Successive approximations for charged particle motion

Successive approximations for charged particle motion

Single-particle dynamics in electron microscopes, ion or electron lithographic instruments, particle accelerators, and particle spectrographs is described by weakly nonlinear ordinary differential equations. Therefore, the linear part of the equation of motion is usually solved and the nonlinear effects are then found in successive order by iteration methods. When synchrotron radiation is not i...

Three-body equations of motion in successive post-newtonian approximations

Motion of a Classical Charged Particle Physical

1550-7998=20 The Lorentz-Dirac equation is not an unavoidable consequence of solely linear and angular momenta conservation for a point charge. It also requires an additional assumption concerning the elementary character of the charge. We here use a less restrictive elementarity assumption for a spinless charge and derive a system of conservation equations that are not properly the equation of...

2 Noether symmetries for two - dimensional charged particle motion

We find the Noether point symmetries for non–relativistic two-dimensional charged particle motion. These symmetries are composed of a quasi–invariance transformation, a time–dependent rotation and a time–dependent spatial translation. The associated electromagnetic field satisfy a system of first–order linear partial differential equations. This system is solved exactly, yielding three classes ...

2 Lie symmetries for two - dimensional charged particle motion

We find the Lie point symmetries for non–relativistic two-dimensional charged particle motion. These symmetries comprise a quasi–inva-riance transformation, a time–dependent rotation, a time–dependent spatial translation and a dilatation. The associated electromagnetic fields satisfy a system of first–order linear partial differential equations. This system is solved exactly, yielding four clas...