Deflections in Magnet Fringe Fields

A transverse multipole expansion is derived, including the longitudinal components necessarily present in regions of varying magnetic field profile. It can be used for exact numerical orbit following through the fringe field regions of magnets whose end designs introduce no extraneous components, {\it i.e.} fields not required to be present by Maxwell's equations. Analytic evaluations of the deflections are obtained in various approximations. Mainly emphasized is a ``straight-line approximation'', in which particle orbits are treated as straight lines through the fringe field regions. This approximation leads to a readily-evaluated figure of merit, the ratio of r.m.s. end deflection to nominal body deflection, that can be used to determine whether or not a fringe field can be neglected. Deflections in ``critical'' cases (e.g. near intersection regions) are analysed in the same approximation.Comment: To be published in Physical Review

Taylor models and floating-point arithmetic: proof that arithmetic operations are validated in COSY

The goal of this paper is to prove that the implementation of Taylor models in COSY, based on floating-point arithmetic, computes results satisfyin- g the «containment property», i.e. guaranteed results. First, Taylor models are defined and their implementation in the COSY software by Makino and Berz is detailed. Afterwards IEEE-754 floating-point arithmetic is introduced. Then the core of this paper is given: the algorithms implemented in COSY for multiplying a Taylor model by a scalar, for adding or multiplying two Taylor models are given and are proven to return Taylor models satisfying the containment property.L'objectif de ce travail est de démontrer que l'implantation des modèles de Taylor, telle qu'elle est réalisée dans le logiciel COSY, calcule des résultats qui sont garantis, c'est à dire qu''ils satisfont la propriété d'inclusion.Tout d'abord, les modèles de Taylor sont définis et leur implantation par Makino et Berz dans le logiciel COSY est détaillée. Ensuite l'arithmétique flottante, telle qu'elle est spécifiée par la norme IEEE-754, est présentée. Enfin on arrive au cœur du sujet : les algorithmes implantés dans COSY pour la multiplication d'un modèle de Taylor par un scalaire et pour la somme et le produit de deux modèles de Taylor sont donnés; il est démontré que ces algorithmes retournent de s modèles de Taylor qui satisfont la propriété d'inclusion

CW high intensity non-scaling FFAG proton drivers

Accelerators are playing increasingly important roles in basic science, technology, and medicine including nuclear power, industrial irradiation, material science, and neutrino production. Proton and light-ion accelerators in particular have many research, energy and medical applications, providing one of the most effective treatments for many types of cancer. Ultra high-intensity and high-energy (GeV) proton drivers are a critical technology for accelerator-driven sub-critical reactors (ADS) and many HEP programs (Muon Collider). These high-intensity GeV-range proton drivers are particularly challenging, encountering duty cycle and space-charge limits in the synchrotron and machine size concerns in the weaker-focusing cyclotrons; a 10-20 MW proton driver is not presently considered technically achievable with conventional re-circulating accelerators. One, as-yet, unexplored re-circulating accelerator, the Fixed-field Alternating Gradient, or FFAG, is an attractive alternative to the cyclotron. Its strong focusing optics are expected to mitigate space charge effects, and a recent innovation in design has coupled stable tunes with isochronous orbits, making the FFAG capable of fixed-frequency, CW acceleration, as in the classical cyclotron. This paper reports on these new advances in FFAG accelerator technology and references advanced modeling tools for fixed-field accelerators developed for and unique to the code COSY INFINITY.Comment: 3 pp. Particle Accelerator, 24th Conference (PAC'11) 2011. 28 Mar - 1 Apr 2011. New York, US

Enhanced Optical Cooling of Ion Beams for LHC

The possibility of the enhanced optical cooling (EOC) of Lead ions in LHC is investigated. Non-exponential feature of cooling and requirements to the ring lattice, optical and laser systems are discussed. Comparison with optical stochastic cooling (OSC) is represented.Comment: 4 page

Fringe Fields and Dynamic Aperture in the FNAL Muon Storage Ring

Quadrupole fringe fields can limit the dynamic aperture of muon storage rings.Using the computer code COSY INFINITY for particle tracking and normal-form analysis, we evaluate the importance of fringe fields in the FNAL muon storage ring, and identify the regions of the machine where they are most critical. Dynamic aperture and linear tune shifts with amplitude are calculated considering an ideal machine without any errors or misalignments. We also explore the efficiency of various nonlinear correction schemes, study the momentum acceptance, and evaluate the spin decoherence over the transverse phase space

Validation of transfer map calculation for electrostatic deflectors in the code COSY INFINITY

The code COSY INFINITY uses a beamline coordinate system with a Frenet–Serret frame relative to the reference particle, and calculates differential algebra-valued transfer maps by integrating the ODEs of motion in the respective vector space over a differential algebra (DA). We described and performed computation of the DA transfer map of an electrostatic spherical deflector in a laboratory coordinate system using two conventional methods: (1) by integrating the ODEs of motion using a numerical integrator and (2) by computing analytically and in closed form the properties of the respective elliptical orbits from Kepler theory. We compared the resulting transfer maps with (3) the DA transfer map of COSY INFINITY ’s built-in electrostatic spherical deflector element ESP and (4) the transfer map of the electrostatic spherical deflector computed using the program GIOS, which uses analytic formulas from a paper1 by Hermann Wollnik regarding second-order aberrations. In addition to the electrostatic spherical deflector, we studied an electrostatic cylindrical deflector, where the Kepler theory is not applicable. We computed the DA transfer map by the ODE integration method (1), and we compared it with the transfer maps by (3) COSY INFINITY ’s built-in electrostatic cylindrical deflector element ECL and (4) GIOS. The transfer maps of electrostatic spherical and cylindrical deflectors obtained using the direct calculation methods (1) and (2) are in excellent agreement with those computed using (3) COSY INFINITY. On the other hand, we found a significant discrepancy with (4) the program GIOS

Propagation of Large Uncertainty Sets in Orbital Dynamics by Automatic Domain Splitting

Current approaches to uncertainty propagation in astrodynamics mainly refer to linearized models or Monte Carlo simulations. Naive linear methods fail in nonlinear dynamics, whereas Monte Carlo simulations tend to be computationally intensive. Differential algebra has already proven to be an efficient compromise by replacing thousands of pointwise integrations of Monte Carlo runs with the fast evaluation of the arbitrary order Taylor expansion of the flow of the dynamics. However, the current implementation of the DA-based high-order uncertainty propagator fails when the non-linearities of the dynamics prohibit good convergence of the Taylor expansion in one or more directions. We solve this issue by introducing automatic domain splitting. During propagation, the polynomial expansion of the current state is split into two polynomials whenever its truncation error reaches a predefined threshold. The resulting set of polynomials accurately tracks uncertainties, even in highly nonlinear dynamics. The method is tested on the propagation of (99942) Apophis post-encounter motion