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

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*

Application of Dynamical Maps to the FFAG EMMA Commissioning*

Abstract The lattice of the Non Scaling FFAG EMMA has four degrees of freedom (strengths and transverse positions of each of the two quadrupoles in each periodic cell). Dynamical maps computed from an analytical representation of the magnetic field may be used to predict the beam dynamics in any configuration of the lattice. An interpolation technique using a mixed variable generating function representation for the map provides an efficient way to generate the map for any required lattice configuration, while ensuring symplecticity of the map. The interpolation technique is used in an optimisation routine, to identify the lattice configuration most closely machine specified dynamical properties, including the variation of time of flight with beam energy (a key characteristic for acceleration in EMMA)

SETTING THE BEAM ONTO THE REFERENCE ORBIT IN NON SCALING FFAG ACCELERATORS

Abstract Described in the paper are systematic procedures to inject and keep the beam on the reference trajectory for a fixed energy, as applied to the EMMA non scaling FFAG accelerator. The notion of accelerated orbits in FFAG accelerators has been introduced and some of their properties have been studies in detail

Use of transfer maps for modeling beam dynamics in a nonscaling fixed-field alternating-gradient accelerator

Transfer maps for magnetic components are fundamental to studies of beam dynamics in accelerators. In the work presented here, transfer maps are computed in Taylor form for a particle moving through any specified magnetostatic field by applying an explicit symplectic integrator in a differential algebra code. The techniques developed are illustrated by their application to study the beam dynamics in the electron model for many applications (EMMA), the first nonscaling fixed-field alternating-gradient accelerator ever built. The EMMA lattice has 4 degrees of freedom (strength and transverse position of each of the two quadrupoles in each periodic cell). Transfer maps may be used to predict efficiently the dynamics in any lattice configuration. The transfer map is represented by a mixed variable generating function, obtained by interpolation between the maps for a set of reference configurations: use of mixed variable generating functions ensures the symplecticity of the map. An optimization routine uses the interpolation technique to look for a lattice defined by four constraints on the time of flight at different beam energies. This provides a way to determine the lattice configuration required to produce the desired dynamical characteristics. These tools are benchmarked against data from the recent EMMA commissioning

TUNE MEASUREMENT IN NON SCALING FFAG EMMA WITH MODEL INDEPENDENT ANALYSIS

The Non Scaling Fixed Field Alternating Gradient (NSFFAG) EMMA accelerator has a purely linear lattice, and the crossing of resonances during acceleration is therefore a key characteristic of the beam dynamics. An accurate measurement of the tune is essential for a full understanding of the machine behaviour. However, commonly used measurement techniques require the beam to perform a large number of turns in the machine. Simulations have shown us that rapid decoherence of the beam requires a technique capable of providing a tune measurement from just one or two turns of the ring. Model independent analysis(MIA) has been investigated as a possible approach. The singular value decomposition of a matrix composed of BPM readings from the trajectories of different bunches provides information on the machine optics. Simulations indicate that it should be possible to derive an accurate value of the tune using MIA, even in the presence of BPM noise and beam decoherence