Eberhard Keil

The MAD program

The Methodical Accelerator Design (MAD) program for circular accelerators is in regular use for the design and modeling of the Large Electron Positron Collider (LEP), the Large Hadron Collider (LHC), the Proton Synchrotron (PS), and the Super Proton Synchrotron (SPS) at CERN, and in 10 to 20 other laboratories. It includes the following new accelerator physics features: (i) machine imperfections, e.g. random and systematic errors in the alignment and excitation of the magnetic elements and read-out errors of the beam-position monitors; (ii) closed-orbit correction using the MICADO algorithm; (iii) Lie-algebraic techniques for concatenating beam lines, for tracking trajectories, and for higher-order orbit functions; (iv) systematic energy loss due to synchrotron radiation and its effects on the closed orbit and the orbit functions in all three degrees of freedom; and (v) spin dynamics in SMILE style. The data describing the machine are held as data modules in a dynamically managed memory pool, including garbage collection and overflow onto external files. Graphics is interfaced to the standard graphics kernel system (GKS) and used for plotting orbit functions along the orbit and versus the momentum error, and for phase space plots, Fourier spectra of particle orbits, etc. MAD is implemented on Cray, IBM, Nord, and VAX systems and on Apollo and sun workstations.<<ETX>>

Diffraction radiation of charged rings moving in a corrugated cylindrical pipe A model of radiation losses in an electron ring accelerator

Abstract The energy loss of a charged ring passing an infinitely long periodic sequence of rf accelerating cavities which has recently received much attention in connection with the collective acceleration of ions in electron rings is calculated by expanding the vector potential into a series of eigenfunctions of the empty waveguide and computing their individual excitation. The frequency spectra obtained are compared to the predictions of simpler analytical models from which a set of formulae for the practical design of rf accelerating structures for electron rings can be derived. The energy loss becomes independent of γ when the electron rings have a highly relativistic speed.

The Large Hadron Collider (LHC) in the LEP tunnel

After the remarkable start-up of LEP, the installation of a Large Hadron Collider, LHC, in the LEP tunnel will open a new era for the High Energy Physics. This report summarizes the main LHC parameters and subsytems and describes the more recent studies and developments.

Barycentre motion of beams due to beam-beam interaction in asymmetric ring colliders

Abstract The effects of the beam-beam interaction on the coherent motion of the barycentres of the colliding bunches are considered for asymmetric (two-ring) e + e − colliders, where circumference, energy, tune, etc. may be different between two rings. As well as integer and half-integer resonances, sum resonances occur. These resonances may be quite dense in the tune diagram, for the cases with different circumferences. This effectt poses a severe restriction on the choice of the circumference ratio. On these resonances, the beams separate spontaneously at the interaction point. In particular, on the sum resonance, the barycentres follow a limit cycle in four-dimensional phase space, rather than reaching a fixed point. This causes a severe drop in the luminosity. Results of analytical calculations and computer simulations for the motion of the barycentres and the excitation of the resonances are presented.

A cost-effective design for a neutrino factory

Abstract The design of a neutrino factory based on a muon storage ring draws upon several tried and tested technologies, upon existing design work for other accelerator projects, e.g. neutron spallation sources, but it also depends on the development of technical solutions to certain specific requirements. These include the efficient capture of muons in a large volume of phase-space, some reduction in overall phase-space volume by ionization cooling, fast acceleration to the desired energy to avoid unacceptable decay losses and storage in a decay ring optimized for its purpose as a neutrino source. There is no obvious single combination of machines to achieve this aim. Here we present a scenario which relies to a large extent upon known technologies together with a relatively unambitious mix of new schemes. Some will be tried and tested during design and construction; others during the early operational phase of the facility leading to a staged upgrade path – a well-proven strategy in the development of accelerator complexes.

Study of non-linear effects of a resonant cavity on the longitudinal dynamics of a costing particle beam

Abstract A computational method has been developed to stimulate the longitudinal motion of a relativistic beam charged particles circulating in a strong focusing method has been synchrotron or storage ring. Unlike most analytical approaches the stimulation is not restricted to small pertubations and thus the growth of instabilities can be followed into the non-linear region. The investigations show that, as a result of an instability, the final energy spread of an initially unbunched beam interacting with a resonant cavity is larger than the vale at threshold and tends to a limit which depends on both the initial energy spread and on the spread at threshold. Although the cavity has a high impedanceonly at the revolution frequency of the beam, the particle distributions contain Fourier components at multiples of the revolution frequency. The growth rate and threshold agree well with those obtained from linear theory, if the cavity filling time is small compared to the growth time of the instability, and if the frequency spread within the beam is small compared to the width of the cavity resonance. If the first condition does not hold, the growth time becomes longer; and a frequency spread within the beam larger than the width of the cavity resonance results in a slight reduction of the threshold spread, and the overshoot of the final energy spread over this spread becomes smaller.

FFAGS for muon acceleration

Due to their finite lifetime, muons must be accelerated very rapidly. It is challenging to make the magnets ramp fast enough to accelerate in a synchrotron, and accelerating in a linac is very expensive. One can use a recirculating accelerator (like CEBAF), but one needs a different arc for each turn, and this limits the number of turns one can use to accelerate, and therefore requires significant amounts of RF to achieve the desired energy gain. An alternative method for muon acceleration is using a fixed field alternating gradient (FFAG) accelerator. Such an accelerator has a very large energy acceptance (a factor of two or three), allowing one to use the same arc with a magnetic field that is constant over time. Thus, one can in principle make as many turns as one can tolerate due to muon decay, therefore reducing the RF cost without increasing the arc cost. This paper reviews the current status of research into the design of FFAGs for muon acceleration. Several current designs are described and compared. General design considerations are also discussed

Design Concept for a 100 GeV E+-E- Storage Ring

A conceptual design of a 100 GeV e+-e- storage ring (LEP) being studied at CERN and some of the problems encountered are presented. The 20 GeV fastcycling injector synchrotron is studied at the Rutherford Laboratory.1 To obtain a luminosity L = 1 × 1032 cm-2 s-1 at 100 GeV, the product of bending radius ¿ and the RF power PB delivered to both beams must be PB ¿ = 136 GWm, assuming optimum coupling, a maximum permissible beam-beam tune shift ¿Q = 0.06, and a vertical amplitude function ßy* = 0.01 m at the crossings. The bending radius ¿ = 6.1 km was obtained by cost optimisation.2

Synchrotron radiation dominated hadron colliders

The synchrotron radiation damping time becomes small compared to the beam lifetime when the beam energy in a circular hadron collider reaches about 100 TeV and the dipole field about 10 T. This paper discusses an approach to the design of these colliders such that the desired performance parameters, e.g. beam-beam tune shift and luminosity are achieved at the equilibrium values of the beam emittance and momentum spread. The design procedure is described, involving the design of the interaction regions, the arcs, and the RF system. The thresholds and/or growth rates of several collective effects, and the growth times for intra-beam scattering are estimated. The consequences of the synchrotron radiation are discussed in the conclusions.

The First High-Luminosity Insertion in the ISR

One of the means proposed to increase the luminosity in storage rings, a so-called low-ß insertion, has been put successfully into operation in the Intersecting Storage Rings (ISR). By installing five quadrupoles in each ring around one intersection, a reduction of beam height by a factor 2.3 has been measured, and, with proper matching, the perturbation to the rest of the machine was found to be negligible. With circulating beams of 20 A and 24 A a luminosity of 2.11 x 1031 cm-2s-1 has been achieved. This paper reports the results of tests conducted, compares them with the theoretical forecasts, and gives a short description of the hardware used.