Modeling of self-consistent distributions for longitudinally non-uniform beams

Drivotin, O. I.; Ovsyannikov, Dmitri

doi:10.1016/j.nima.2005.11.082

Cited by 9 publications

(9 citation statements)

References 13 publications

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“…In fact, such approach was used in numerous works devoted to self-consistent distributions for a cylindrical beam and for a beam with varying cross-section radius ("breathing" beam) [8][9][10][11][12][13][14][15]. In these works, the space of motion integrals was introduced, and particle density was defined in this space.…”

Section: ковариантное описание распределений в фазовом пространствеmentioning

confidence: 99%

“…It gave possibility to construct new solutions of the Vlasov equation. For example, they can be obtained as a linear combinations of degenerate distributions, or as solutions of some integral equation [9][10][11][12][13][14][15].…”

Section: ковариантное описание распределений в фазовом пространствеmentioning

confidence: 99%

“…One of the purposes of this article is to write down such equation. Therefore, formalization of the approach applied in works [8][9][10][11][12][13][14][15] is offered in this article.…”

Section: ковариантное описание распределений в фазовом пространствеmentioning

confidence: 99%

“…Transverse particle motion is described by equations (8) and (9) where E r = e 0 r/(2ε 0 ), E ϕ = E z = 0, B rϕ = μ 0 rH z , B rz = B ϕz = 0. Integrating these equations, we get following integrals of transverse motion [8][9][10][11][12][13][14][15]:…”

Section: ковариантное описание распределений в фазовом пространствеmentioning

confidence: 99%

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Covariant description of phase space distributions

Drivotin¹

2016

Vestnik SPbSU. Applied Mathematics. Computer Science. Control P

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The concept of phase space for particles moving in the 4-dimensional space time is formulated. Definition of particle distribution density as differential form is given. The degree of the distribution density form may be different in various cases. The Liouville and the Vlasov equations are written in tensor form with use of such tensor operations as the Lie dragging and the Lie derivative. The presented approach is valid in both non-relativistic and relativistic cases. It should be emphasized that this approach does not include the concepts of phase volume and distribution function. The covariant approach allows using arbitrary systems of coordinates for description of the particle distribution. In some cases, making use of special coordinates grants the possibility to construct analytical solutions. Besides, such an approach is convenient for description of degenerate distributions, for example, of the Kapchinsky-Vladimirsky distribution, which is well-known in the theory of charged particle beams. It can be also applied for description of particle distributions in curved space time. Refs 25.

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Section: ковариантное описание распределений в фазовом пространствеmentioning

confidence: 99%

Section: ковариантное описание распределений в фазовом пространствеmentioning

confidence: 99%

“…One of the purposes of this article is to write down such equation. Therefore, formalization of the approach applied in works [8][9][10][11][12][13][14][15] is offered in this article.…”

Section: ковариантное описание распределений в фазовом пространствеmentioning

confidence: 99%

Section: ковариантное описание распределений в фазовом пространствеmentioning

confidence: 99%

See 2 more Smart Citations

Covariant description of phase space distributions

Drivotin¹

2016

Vestnik SPbSU. Applied Mathematics. Computer Science. Control P

View full text Add to dashboard Cite

show abstract

“…In fact, such approach was used in numerous works devoted to selfconsistent distributions for a cylindrical beam and for a beam with varying cross-section radius ("breathing" beam) [8][9][10][11][12][13] . In these works, the space of motion integrals was introduced, and particle density was defined in this space.…”

Section: Introductionmentioning

confidence: 99%

Covariant formulation of the Liouville and the Vlasov equations

Drivotin¹

2016

Preprint

View full text Add to dashboard Cite

The fundamental concept of phase space for particles moving in the four-dimensional spacetime is analyzed. Particle distribution density is defined as differential form, which degree may be different in various cases It should be emphasized that this approach does not include the concepts of phase volume and distribution function. The Liouville and the Vlasov equations are written in tensor form. The presented approach is valid in both non-relativistic and relativistic cases. It allows using arbitrary systems of coordinates for description of the particle distribution. In some cases, making use of special coordinates gives possibility to construct analytical solutions. Besides, such approach is convenient for description of degenerate distributions, for example, of the Kapchinsky-Vladimirsky distribution, which is well-known in the theory of charged particle beams. It can be also applied for description of mass distributions in curved spacetime.

show abstract

Multicriterial approach to beam dynamics optimization problem

Vladimirova

2016

J. Phys.: Conf. Ser.

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Modeling of self-consistent distributions for longitudinally non-uniform beams

Cited by 9 publications

References 13 publications

Covariant description of phase space distributions

Covariant description of phase space distributions

Covariant formulation of the Liouville and the Vlasov equations

Multicriterial approach to beam dynamics optimization problem

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