Simulation of Space Charge Dynamics in High Intensive Beams on Hybrid Systems
The method for construction of analytical expressions for electric and magnetic fields for some set of the distributions of the charge density is described. These expressions are used for symbolic computation of the corresponding electric and magnetic fie
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Abstract. The method for construction of analytical expressions for electric and magnetic fields for some set of the distributions of the charge density is described. These expressions are used for symbolic computation of the corresponding electric and magnetic fields generated by the beam during the evolution in accelerators. Here we focus on the use of the matrix form for Lie algebraic methods for calculating the beam dynamics in the presence of self-field of the beam. In particular, the corresponding calculations are based on the predictor-corrector method. The suggested approach allows not only to carry out numerical experiments, but also to provide accurate analytical analysis of the impact of different effects with the use of ready-made modules in accordance with the concept of Virtual Accelerator Laboratory. To simulate the large number of particle distributed resources for computations are used. Pros and cons of using described approach on hybrid systems are discussed. In particular, the investigation of overall performance of the predictor-corrector method is made.
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Introduction
It is not necessary to say how popular and important accelerators are presently. There are a lot of facilities all over the world created for different purposes. The number of various software packages based on different approaches is even bigger that the accelerators we have. It is better to give a brief survey of methods that are used today to calculate the dynamics of beam with space charge. High intensive beams are interesting from both side – the theoretical and practical point of view. More particles we have, more information about the beam we will get. On the other hand, intensive beams play a great role in medicine, when needed to irradiate only diseased cells, but not the healthy ones. But it is obvious that with intensity different effects of the beam that can not be denied occur. On of this is the forces of the self field of the particles. In the works [1–4] pay attention on the impact of space charge forces especially in the case that it can lead to the so called the filamentation effect or to the Halo (e.g. see Fig. 1). And for that purposes it is important to consider the space charge forces. The work is supported by SPbSU 0.37.155.2014 and RFBR 16-07-01113A. c Springer International Publishing Switzerland 2016 O. Gervasi et al. (Eds.): ICCSA 2016, Part I, LNCS 9786, pp. 284–295, 2016. DOI: 10.1007/978-3-319-42085-1 22
Simulation of Space Charge Dynamics
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Fig. 1. (a) Filamentation, (b) Halo
The method which is commonly used [5–7] is Particle-in-Cell method (PIC). The methods popularity caused its conceptual simplicity, the relative ease at which simulations may be implemented. Often, PIC simulations are implemented from first-principles (without the need for an approximate equation of state). However, these simulations often are computationally expensive with restrictive time step and mesh spacing limitations [8]. The Fortran-based environment COSY INFINITY [9] is also well known and used. The main use of the code li
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