Time Integration Methods for Particle Beam Simulations with the Finite Integration Theory

Abstract

In this contribution two novel time integration methods designed for the solution of Maxwell's equations in the time domain using the Finite Integration Theory (FIT) are presented. This work was motivated by the need for simulating particle beams in electrically long structures, e.g., Linear Particle Accelerators. The extension of such a structure along the beam propagation axis is much larger than the transversal dimensions. The simulation of this structures is usually performed by the Staggered Leap-Frog (SLF) time integration within the framework of the FIT spatial discretization. Unfortunately, the numerical dispersion error of this algorithm is large along the beam propagation axis. Contrary to this, the proposed methods have a minimal error, vanishing for the Courant time step, along this direction. This property allows for a longer simulation time and for more accurate field solutions in accelerator structures.The two sets of equations are coupled through the total charge and current q j , which are carried in time and space by the system of charged particles. Frequenz 59 (2005) 9-10 Brought to you by | University of Arizona Authenticated Download Date | 5/30/15 8:34 AM

Extension of the Finite Integration Technique including dynamic mesh refinement and its application to self-consistent beam dynamics simulations

“…Typically, the leap-frog scheme is applied for their integration in time. Alternatively, one may apply the longitudinaltransverse split operator scheme introduced in [6,7] for the time integration, which offers better numerical dispersion properties. The latter approach is referred to as LT-FIT standing for Longitudinal-Transverse-FIT.…”

A hybrid Finite Integration–Finite Volume Scheme

“…The above idea of splitting the curl operator was proposed in [12]. There, however, the FIT discretization was used exclusively.…”

Numerical Analysis of a Single-Stage Fast Linear Transformer Driver Using Field-Circuit Coupled Time-Domain Finite Integration Theory

“…The PEEC method can directly embed transient EM model of the multi-conductor system into circuit model [27], but it is difficult to model materials with intricate distribution [28]. The finite integration theory (FIT) is proposed by Weiland [29] and then it is combined with particle-in-cell algorithm for simulating particle accelerators [30][31][32]. FIT starts with Maxwell's equations in integral form and defines integration of field quantity on the edge or facet of a grid as degree of freedom (DoF) [31].…”