Motion of a charged particle in an axisymmetric longitudinal magnetic field that is inversely proportional to the radius

Кабин, К.; Bonner, G.

doi:10.1016/j.cpc.2014.12.001

Cited by 7 publications

(4 citation statements)

References 17 publications

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“…После этого подставим это выражение в равенство (14), тогда результат этой подстановки с противоположным знаком равен правой части второго уравнения системы (13):…”

Section: уравнения движения и их симметрияunclassified

“…Классической задачей является моделирование движения заряженной частицы в различных магнитных полях, в частности, построение уравнений движения и нахождение траектории частицы, зависящей от конкретной конфигурации магнитного поля [12,13,14]. К сожалению, таких точно решаемых задач очень мало.…”

Section: Introductionunclassified

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Modeling the Dynamics of a Charged Particle in a Force-Free Magnetic Field

Boldyreva¹,

Магазев²

2019

AM&FI

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Аннотация. В статье рассмотрены вопросы моделирования движения классической заряженной частицы в бессиловом магнитном поле. Выписана система Гамильтона данной задачи и соответствующая ей редуцированная система. В результате анализа редуцированной системы построены графики, отражающие динамику классической заряженной частицы в бессиловом поле при финитном и инфинитном движении, получена сепаратрисная кривая. Проведено сравнение с результатами численного моделирования. Ключевые слова: бессиловое магнитное поле, система Гамильтона, редукция уравнений движения.

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Section: уравнения движения и их симметрияunclassified

Section: Introductionunclassified

Modeling the Dynamics of a Charged Particle in a Force-Free Magnetic Field

Boldyreva¹,

Магазев²

2019

AM&FI

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“…For dipole field, these threshold energies are discussed, for example, by Avrett []. A detailed discussion of all possible types of orbits of charged particles in a magnetic field B ∼ 1/ r , where an analytical solution is possible, is described by Kabin and Bonner []. While no analytical solution is possible for the magnetic field used in the current work, the types of the possible trajectories are the same.…”

Section: Particle Trajectoriesmentioning

confidence: 99%

“…Maximum kinetic energy of a trapped proton in static magnetotail field (before the dipolarization at t = 0) as a function of the direction of its initial velocity (measured counterclockwise from eastward) for three initial proton positions: 7 R E , 9 R E , and 11 R E . Kabin and Bonner [2015]. While no analytical solution is possible for the magnetic field used in the current work, the types of the possible trajectories are the same.…”

Section: Proton Dynamicsmentioning

confidence: 99%

Particle energization by a substorm dipolarization

et al. 2017

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Magnetotail dipolarizations, often associated with substorms, produce significant energetic particle enhancements in the nighttime magnetosphere. In this paper, we apply our recently developed magnetotail dipolarization model to the problem of energizing electrons and ions. Our model is two‐dimensional in the meridional plane and is characterized by the ability to precisely control the location of the transition from the dipole‐like to tail‐like magnetic fields. Both magnetic and electric fields are calculated, self‐consistently, as the transition zone retreats farther into the tail and the area around the Earth occupied by dipole‐like lines increases in size. These fields are used to calculate the motion of electrons and ions and changes in their energies. We consider the energizing effects of the fields restricted to ±15° and ±30° sectors around the midnight meridian, as well the axisymmetric case. Energies of some electrons increase by a factor of 25, which is more than enough to produce observable ionospheric signatures. Electrons are treated using the Guiding Center approximation, while protons and heavier particles generally require description based on the Lorentz equations.

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Two examples of exact calculations of the adiabatic invariant for charged particle motion in non-uniform axisymmetric magnetic fields

Кабин

2019

Physics of Plasmas

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This paper discusses the calculation of the adiabatic invariant of a charged particle moving in an axisymmetric magnetic field with straight field lines. This calculation can be reduced to quadratures, and in several cases, the exact analytical results can be obtained. In particular, an exact expression is obtained for the charged particle motion in the equatorial field of a magnetic dipole, which can have important applications to the high-order guiding center theory for the particles in the terrestrial radiation belts. Another closed-form analytical result corresponds to magnetic field intensity which is inversely proportional to the radius. The results represent an extension of the classical series expansions of Kruskal for these specific magnetic fields.

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Motion of a charged particle in an axisymmetric longitudinal magnetic field that is inversely proportional to the radius

Cited by 7 publications

References 17 publications

Modeling the Dynamics of a Charged Particle in a Force-Free Magnetic Field

Modeling the Dynamics of a Charged Particle in a Force-Free Magnetic Field

Particle energization by a substorm dipolarization

Two examples of exact calculations of the adiabatic invariant for charged particle motion in non-uniform axisymmetric magnetic fields

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