangulated dg category of complex of sheaves on M_\bR with compactly supported, constructible cohomology whose singular support lies in $\Lambda$. This equivalence is monoidal---it intertwines the tensor product of coherent sheaves on $X$ with the convolution product of constructible sheaves on M_\bR.Comment: 20 pages. This is a strengthened version of the first half of arXiv:0811.1228v3, with new results; the second half becomes arXiv:0811.1228v

R&D ERL: Photocathode Deposition and Transport System

The purpose of the photocathode deposition and transport system is to (1) produce a robust, high yield multialkali photocathode and (2) have a method of transporting the multialkali photocathode for insertion into a super conducting RF electron gun. This process is only successful if a sufficient quantum efficiency lifetime of the cathode, which is inserted in the SRF electron gun, is maintained. One important element in producing a multialkali photocathode is the strict vacuum requirements of 10{sup -11} torr to assure success in the production of longlived photocathodes that will not have their QE or lifetime depleted due to residual gas poisoning in a poor vacuum. A cutaway view of our third generation deposition system is shown in figure 1. There are certain design criteria and principles required. One must be able to install, remove, rejuvenate and replace a cathode without exposing the source or cathode to atmosphere. The system must allow one to deposit Cs, K, and Sb on a cathode tip surface at pressures in the 10{sup -10} to 10{sup -9} torr range. The cathode needs to be heated to as high as 850 C for cleaning and maintained at 130 C to 150 C during deposition. There should also be the capability for in-situ QE measurements. In addition the preparation of dispenser photocathodes must be accounted for, thus requiring an ion source for cathode cleaning. Finally the transport cart must be mobile and be able to negotiate the ERL facility labyrinth