Study of Offset Collisions and Beam Adjustment in the LHC Using a Strong-Strong Simulation Model

The bunches of the two opposing beams in the LHC do not always collide head-on. The beam-beam effects cause a small, unavoidable separation under nominal operational conditions. During the beam adjustment and when the beams are brought into collision the beams are separated by a significant fraction of the beam size. A result of small beam separation can be the excitation of coherent dipole oscillations or an emittance increase. These two effects are studied using a strong-strong multi particle simulation model. The aim is to identify possible limitations and to find procedures which minimise possible detrimental effects

Analytical expressions for fringe fields in multipole magnets

Fringe fields in multipole magnets can have a variety of effects on the linear and nonlinear dynamics of particles moving along an accelerator beamline. An accurate model of an accelerator must include realistic models of the magnet fringe fields. Fringe fields for dipoles are well understood and can be modelled at an early stage of accelerator design in such codes as MAD8, MADX or ELEGANT. However, usually it is not until the final stages of a design project that it is possible to model fringe fields for quadrupoles or higher order multipoles. Even then, existing techniques rely on the use of a numerical field map, which will usually not be available until the magnet design is well developed. Substitutes for the full field map exist but these are typically based on expansions about the origin and rely heavily on the assumption that the beam travels more or less on axis throughout the beam line. In some types of machine (for example, a non-scaling FFAG such as EMMA) this is not a good assumption. In this paper, a method for calculating fringe fields based on analytical expressions is presented, which allows fringe field effects to be included at the start of an accelerator design project. The magnetostatic Maxwell equations are solved analytically and a solution that fits all orders of multipoles derived. Quadrupole fringe fields are considered in detail as these are the ones that give the strongest effects. Two examples of quadrupole fringe fields are presented. The first example is a magnet in the LHC inner triplet, which consists of a set of four quadrupoles providing the final focus to the beam, just before the interaction point. Quadrupoles in EMMA provide the second example. In both examples, the analytical expressions derived in this paper for quadrupole fringe fields provide a good approximation to the field maps obtained from a numerical magnet modelling code.Comment: 27 pages, 39 figures. The figures are new with respect to the previous version, Several mistakes also correcte

Luminosity levelling techniques for the LHC

We present the possibilities for doing luminosity levelling at the LHC. We explore the merits and drawbacks of each option and briefly discuss the operational implications. The simplest option is levelling with an offset between the two beams. Crab cavities may also be used for levelling, as may a squeezing of the beam. There is also the possibility of using the crossing angle in order to do luminosity levelling. All of these options are explored, for the LHC and other possible new projects, together with their benefits and drawbacks.Comment: 5 pages, contribution to the ICFA Mini-Workshop on Beam-Beam Effects in Hadron Colliders, CERN, Geneva, Switzerland, 18-22 Mar 201

Start to end simulations of the ERL prototype at Daresbury Laboratory

Daresbury Laboratory is currently building an Energy Recovery Linac Prototype (ERLP) that will serve as a research and development facility for the study of beam dynamics and accelerator technology important to the design and construction of the proposed 4th Generation Light Source (4GLS) project. Two major objectives of the ERLP are the demonstration of energy recovery and of energy recovery from a beam disrupted by an FEL interaction as supplied by an infrared oscillator system. In this paper we present start-to-end simulations of the ERLP including such an FEL interaction. The beam dynamics in the highbrightness injector, which consists of a DC photocathode Gun and a superconducting booster, have been modelled using the particle tracking code ASTRA. After the booster the particles have been tracked with the code elegant. The 3D code GENESIS 1.3 was used to model the FEL interaction with the electron beam at 35 MeV. A brief summary of impedance and wakefield calculations for the whole machine is also given

Hopf instantons and the Liouville equation in target space

We generalise recent results on Hopf instantons in a Chern--Simons and Fermion theory in a fixed background magnetic field. We find that these instanton solutions have to obey the Liouville equation in target space. As a consequence, these solutions are given by a class of Hopf maps that consist of the composition of the standard Hopf map with an arbitrary rational map.Comment: Latex file, 11 pages, no figure