RUPAC2018 - List of Authors (Drivotin, O.I.)

Paper	Title	Page
TUPSA09	Degenerate Self-Consistent Distributions for Charged Particle Beam in Linear Transverse Field	161
	O.I. Drivotin St. Petersburg State University, St. Petersburg, Russia
	The present report is devoted to covariant description of the microcanonical distributions for a charged particle beam on the base of the covariant approach previously developed in the works of the author. For microcanonical distribution, particles are distributed on surface of some ellipsoid in the phase space. Here, we consider most general case of arbitrary orientation of the ellipsoid. For description of such distributions, we make use the density of particles on surface of the ellipsoid. Covariant approach give us an opportunity to follow the evolution of these distributions using various systems of coordinates in the phase space. Using such approach, we found new distributions, which can be considered as generalizations of the Kapchinsky-Vladimirsky distribution. The results can be useful in many applied problems, for example, problems of optimization of beam transport channel. O.I. Drivotin. Covariant Formulation of the Vlasov Equation. Proc. IPAC'2011; Covariant Description of Phase Space Distributions. Vestnik of St.Petersburg Univ. Ser.10. 2016, iss.3. P.39-52.
DOI •	reference for this paper ※ https://doi.org/10.18429/JACoW-RUPAC2018-TUPSA09
Export •	reference for this paper using ※ BibTeX, ※ LaTeX, ※ Text/Word, ※ RIS, ※ EndNote (xml)

TUPSA10	Control Theory Model for RFQ Channel Optimization	164
	O.I. Drivotin St. Petersburg State University, St. Petersburg, Russia
	The common approach for RFQ channel design* allows to find geometric parameters of sections of the channel including cell lengths, apertures and coefficients of modulation of electrodes forming the channel. According to that approach, the phase of so called synchronous particle changes slowly. Our previous computations** indicate that quality of beam in this channel can be better, if synchronous phase changes more quickly with some oscillations. To find opportunity for improving the structure, we propose a control theory model for charged particle beam in the RFQ channel. The model includes some particle distribution with density satisfying to the Liouville equation, dynamics equations containing control functions, and a quality functional. The synchronous phase is chosen as one of the control functions. Great attention is paid to choice of the quality functional. A numerical solution of such problem can be achieved by an iterative method based on computation of the functional variations. In real problems, we can parametrize the control functions. Then functional variations can be approximated by derivatives of functional over control functions parameters. * I.Kapchinsky. Theory of Resonance Linear Accelerators. New York, Harwood Academic Publ., 1985. ** O.I. Drivotin, D.A. Ovsyannikov, Yu.A. Svistunov, M.F. Vorogushin. Proc. EPAC'98.
DOI •	reference for this paper ※ https://doi.org/10.18429/JACoW-RUPAC2018-TUPSA10
Export •	reference for this paper using ※ BibTeX, ※ LaTeX, ※ Text/Word, ※ RIS, ※ EndNote (xml)

Paper

Title

Page

Degenerate Self-Consistent Distributions for Charged Particle Beam in Linear Transverse Field

161

O.I. Drivotin
St. Petersburg State University, St. Petersburg, Russia

The present report is devoted to covariant description of the microcanonical distributions for a charged particle beam on the base of the covariant approach previously developed in the works of the author*. For microcanonical distribution, particles are distributed on surface of some ellipsoid in the phase space. Here, we consider most general case of arbitrary orientation of the ellipsoid. For description of such distributions, we make use the density of particles on surface of the ellipsoid. Covariant approach give us an opportunity to follow the evolution of these distributions using various systems of coordinates in the phase space. Using such approach, we found new distributions, which can be considered as generalizations of the Kapchinsky-Vladimirsky distribution. The results can be useful in many applied problems, for example, problems of optimization of beam transport channel.
* O.I. Drivotin. Covariant Formulation of the Vlasov Equation. Proc. IPAC'2011; Covariant Description of Phase Space Distributions. Vestnik of St.Petersburg Univ. Ser.10. 2016, iss.3. P.39-52.

DOI •

reference for this paper ※ https://doi.org/10.18429/JACoW-RUPAC2018-TUPSA09

Export •

reference for this paper using ※ BibTeX, ※ LaTeX, ※ Text/Word, ※ RIS, ※ EndNote (xml)

TUPSA10

Control Theory Model for RFQ Channel Optimization

164

O.I. Drivotin
St. Petersburg State University, St. Petersburg, Russia

The common approach for RFQ channel design* allows to find geometric parameters of sections of the channel including cell lengths, apertures and coefficients of modulation of electrodes forming the channel. According to that approach, the phase of so called synchronous particle changes slowly. Our previous computations** indicate that quality of beam in this channel can be better, if synchronous phase changes more quickly with some oscillations. To find opportunity for improving the structure, we propose a control theory model for charged particle beam in the RFQ channel. The model includes some particle distribution with density satisfying to the Liouville equation, dynamics equations containing control functions, and a quality functional. The synchronous phase is chosen as one of the control functions. Great attention is paid to choice of the quality functional. A numerical solution of such problem can be achieved by an iterative method based on computation of the functional variations. In real problems, we can parametrize the control functions. Then functional variations can be approximated by derivatives of functional over control functions parameters.
* I.Kapchinsky. Theory of Resonance Linear Accelerators. New York, Harwood Academic Publ., 1985.
** O.I. Drivotin, D.A. Ovsyannikov, Yu.A. Svistunov, M.F. Vorogushin. Proc. EPAC'98.

DOI •

reference for this paper ※ https://doi.org/10.18429/JACoW-RUPAC2018-TUPSA10

Export •

reference for this paper using ※ BibTeX, ※ LaTeX, ※ Text/Word, ※ RIS, ※ EndNote (xml)