Parallel beam dynamics simulation in injection systems taking into account particle interactions

Abstract

The problem of 3D beam dynamics simulation in injection systems is considered. Accelerating electrostatic field is simulated as a result of the solution of boundary value problem for Laplace equation by finite difference method. The computation of the beam field is based on the analytical solution of boundary value problem set for Poisson equation with use of MPI based parallel computations. High efficiency of the proposed computational method is shown in the examples.When developing an accelerator complex, the injection system design is of importance, because it largely determines the output characteristics of the beam. For the design of such systems it is necessary to carry out numerical simulation and optimization of beam dynamics in the electro-magnetic fields, which necessitated the development and improvement of mathematical models of charged particle beams. Many works [1] -[4] are devoted to the problems of modeling and optimization of the dynamics of charged particles in the injection system. Under beam dynamics simulation an ensemble of model particles is usually used for the representation of the beam ('large' particle method). For the intense beam to take into account the Coulomb interaction between the particles is of great importance. The most effective numerical methods for charged particle beam field simulation are based on the numerical solution of boundary value problem for the Poisson equation by the grid method. However, these methods are not applicable for beam dynamics optimization with analytical representation for the internal and external fields in the accelerating structures [4]. Therefore, it seems urgent to develop mathematical models that admit an analytical representation for the Coulomb field of the charged beams.In this paper we use both numerical and analitical methods for beam field computation. Numerical method is based on the solution by grid method of the Poisson equation for the beam field potential with the boundary conditions which take into account the actual geometry of the accelerating structure. Analytical method for beam field modeling is presented in [5], where the charged particles beam is modeled by a set of nested circular cylinders. We assume that the beam is unlimited and periodical in the longitudinal coordinate. Assume also that the beam is in a coaxial circular metal tube of radius a and has azimuthal symmetry. To determine the Coulomb field we consider the beam as a set of annular cylindrical coaxial layers. Each layer is non-uniform in the longitudinal coordinate and in each cross-section the layer density is constant. The intensity vector of the beam Coulomb field is calculated as the sum of the intensity vectors of each layer:where E i -Coulomb field intensity vector of the i-th annular layer; N -number of annular layers, zero layer -axial cylindrical layer. This model allows to take into account both longitudinal and transverse beam heterogeneity under calculation of its Coulomb field.We introduce a cylindrical coordinate system (z, θ, r), where Oz axis co...

Development of the Object-Oriented Dynamic Simulation Models Using Visual C++ Freeware

“…Essentially, the presented results can be applied to all kinds of simulation: continuous, hybrid, and even discrete-event applications. The approach has already been used in developing the research software in the field of designing particle accelerators, which was carried out by S. Kozynchenko and V. Kozynchenko [16][17][18].…”