Particle Tracking Studies Using Dynamical Map Created from Finite Element Solution of the EMMA Cell

The un­con­ven­tion­al size and the pos­si­bil­i­ty of trans­verse dis­place­ment of the mag­nets in the EMMA non-scal­ing FFAG mo­ti­vates a care­ful study of par­ti­cle be­hav­ior with­in the EMMA ring. The mag­net­ic field map of the dou­blet cell is com­put­ed using a Fi­nite El­e­ment Method solver; par­ti­cle mo­tion through the field can then be found by nu­mer­i­cal in­te­gra­tion, using (for ex­am­ple) OPERA, or ZGOUBI. How­ev­er, by ob­tain­ing an an­a­lyt­i­cal de­scrip­tion of the mag­net­ic field (by fit­ting a Fouri­er-Bessel se­ries to the nu­mer­i­cal data) and using a dif­fer­en­tial al­ge­bra code, such as COSY, to in­te­grate the equa­tions of mo­tion, it is pos­si­ble to pro­duce a dy­nam­i­cal map in Tay­lor form. This has the ad­van­tage that, after once com­put­ing the dy­nam­i­cal map, mul­ti-turn track­ing is far more ef­fi­cient than re­peat­ed­ly per­form­ing nu­mer­i­cal in­te­gra­tions. Also, the dy­nam­i­cal map is small­er (in terms of com­put­er mem­o­ry) than the full mag­net­ic field map; this al­lows dif­fer­ent con­fig­u­ra­tions of the lat­tice, in terms of mag­net po­si­tions, to be rep­re­sent­ed very eas­i­ly using a set of dy­nam­i­cal maps, with in­ter­po­la­tion be­tween the co­ef­fi­cients in dif­fer­ent maps*

Electron Cloud in Linear Collider Damping Rings

No abstract prepared

Beam dynamics in NF-FFAG EMMA with dynamical maps

Copyright @ 2010 by IPAC'10/ACFAThe Non-Scaling Fixed Field Alternating Gradient accelerator EMMA has a compact linear lattice, in which the effects of magnet fringe fields need to be modelled carefully. A numerical magnetic field map can be generated frommagnetmeasurements ormagnet design software. We have developed a technique that produces from the numerical field map, a dynamical map for a particle travelling in a full EMMA cell, for a given reference energy, without acceleration. Since the beam dynamics change with energy, a set of maps have been produced with various reference energies between 10MeV and 20MeV. For each reference energy, the simulated tune and time of flight have been compared with results in Zgoubi - tracking directly through numerical field map. The range of validity of a single map has been investigated by tracking particles with large energy deviation: the results can be used to implement a model of acceleration based on dynamical mapsThis work was supported by the Engineering and Physical Sciences Research Council (EPSRC), UK

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

Units on the local history of Chelsea to supplement a course in American history.

Thesis (Ed.M.)--Boston Universit

Multidecadal variability in hydro-climate of Okavango river system, southwest Africa, in the past and under future climate

The focus of this paper is to understand the multi-decadal oscillatory component of variability in the Okavango River system, in southwestern Africa, and its potential evolution through the 21st century under climate change scenarios. Statistical analyses and hydrological modelling are used to show that the observed multi-decadal wet and dry phases in the Okavango River and Delta result from multi-decadal oscillations in rainfall, which are likely to be related to processes of internal variability in the climate system, rather than external natural or anthropogenic forcing. Analyses of changes in this aspect of variability under projected climate change scenarios are based on data from a multi-model ensemble of 19 General Circulation Models, which are used to drive hydrological models of the Okavango River and Delta. Projections for the 21st century indicate a progressive shift towards drier conditions attributed to the influence of increasing temperatures on water balance. It is, however, highly likely that multi-decadal oscillations, possibly of similar magnitude to that of 20th century, will be superimposed on the overall trend. These may periodically offset or amplify the mean drying trend. This effect should be accounted for in water and catchment management and climate change adaptation strategies