PAC2013 - List of Authors (Kharkov, Y.)

Paper

Title

Page

A Model Ring With Exactly Solvable Nonlinear Motion

78

T.V. Zolkin
University of Chicago, Chicago, Illinois, USA
Y. Kharkov, I.A. Morozov
BINP SB RAS, Novosibirsk, Russia
S. Nagaitsev
Fermilab, Batavia, USA

Recently, a concept of nonlinear accelerator lattices with two analytic invariants has been proposed. Based on further studies, the Integrable Optics Test Accelerator (IOTA) was designed and is being constructed at the FNAL. Despite the clarity and transparency of the proposed idea, the detailed analysis of the beam motion remains quite complicated and should be understood better even for the case when no perturbations are taken into account. In this paper we will review one of the three proposed realizations of the integrable optics, where the variables separation is possible in polar coordinates. This system allows for an exact analytical solution expressed in terms of elliptic integrals and Jacobi elliptic functions. It gives the possibility to check numerical algorithms used for tracking and to perform more rigorous analysis of the motion in comparison with the "crude" analysis of the topology of the phase space. In addition we will discuss some difficulties associated with numerical simulations of such a comparatively complex dynamical system and will take a look at the possible perturbations for a model machine.

Slides MOODB2 [0.987 MB]

Paper	Title	Page
MOODB2	A Model Ring With Exactly Solvable Nonlinear Motion	78
	T.V. Zolkin University of Chicago, Chicago, Illinois, USA Y. Kharkov, I.A. Morozov BINP SB RAS, Novosibirsk, Russia S. Nagaitsev Fermilab, Batavia, USA
	Recently, a concept of nonlinear accelerator lattices with two analytic invariants has been proposed. Based on further studies, the Integrable Optics Test Accelerator (IOTA) was designed and is being constructed at the FNAL. Despite the clarity and transparency of the proposed idea, the detailed analysis of the beam motion remains quite complicated and should be understood better even for the case when no perturbations are taken into account. In this paper we will review one of the three proposed realizations of the integrable optics, where the variables separation is possible in polar coordinates. This system allows for an exact analytical solution expressed in terms of elliptic integrals and Jacobi elliptic functions. It gives the possibility to check numerical algorithms used for tracking and to perform more rigorous analysis of the motion in comparison with the "crude" analysis of the topology of the phase space. In addition we will discuss some difficulties associated with numerical simulations of such a comparatively complex dynamical system and will take a look at the possible perturbations for a model machine.
	Slides MOODB2 [0.987 MB]