Paper  Title  Page 

TUEPPB003  Nonlinear Accelerator with Transverse Motion Integrable in Normalized Polar Coordinates  1116 


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). 

MOEPPB008  Simulation of Hollow Electron Beam Collimation in the Fermilab Tevatron Collider  94 


Funding: Fermi Research Alliance, LLC operates Fermilab under Contract DEAC0207CH11359 with the US Department of Energy. This work was partially supported by the US LHC Accelerator Research Program (LARP). The concept of augmenting the conventional collimation system of highenergy storage rings with a hollow electron beam was successfully demonstrated in experiments at the Tevatron. A reliable numerical model is required for understanding particle dynamics in the presence of a hollow beam collimator. Several models were developed to describe imperfections of the electron beam profile and alignment. The features of the imperfections are estimated from electron beam profile measurements. Numerical simulations of halo removal rates are compared with experimental data taken at the Tevatron. 
