Author: Ivanov, A.N.
Paper Title Page
TUADI1 Storage Ring EDM Simulation: Methods and Results 99
 
  • Y. Senichev, A. Lehrach, R. Maier, D. Zyuzin
    FZJ, Jülich, Germany
  • S.N. Andrianov, A.N. Ivanov
    St. Petersburg State University, St. Petersburg, Russia
  • M. Berz, K. Makino
    MSU, East Lansing, Michigan, USA
 
  The idea of Electric Dipole Moment search using the electrostatic storage ring with polarized beam is based on accumulation of additional tiny spin rotation, about one-billionth of radians per second, occurred only in the presence of EDM. This method can be realized under condition of the long-time spin coherency ~1000 seconds. During this time each particle performs about 109 turns in ring moving on different trajectories. At such conditions the spin-rotation aberrations associated with various types of space and time dependent nonlinearities start playing a crucial role. To design such a ring the computer simulation is necessary taking into account all factors affecting the spin. We used COSY-Infinity and integrating program with symplectic Runge-Kutta methods in composition with analytic methods. We developed a new lattice based on the alternating spin rotating. As a result, we can achieve the SCT of ~5000 seconds. The difficulties of these studies are still in the fact that the aberrations growth is observed in the scale of 109 turns and few million particles. For this simulation we use a supercomputer with parallel computing process.  
slides icon Slides TUADI1 [0.951 MB]  
 
WEP06 Particle Tracking in Electrostatic Fields with Energy Conservation 149
 
  • A.N. Ivanov
    St. Petersburg State University, St. Petersburg, Russia
 
  The key idea of the research is to consider spin dynamics in electrostatic fields. Due to the fact, that spin rotation frequency explicitly depends on velocity of the particle and its kinetic energy is changed in electrostatic fields it is important to use some technique that provides both conservation energy and symplicticity condition. An appropriate mathematical model is described and the results of numerical calculation are shown. In conclusion, fringe fields influence is examined and compared with case of ideal fields.  
 
WEACC3 Matrix Formalism for Long-term Evolution of Charged Particle and Spin Dynamics in Electrostatic Fields 187
 
  • A.N. Ivanov, S.N. Andrianov
    St. Petersburg State University, St. Petersburg, Russia
 
  The matrix formalism as a numerical approach for solving of ODE equations is considered. It is a map method and has several advantages over classical step-by-step integration methods. This approach allows to present the solution as set of numerical matrices. A complete derivation of the equations this method is based on will be shown. Problems of symplectification and computing performance are discussed. We have developed an application that provides a tool for differential equations solving. The developed program allows to generate the final programming codes on C++, Fortran, MATLAB, C#, Java languages. The given approach is applied to long-term evolution of charged particle and spin dynamics in electrostatic fields.  
slides icon Slides WEACC3 [1.441 MB]