Author: Kharkov, Y.
Paper Title Page
TUEPPB003 Nonlinear Accelerator with Transverse Motion Integrable in Normalized Polar Coordinates 1116
  • T.V. Zolkin
    University of Chicago, Chicago, Illinois, USA
  • Y. Kharkov, I.A. Morozov
    BINP SB RAS, Novosibirsk, Russia
  • S. Nagaitsev
    Fermilab, Batavia, USA
  Several families of nonlinear accelerator lattices with integrable transverse motion were suggested recently*. One of the requirements for the existence of two analytic invariants is a special longitudinal coordinate dependence of fields. This paper presents the particle motion analysis when a problem becomes integrable in the normalized polar coordinates. This case is distinguished from the others: it yields an exact analytical solution and has a uniform longitudinal coordinate dependence of the fields (since the corresponding nonlinear potential is invariant under the transformation from the Cartesian to the normalized coordinates). A number of interesting features are revealed: while the frequency of radial oscillations is independent of the amplitude, the spread of angular frequencies in a beam is absolute. A corresponding spread of frequencies of oscillations in the Cartesian coordinates is evaluated via the simulation of transverse Schottky noise.
V. Danilov and S. Nagaitsev, Phys. Rev. ST Accel. Beams 13 084002 (2010).