Related papers: Jacobi equations and particle accelerator beam dyn…
We discuss and compare several geometric structures which imply an upper bound to the acceleration of a particle measured in its rest system. While all of them have the same implications on the motion of a point particle, they differ in…
A geometric approach to integrability and reduction of dynamical system is developed from a modern perspective. The main ingredients in such analysis are the infinitesimal symmetries and the tensor fields that are invariant under the given…
The performance and safe operation of a particle accelerator is closely connected to the transverse emittance of the beams it produces. For this reason many techniques have been developed over the years for monitoring the transverse…
An overview of dynamical systems in accelerator physics is presented with a suggestion of a few issues to be addressed. Also mentioned are a few possible developments in the future. Technical details supporting the views are not presented.
The generalized Jacobi equation is a differential equation in local coordinates that describes the behavior of infinitesimally close geodesics with an arbitrary relative velocity. In this note we study some transformation properties for…
Transformation rules for coordinates, velocities and accelerations in accelerated reference frames are derived. A generalized approach of the special relativity is taken for a basis. A 7-dimensional space including projections of velocity…
Coupled wave equations are popular tool for investigating longitudinal dynamical effects in semiconductor lasers, for example, sensitivity to delayed optical feedback. We study a model that consists of a hyperbolic linear system of partial…
The main features of radio-frequency linear accelerators are introduced, reviewing the different types of accelerating structures and presenting the main characteristics aspects of linac beam dynamics.
It is shown that any dynamic equation on a configuration bundle $Q\to R$ of non-relativistic time-dependent mechanics is associated with connections on the affine jet bundle $J^1Q\to Q$ and on the tangent bundle $TQ\to Q$. As a consequence,…
A representation is put forward for wave functions of quantum particles in periodic lattice potentials subjected to homogeneous time-periodic forcing, based on an expansion with respect to Bloch-like states which embody both the spatial and…
We construct a generalized dynamics for particles moving in a symmetric space-time, i.e. a space-time admitting one or more Killing vectors. The generalization implies that the effective mass of particles becomes dynamical. We apply this…
In this work we revisit the geometric approach to chaos in Hamiltonian dynamics, by means of the Jacobi-Levi-Civita equation (JLCE). We inspect numerically two low-dimensional dynamical systems; show that, along chaotic orbits, the…
The standard text-book Jacobi equation (equation of geodesic deviation) arises by linearizing the geodesic equation around some chosen geodesic, where the linearization is done with respect to the coordinates and the velocities. The…
The interaction of a charged particle beam with radio-frequency (RF) systems in most linear or circular accelerators is an non-linear process. The large longitudinal electric fields for acceleration and longitudinal beam manipulations can…
A new particle acceleration process in a developing Alfv\'{e}n turbulence in the course of successive parametric instabilities of a relativistic pair plasma is investigated by utilyzing one-dimensional electromagnetic full particle code.…
It is generally accepted that the dynamics of relativistic particles in the lab frame can be described by taking into account the relativistic dependence of the particles momenta on the velocity, with no reference to Lorentz…
The generalization of the Maupertuis principle to second-order Variational Calculus is performed. The stability of the solutions of a natural dynamical system is thus analyzed via the extension of the Theorem of Jacobi. It is shown that the…
We consider the Lorenz equations, a system of three dimensional ordinary differential equations modeling atmospheric convection. These equations are chaotic and hard to study even numerically, and so a simpler "geometric model" has been…
The study of reflector surfaces in geometric optics necessitates the analysis of certain nonlinear equations of Monge-Amp\`ere type known as generated Jacobian equations. These equations, whose general existence theory has been recently…
The dynamics and radiation of ultrarelativistic electrons in strong counterpropagating laser beams are investigated. Assuming that the particle energy is the dominant scale in the problem, an approximate solution of classical equations of…