A general study of charged particles dynamics near magnetic planets

In this paper, the effect of time is explored on the dynamics of neutral and charged particles around the Schwarzschild (Sch) black hole (BH) environed by quintessence. We introduce a general time conformal factor [Formula: see text] to the quintessential Sch spacetime, where [Formula: see text] is a time ([Formula: see text])-dependent function and [Formula: see text], a small parameter, that causes perturbation in the corresponding spacetime. The Noether symmetry equation is obtained with the help of Lagrangian corresponding to time conformal Sch spacetime environed by quintessence. Consequently, we get a 19 partial differential equations (PDEs) system. The solution of this system gives Noether symmetries, Noether approximate symmetries, and the corresponding conservation laws. The dynamics of neutral/charged particles are studied as well as graphically analyzed at the foot of these invariants.

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Application of Lie Algebra in Constructing Volume-Preserving Algorithms for Charged Particles Dynamics

Communications in Computational Physics ◽

10.4208/cicp.scpde14.33s ◽

2016 ◽

Vol 19 (5) ◽

pp. 1397-1408 ◽

Cited By ~ 1

Author(s):

Ruili Zhang ◽

Jian Liu ◽

Hong Qin ◽

Yifa Tang ◽

Yang He ◽

...

Keyword(s):

Phase Space ◽

Lie Algebra ◽

Charged Particles ◽

Second Order ◽

Algebra Structure ◽

Phase Space Volume ◽

Volume Preserving ◽

Particles Dynamics ◽

Space Volume

AbstractVolume-preserving algorithms (VPAs) for the charged particles dynamics is preferred because of their long-term accuracy and conservativeness for phase space volume. Lie algebra and the Baker-Campbell-Hausdorff (BCH) formula can be used as a fundamental theoretical tool to construct VPAs. Using the Lie algebra structure of vector fields, we split the volume-preserving vector field for charged particle dynamics into three volume-preserving parts (sub-algebras), and find the corresponding Lie subgroups. Proper combinations of these subgroups generate volume preserving, second order approximations of the original solution group, and thus second order VPAs. The developed VPAs also show their significant effectiveness in conserving phase-space volume exactly and bounding energy error over long-term simulations.

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The Jovian ring

International Astronomical Union Colloquium ◽

10.1017/s0252921100101174 ◽

1984 ◽

Vol 75 ◽

pp. 203-209

Author(s):

Joseph A. Burns

Keyword(s):

Equatorial Plane ◽

Charged Particles ◽

Dynamical Evolution ◽

Main Band ◽

Small Grains ◽

Three Components

ABSTRACTLying in Jupiter's equatorial plane is a diaphanous ring having little substructure within its three components (main band, faint disk, and halo). Micron-sized grains account for much of the visible ring, but particles of centimeter sizes and larger must also be present to absorb charged particles. Since dynamical evolution times and survival life times are quite short (≲102-3yr) for small grains, the Jovian ring is being continually replenished; probably most of the visible ring is generated by micrometeoroids colliding into unseen parent bodies that reside in the main band.

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Atomic orientation effects in proton stopping at low velocity

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100077116 ◽

1983 ◽

Vol 41 ◽

pp. 708-709

Author(s):

Kin Lam

Keyword(s):

Polycrystalline Material ◽

Charged Particles ◽

Target Material ◽

Stopping Power ◽

Low Velocity ◽

Electronic Density ◽

Interatomic Distances ◽

Frame Work ◽

Image Position ◽

Atomic Orientation

The energy of moving ions in solid is dependent on the electronic density as well as the atomic structural properties of the target material. These factors contribute to the observable effects in polycrystalline material using the scanning ion microscope. Here we outline a method to investigate the dependence of low velocity proton stopping on interatomic distances and orientations.The interaction of charged particles with atoms in the frame work of the Fermi gas model was proposed by Lindhard. For a system of atoms, the electronic Lindhard stopping power can be generalized to the formwhere the stopping power function is defined as

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Inelastic scattering at surfaces and interfaces

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100143560 ◽

1986 ◽

Vol 44 ◽

pp. 392-393

Author(s):

R. H. Ritchie ◽

A. Howie

Keyword(s):

Inelastic Scattering ◽

Surface Properties ◽

Correlation Energy ◽

Condensed Matter ◽

Charged Particles ◽

Condensed Matter Physics ◽

Optical Phonons ◽

Exchange Correlation ◽

Surfaces And Interfaces ◽

Inelastic Interactions

An important part of condensed matter physics in recent years has involved detailed study of inelastic interactions between swift electrons and condensed matter surfaces. Here we will review some aspects of such interactions.Surface excitations have long been recognized as dominant in determining the exchange-correlation energy of charged particles outside the surface. Properties of surface and bulk polaritons, plasmons and optical phonons in plane-bounded and spherical systems will be discussed from the viewpoint of semiclassical and quantal dielectric theory. Plasmons at interfaces between dissimilar dielectrics and in superlattice configurations will also be considered.

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