Related papers: Jacobi equations and particle accelerator beam dyn…
The Jacobi equation in pseudo-Riemannian geometry determines the linearized geodesic flow. The linearization ignores the relative velocity of the geodesics. The generalized Jacobi equation takes the relative velocity into account; that is,…
An interpretation of the formation of halo in accelerators based on quantum-like theory by a diffraction model is given in terms of the transversal beam motion. Physical implications of the longitudinal dynamics are also examined.
An explicit expression for the Jacobi metric for a general Lagrangian system is obtained as a series expansion in the square root of the kinetic energy of the system and the corresponding geodesics are described in terms of an appropriate…
Non-linear effects in accelerator physics are important for both successful operation of accelerators and during the design stage. Since both of these aspects are closely related, they will be treated together in this overview. Some of the…
The Lorentz transformations are represented by Einstein velocity addition on the ball of relativistically admissible velocities. This representation is by projective maps. The Lie algebra of this representation defines the relativistic…
This paper gives a very brief summary of longitudinal beam dynamics for both linear and circular accelerators. After discussing synchronism conditions in linacs, it focuses on particle motion in synchrotrons. It summarizes the equations of…
In this Chapter we briefly recall and summarize the main linear optics concepts of the accelerators beam dynamics theory. In doing so we put our emphasis on the related computational aspects: the reader will be provided with the basic…
This paper gives an introduction of longitudinal beam dynamics for circular accelerators. After briefly discussing some types of circular accelerators, it focuses on particle motion in synchrotrons. It summarizes the equations of motion,…
Both the physical picture of the dynamics of atoms and molecules in intense infrared fields and its theoretical description use the concept of electron trajectories. Here we address a key question which arises in this context: Are…
In this article, we investigate the transverse dynamics of a single particle in a model integrable accelerator lattice, based on a McMillan axially-symmetric electron lens. Although the McMillan e-lens has been considered as a device…
General covariant expressions for measurable angles, distances, velocities, and accelerations are provided in terms of fundamental parameters that can be applied in any setup. The relativistic aberration of light relationship is presented…
In this paper we discuss design considerations and beam dynamics challenges associated with laser-driven plasma-based accelerators as applied to multi-TeV-scale linear colliders. Plasma accelerators provide ultra-high gradients and…
Constraints imposed directly on accelerations of the system leading to the relation of constants of motion with appropriate local projectors occurring in the derived equations are considered. In this way a generalization of the Noether's…
This chapter gives an overview of the longitudinal dynamics of the particles in an accelerator and, closely related to that, the issue of synchronization between the particles and the accelerating field. Beginning with the trivial case of…
A geometric theory for spacetimes whose world lines associated with physical particles have an upper bound for the proper acceleration is developed. After some fundamental remarks on the requirements that the classical dynamics for point…
An exact solution of the Maxwell equations in Rindler coordinates is obtained. The electromagnetic field represents a wave preserving its shape in a relativistic uniformly accelerated frame. The relation with Airy beams is shown explicitly…
In this series of eight papers we present the applications of methods from wavelet analysis to polynomial approximations for a number of accelerator physics problems. In this part we consider orbital motion in transverse plane for a single…
An interpretation of the formation of halo in accelerators based on quantum-like theory by a diffraction model is given in terms of the transversal beam motion. Physical implications of the longitudinal dynamics are also examined
Different (not only by sign) affine connections are introduced for contravariant and covariant tensor fields over a differentiable manifold by means of a non-canonical contraction operator, defining the notion dual bases and commuting with…
The course gives a summary of longitudinal beam dynamics for both linear and circular accelerators. After discussing different types of acceleration methods and synchronism conditions, it focuses on the particle motion in synchrotrons.