Paper 
Title 
Page 
MOPWO018 
Cellular Automaton Simulating the Motion of the Charged Particles Beam 
918 

 S.N. Andrianov, N.V. Kulabukhova
St. Petersburg State University, St. Petersburg, Russia
 V. Ryabusha
Saint Petersburg State University, Saint Petersburg, Russia



In this research we formulate and formalize the rules for the cellular automaton that emulates the motion of the charged particles beam under the effect of Coulomb force for one, two and threedimensional cases. In this research we also describe the main principles of the realization of this approach in a paralleled cluster environment.



MOPWO019 
An IDE for Spinorbit Dynamics Simulation 
921 

 A.N. Ivanov, N.V. Kulabukhova
St. Petersburg State University, St. Petersburg, Russia



In this paper a prototype of an IDE for simulation of spinorbit motion is described. It is based on the component software development and provides a flexible graphic user interface. One of the main parts of it is numerical methods for ordinary differential equations integration. For numerical simulation it is possible use either the matrix map algorithm or traditional stepbystep methods. This workflow allows choosing one of numerical algorithms and to provide necessary computational experiments. It is also contains both a visual designer of an accelerator lattice and additional tools for control parameters of the model. There is also exists possibility for code generation in different programming languages and computation on highperformance systems.



MOPWO020 
Space Charge Dominated Envelope Dynamics using GPUs 
924 

 N.V. Kulabukhova
St. Petersburg State University, St. Petersburg, Russia



High power accelerator facilities lead to necessity to consider space charge forces. It is therefore important to study the space charge dynamics in the corresponding channels. To represent the space charge forces of the beam we have developed special software based on some analytical models for space charge distributions. Because calculations for space charge dynamics become extremely time consuming, we use a special algorithm for predictorcorrector method for evaluation scheme for beam map evaluation including the space charge forces. This method allows us to evaluate the map along the references trajectory and to create the beam envelope dynamics. The corresponding computer codes are realized using CUDA implementation of maps for particle dynamics. Some numerical results for different types of the beam channels are discussed. The survey of advantages and disadvantages of using different methods of parallelization and some parallel approaches will be done.



MOPWO021 
Data Management and Analysis for Beam Dynamics Simulation 
927 

 D. Zyuzin
FZJ, Jülich, Germany
 S.N. Andrianov, N.V. Kulabukhova
St. Petersburg State University, St. Petersburg, Russia



Computer simulation of modern accelerator system is based on a number of specialized computer codes. Complexity of concerned processes and interpretation of simulation results requires comfortable and effective tools to design accelerator structure and beam characteristics, carry out computer experiments, process and visualize data. This paper proposes a prototype system with webinterface which allows the full research cycle: from lattice generation to data visualization. This approach represents a valuable tool for beam physicist providing methods to benchmark simulation engines as well as providing additional instruments for understanding physical processes in accelerator. The corresponding tools were used in application to the spinorbit motion problems in electrostatic accelerators.



WEPEA036 
Spin Tune Decoherence Effects in Electro and Magnetostatic Structures 
2579 

 Y. Senichev, R. Maier, D. Zyuzin
FZJ, Jülich, Germany
 N.V. Kulabukhova
St. Petersburg State University, St. Petersburg, Russia



In Electric Dipole Moment search experiments with polarized beams the coherence of spin oscillations of particles has a crucial role. The decoherent effects arise due to spin tune dependence on particle energy and particle trajectory in focusingdeflecting fields. They are described through the nth order spin tune aberrations. Since the first order is suppressed by RF field, the second order plays crucial role. It depends on the orbit lengthening and on the odd order field components. We consider the spin decoherence effects and methods of their compensation in different channels, electrostatic, magnetostatic linking the decoherence effects with common characteristics such as the momentum compaction factor, the chromaticity and others.



WEPEA037 
Testing of Symplectic Integrator of Spinorbit Motion Based on Matrix Formalism 
2582 

 A.N. Ivanov, S.N. Andrianov, N.V. Kulabukhova
St. Petersburg State University, St. Petersburg, Russia
 R. Maier, Y. Senichev, D. Zyuzin
FZJ, Jülich, Germany



Investigation of spinorbital motion in electromagnetic fields requires different numerical methods. Approaches for longterm evolution modelling need both performance and symplecticity. In this paper we discuss matrix maps method for numerical simulation. We examine symplectification and accuracy in terms of electostatic storage ring. The results are compared with traditional symplectic stepbystep methods.



WEPEA038 
Two and three Dimensional Models for Analytical and Numerical Space Charge Simulation 
2585 

 S.N. Andrianov, N.V. Kulabukhova
St. Petersburg State University, St. Petersburg, Russia



In this article there is described an analytical approach to describe the selffield of two and three dimensional ellipsoidal presentation of space charge distribution. The corresponding results can be evaluated in both numerical and the analytic presentation for some model distributions of charge. The corresponding results can be embedded in the Lie formalism used to describe the map for the beam dynamics. The corresponding linear and nonlinear maps are evaluated in terms of the matrix representation of the evolution operator of the beam. Appropriate solutions for nonlinear differential equations are based on a predictioncorrection method (the converging recursive procedure). These solutions are compared with the Vlasov equation solutions. A special software package for the described approach is presented.


