Nonlinear accelerator lattices with one and two analytic invariants
TLDR
In this paper, the integrable nonlinear motion in accelerators has the potential to introduce a large betatron tune spread to suppress instabilities and to mitigate the effects of space charge and magnetic field errors.Abstract:
Integrable systems appeared in physics long ago at the onset of classical dynamics with examples being Kepler's and other famous problems. Unfortunately, the majority of nonlinear problems turned out to be nonintegrable. In accelerator terms, any 2D nonlinear nonintegrable mapping produces chaotic motion and a complex network of stable and unstable resonances. Nevertheless, in the proximity of an integrable system the full volume of such a chaotic network is small. Thus, the integrable nonlinear motion in accelerators has the potential to introduce a large betatron tune spread to suppress instabilities and to mitigate the effects of space charge and magnetic field errors. To create such an accelerator lattice one has to find magnetic and electric field combinations leading to a stable integrable motion. This paper presents families of lattices with one invariant where bounded motion can be easily created in large volumes of the phase space. In addition, it presents 3 families of integrable nonlinear accelerator lattices, realizable with longitudinal-coordinate-dependent magnetic or electric fields with the stable nonlinear motion, which can be solved in terms of separable variables.read more
Citations
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Journal ArticleDOI
IOTA (Integrable Optics Test Accelerator): Facility and Experimental Beam Physics Program
Sergei Antipov,Daniel Broemmelsiek,David L. Bruhwiler,Dean Edstrom,Elvin Harms,V. A. Lebedev,J. Leibfritz,S. Nagaitsev,Chong Shik Park,Henryk Piekarz,Philippe Piot,E.J. Prebys,Alexander Romanov,Jinhao Ruan,Tanaji Sen,Giulio Stancari,Charles Thangaraj,Randy Thurman-Keup,Alexander Valishev,Vladimir Shiltsev +19 more
TL;DR: The Integrable Optics Test Accelerator (IOTA) as discussed by the authors is a storage ring for advanced beam physics research currently being built and commissioned at Fermilab, USA.
Journal ArticleDOI
CLARA conceptual design report
J. A. Clarke,J. A. Clarke,Deepa Angal-Kalinin,Deepa Angal-Kalinin,N. Bliss,Rachael Buckley,Rachael Buckley,S Buckley,S Buckley,Ryan Cash,P. Corlett,P. Corlett,L Cowie,L Cowie,Graham Cox,G.P. Diakun,G.P. Diakun,David Dunning,David Dunning,Barry Fell,A. Gallagher,P. Goudket,P. Goudket,A. R. Goulden,A. R. Goulden,David M. P. Holland,David M. P. Holland,Steven Jamison,Steven Jamison,J. K. Jones,J. K. Jones,A. Kalinin,A. Kalinin,W Liggins,W Liggins,L. Ma,L. Ma,Kiril Marinov,Kiril Marinov,B. Martlew,P. A. McIntosh,P. A. McIntosh,Julian McKenzie,Julian McKenzie,K. J. Middleman,K. J. Middleman,Boris Militsyn,Boris Militsyn,Andrew Moss,Andrew Moss,Bruno Muratori,Bruno Muratori,M. D. Roper,M. D. Roper,R Santer,R Santer,Yuri Saveliev,Yuri Saveliev,Edward Snedden,Edward Snedden,R. J. Smith,R. J. Smith,S.L. Smith,S.L. Smith,M. Surman,M. Surman,Trina Thakker,Trina Thakker,N.R. Thompson,N.R. Thompson,Reza Valizadeh,Reza Valizadeh,Alan Wheelhouse,Alan Wheelhouse,Peter Williams,Peter Williams,Riccardo Bartolini,Ian Martin,Roger Barlow,A. Kolano,Graeme Burt,Graeme Burt,Subhasis Chattopadhyay,D. Newton,D. Newton,Andrzej Wolski,Andrzej Wolski,R. B. Appleby,R. B. Appleby,Hywel Owen,Hywel Owen,M. Serluca,M. Serluca,Guoxing Xia,Guoxing Xia,Stewart Boogert,Alexey Lyapin,L.T. Campbell,Brian McNeil,V. V. Paramonov +99 more
TL;DR: The conceptual design of a proposed free electron laser test facility called CLARA that will be a major upgrade to the existing VELA accelerator test facility at Daresbury Laboratory in the UK is described in this article.
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Fermilab Proton Accelerator Complex Status and Improvement Plans
TL;DR: Fermilab carries out an extensive program of accelerator-based high energy particle physics research at the Intensity Frontier that relies on the operation of 8 GeV and 120 GeV proton beamlines for a number of fixed target experiments as mentioned in this paper.
Journal ArticleDOI
Single-particle dynamics in a nonlinear accelerator lattice: attaining a large tune spread with octupoles in IOTA
TL;DR: The Integrable Optics Test Accelerator (IOTA) as discussed by the authors is a ring with octupole magnets, which can achieve a tune spread of 0.08 (for particles at large amplitudes) with the dynamical aperture of over 20 beam sigma for a 150-MeV electron beam.
References
More filters
Book
Mathematical Methods for Physicists
TL;DR: In this article, the authors present a model for vector analysis based on the Calculus of Variations and the Sturm-Liouville theory, which includes the following: Curved Coordinates, Tensors.
Journal ArticleDOI
Theory of the Alternating-Gradient Synchrotron
TL;DR: In this paper, it was shown that if n alternates rapidly between large positive and large negative values, the stability of both radial and vertical oscillations can be greatly increased compared to conventional accelerators in which n is azimuthally constant and must lie between 0 and 1.
Journal ArticleDOI
Direct methods for the search of the second invariant
TL;DR: In this paper, the authors discuss the direct methods that can be used to search for the second invariant of a system defined by the Hamiltonian H = 1 2 (p x 2 ) + p y 2 + A(x, y)p x + B(x and y), p y + V(x, y).
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IOTA (Integrable Optics Test Accelerator): Facility and Experimental Beam Physics Program
Sergei Antipov,Daniel Broemmelsiek,David L. Bruhwiler,Dean Edstrom,Elvin Harms,V. A. Lebedev,J. Leibfritz,S. Nagaitsev,Chong Shik Park,Henryk Piekarz,Philippe Piot,E.J. Prebys,Alexander Romanov,Jinhao Ruan,Tanaji Sen,Giulio Stancari,Charles Thangaraj,Randy Thurman-Keup,Alexander Valishev,Vladimir Shiltsev +19 more