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COVARIANT DESCRIPTION OF PHASE SPACE DISTRIBUTIONS. / Drivotin, O. I.
в: ВЕСТНИК САНКТ-ПЕТЕРБУРГСКОГО УНИВЕРСИТЕТА. ПРИКЛАДНАЯ МАТЕМАТИКА. ИНФОРМАТИКА. ПРОЦЕССЫ УПРАВЛЕНИЯ, Том 12, № 3, 2016, стр. 39-52.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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TY - JOUR
T1 - COVARIANT DESCRIPTION OF PHASE SPACE DISTRIBUTIONS
AU - Drivotin, O. I.
PY - 2016
Y1 - 2016
N2 - 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.
AB - 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.
KW - Liouville equation
KW - Vlasov equation
KW - phase space
KW - phase density
KW - particle distribution density
KW - self-consistent distribution
KW - degenerate distribution
KW - уравнение Лиувилля
KW - Уравнение Власова
KW - фазовое пространство
KW - фазовая плотность
KW - плотность распределения частиц
KW - самосогласованное распределение
KW - вырожденное распределение
UR - http://vestnik.spbu.ru/html16/s10/s10v3/04.pdf
U2 - 10.21638/11701/spbu10.2016.304
DO - 10.21638/11701/spbu10.2016.304
M3 - Article
VL - 12
SP - 39
EP - 52
JO - ВЕСТНИК САНКТ-ПЕТЕРБУРГСКОГО УНИВЕРСИТЕТА. ПРИКЛАДНАЯ МАТЕМАТИКА. ИНФОРМАТИКА. ПРОЦЕССЫ УПРАВЛЕНИЯ
JF - ВЕСТНИК САНКТ-ПЕТЕРБУРГСКОГО УНИВЕРСИТЕТА. ПРИКЛАДНАЯ МАТЕМАТИКА. ИНФОРМАТИКА. ПРОЦЕССЫ УПРАВЛЕНИЯ
SN - 1811-9905
IS - 3
ER -
ID: 39948289