ICAP 2002 Abstracts and Posters

USING MACROPARTICLES WITH INTERNAL MOTION FOR BEAM DYNAMICS SIMULATIONS

Abstract

In order to simulate the beam dynamics in particle accelerators the Ensemble Model has been developed [1,2]. Conventional tracking or Particle-In-Cell (PIC) algorithms represent a particle beam by a number of macroparticles which are traced in phase space. Such a macroparticle having fixed size (it can be also a point charge) is described by 6 phase coordinates. The Ensemble Model divides a particle beam in a set of subbeams or Ensembles. Besides the motion of the macroparticle center in phase space an internal motion inside Ensemble is considered. Derived from Vlasov equation the Ensemble Model involves moments of the particle distribution function. Within linear approximation for acting forces one can possible to build a compact self-consistent model based on 6 first- and 21 second order moments of the distribution function. This reduces the number of required macroparticles drastically. It was shown [3], that even with one Ensemble the simulation of the beam sizes and correlations in photoinjector yields good agreement with conventional beam dynamics codes, while the Ensemble Model has demonstrated significant advantage in computation time.

In contrary to the conventional macroparticles Ensemble sizes and correlations in phase space change in accordance with gradients of applied forces. In the case of the intense particle beams not only forces (and their gradients) due to external electromagnetic fields act on an Ensemble but also the internal space charge forces. The space charge implementation makes an Ensemble charge distribution function an issue. The rigorous problem consists of determining the stationary charge distribution (which does not explicitly depend on time), which corresponds to the linear applied forces. The distributions in which the forces are linear and the phase space areas remain constant is known as microcanonical distribution. An ellipsoid beam distribution, known as K-V distribution [4] leads to a perfect linear space charge force within the beam radius, but in general case it is extremely difficult in implementation. The space charge model for the Single Ensemble Model (SEM) is based on the homogeneously charged ellipsoid. An analytical approximation for the space charge force gradient calculation implies integration over thin shell of uncompensated charges [3]. Such an approach, being very efficient for the SEM, has significant difficulties for application to Multi Ensemble Model (MEM). As an alternative approach the 6D Gaussian distribution has been considered, and Multi-Centered Gaussian Expansion (MCGE) for the space charge force calculation has been studied [5].

The V-Code, based on the Ensemble Model, has been developed for the on-line beam dynamics simulations [3,6]. The beam line data base is designed in order to be compatible with a given accelerator control system (e.g. TESLA Test Facility - TTF). The goal of the V-Code is fast beam dynamics simulations for the beam line parameters as close to the real machine parameters as possible. Peculiarities of the Ensemble Model implementation into V-Code are discussed. The V-Code has been elaborated within object-oriented approach, which provides an opportunity of the flexible code updating by introduction of new beam line elements and effects (e.g. devices imperfections). One of the practical applications of the V-Code is the beam-based alignment of the TTF rf-gun [7].

The present status of the Ensemble Model and V-Code is presented.

[1] A. Novokhatski and T. Weiland, PAC’99, New York, March

1999 [2] A. Novokhatski and T. Weiland, ICAP’98, Monterey, Sept.

1998. [3] M. Krassilnkov et al., ICAP 2000, Darmstadt, Sept. 2000

[4] I.M. Kapchinskiy “Theory of Resonance Linear

Accelerators”, Harwood Acad.Pub., 1985. [5] M. Krassilnikov, T. Weiland, LINAC’02, Gyeongju, August

2002. [6] A. Novokhatski et al., LINAC 2000, Monterey, August 2000.

[7] R. Cee et al., PAC 2001, Chicago 2001.

The work is supported in part by DESY, Hamburg.

M. Krassilnikov, T. Weiland, FB18-TEMF, Technische University Darmstadt, Germany

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