Cumulative beam breakup in linear accelerators with arbitrary beam current profile

Abstract

An analytical formalism for the solution of cumulative beam breakup in linear accelerators with arbitrary time dependence of beam current is presented, and a closed-form expression for the time and position dependence of the transverse displacement is obtained. It is applied to the behavior of a single bunch and to the steady-state and transient behavior of dc beams and beams composed of pointlike and finite-length bunches. This formalism is also applied to the problem of cumulative beam breakup in the presence of random displacement of cavities and focusing elements, and a general solution is presented.

Transverse effect due to short-range resistive wall wakefield

“…With the full wake, we can take the series solution approach [6] to study the transverse wake effect for electron bunch with arbitrary longitudinal shape. In this paper, we will not discuss the misalignment effect, hence we set…”

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

“…Finally, ǫ(σ)=ǫ r (γ 0 /γ(σ)) is the factor coupling the particle betatron motion (described by the homogeneous form of the previous equation) to the wake field driving term. It is given by [54]:…”

“…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]:…”

Cumulative beam breakup due to resistive-wall wake

“…The cumulative beam breakup (BBU) problem in a periodic linear accelerator (linac) excited by the resonance wake is well understood [1][2][3][4]. However, there are no systematic studies for the corresponding problem excited by the resistive-wall impedance.…”