ICAP2012 - List of Authors (Andrianov, S.N.)

Paper

Title

Page

The Convergence and Accuracy of the Matrix Formalism Approximation

93

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

Funding: The work is supported by Federal Targeted Program "Scientific and Scientific-Pedagogical Personnel of the Innovative Russia in 2009-2013" (Governmental Contract no. p 793)
To the present time there has been developed a large number of different codes for the particles beam dynamics modeling. However, their precision, accuracy and reliability of the numerical results are not sufficiently guaranteed in the case of long-term evolution of particle beams in circular accelerators. Here we discuss convergence estimates of the matrix presentation for Lie series. We also consider some problems of the matrix formalism accuracy for constructing the evolution operator of the particle beam. In this article there is paid a special attention to problems of symplecticity and energy conservation for long time evolution of particle beams.

Slides TUSCC2 [1.475 MB]

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 TUADI1 [0.951 MB]

WEP16

Analytical Presentation of Space Charge Forces

173

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

Funding: The work is supported by Federal Targeted Programme "Scientific and Scientific-Pedagogical Personnel of the Innovative Russia in 2009-2013" (Governmental Contract no. p 793)
This paper presents an analytical description of the space charge forces generated by charged particle beams. The suggested approach is based on some set of models for particle distribution function. All necessary calculations have analytical and closed form for different models for beam density distributions. These model distributions can be used for approximation of real beam distributions. The corresponding solutions are included in a general scheme of beam dynamics presentation based on the matrix formalism for Lie algebraic tools. The corresponding computer software is based on corresponding symbolic codes and some parallel technologies. In particular, as computational tools we consider GPU graphic card NVIDIA. As an example, there is considered the problem of modeling the beam dynamics for microprobe focusing systems.

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 WEACC3 [1.441 MB]

Paper	Title	Page
TUSCC2	The Convergence and Accuracy of the Matrix Formalism Approximation	93
	S.N. Andrianov St. Petersburg State University, St. Petersburg, Russia
	Funding: The work is supported by Federal Targeted Program "Scientific and Scientific-Pedagogical Personnel of the Innovative Russia in 2009-2013" (Governmental Contract no. p 793) To the present time there has been developed a large number of different codes for the particles beam dynamics modeling. However, their precision, accuracy and reliability of the numerical results are not sufficiently guaranteed in the case of long-term evolution of particle beams in circular accelerators. Here we discuss convergence estimates of the matrix presentation for Lie series. We also consider some problems of the matrix formalism accuracy for constructing the evolution operator of the particle beam. In this article there is paid a special attention to problems of symplecticity and energy conservation for long time evolution of particle beams.
	Slides TUSCC2 [1.475 MB]

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 TUADI1 [0.951 MB]

WEP16	Analytical Presentation of Space Charge Forces	173
	S.N. Andrianov St. Petersburg State University, St. Petersburg, Russia
	Funding: The work is supported by Federal Targeted Programme "Scientific and Scientific-Pedagogical Personnel of the Innovative Russia in 2009-2013" (Governmental Contract no. p 793) This paper presents an analytical description of the space charge forces generated by charged particle beams. The suggested approach is based on some set of models for particle distribution function. All necessary calculations have analytical and closed form for different models for beam density distributions. These model distributions can be used for approximation of real beam distributions. The corresponding solutions are included in a general scheme of beam dynamics presentation based on the matrix formalism for Lie algebraic tools. The corresponding computer software is based on corresponding symbolic codes and some parallel technologies. In particular, as computational tools we consider GPU graphic card NVIDIA. As an example, there is considered the problem of modeling the beam dynamics for microprobe focusing systems.

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 WEACC3 [1.441 MB]