PAC2013 - List of Authors (Zolkin, T.V.)

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]

THPHO23

Improvement of Digital Filter for the FNAL Booster Transverse Dampers

1349

T.V. Zolkin
University of Chicago, Chicago, Illinois, USA
N. Eddy, V.A. Lebedev
Fermilab, Batavia, USA

Fermilab Booster has a transverse damping system which independently suppresses beam instabilities in the horizontal and vertical planes. A suppression of the common mode signal is achieved by digital notch filter which is based on subtracting beam positions for two consecutive turns. Such system operates well if the orbit position changes sufficiently slow. Unfortunately it is not the case for Fermilab Booster where the entire accelerating cycle consists of about 20,000 turns and successful transition crossing requires the orbit drifts up to about 10 um/turn resulting in excessive power, power amplifier saturation and loss of stability. To suppress this effect we suggest an improvement to the digital filter which can take into account fast orbit changes by using bunch positions of a few previous turns. To take into account the orbit change up to N-th order polynomial in time the system requires (N + 3) turns of "prehistory". In the case of sufficiently small gain the damping rate and the optimal digital filter coefficients are obtained analytically. Numerical simulations verify analytical theory for the small gain and predict a system performance with gain increase.

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]

THPHO23	Improvement of Digital Filter for the FNAL Booster Transverse Dampers	1349
	T.V. Zolkin University of Chicago, Chicago, Illinois, USA N. Eddy, V.A. Lebedev Fermilab, Batavia, USA
	Fermilab Booster has a transverse damping system which independently suppresses beam instabilities in the horizontal and vertical planes. A suppression of the common mode signal is achieved by digital notch filter which is based on subtracting beam positions for two consecutive turns. Such system operates well if the orbit position changes sufficiently slow. Unfortunately it is not the case for Fermilab Booster where the entire accelerating cycle consists of about 20,000 turns and successful transition crossing requires the orbit drifts up to about 10 um/turn resulting in excessive power, power amplifier saturation and loss of stability. To suppress this effect we suggest an improvement to the digital filter which can take into account fast orbit changes by using bunch positions of a few previous turns. To take into account the orbit change up to N-th order polynomial in time the system requires (N + 3) turns of "prehistory". In the case of sufficiently small gain the damping rate and the optimal digital filter coefficients are obtained analytically. Numerical simulations verify analytical theory for the small gain and predict a system performance with gain increase.