Publisher’s Note: Cumulative beam breakup in linear accelerators with random displacement of cavities and focusing elements [Phys. Rev. ST Accel. Beams7, 074402 (2004)]

Abstract

with a formatting error in Eq. (15). It has been corrected as of 16 July 2004.

Cumulative beam breakup in linear accelerators with time-dependent parameters

“…More recently a general analysis of BBU with arbitrary time dependence of the beam current and injection offsets, as well as random displacement of cavities and focusing elements, was developed [17,18]. This analysis is extended here to include time dependence of the focusing and of the coupling between the beam and the dipole mode in order to control or suppress the BBU instability and the resulting emittance growth.…”

Transverse effects due to random displacement of resistive wall segments and focusing elements

“…In the opposite case where focusing is absent, the rms beam displacement is given by [6] ( ) If instead of the wakefield-generating elements, the focusing elements are displaced, then the mean-square displacement of the bunch is given by…”

“…These functions can be calculated for a variety of current distributions [7] and, in particular, for the profile shown in Fig. 1 determines the rms distortion of the beam.…”

“…Under those assumptions, the displacement of the beam as it propagates along the transport system is given by [3,6] …”

Design and Simulation Challenges of a Linac-Based Free Electron Laser in the Presence of Collective Effects

“…of this equation is the homogeneous equation for the betatron motion in the horizontal or vertical plane; the r.h.s. contains the convolution of the transverse wake function with the local current distribution and is also linearly proportional to the relative displacement of the particle from the axis of the accelerating structure [54,55]:…”