Related papers: Longitudinal Beam Dynamics -- Recap
Fluid dynamics corresponds to the dynamics of a substance in the long wavelength limit. Writing down all terms in a gradient (long wavelength) expansion up to second order for a relativistic system at vanishing charge density, one obtains…
First thoughts on the design of the beam vacuum system for the High Energy LHC (HE-LHC) are given with a particular focus on the impact of the synchrotron radiation. In the HE-LHC, the vacuum dynamic effects induced by the circulating beams…
This paper gives an overview of the beam injection and extraction principles for accelerators. After a brief general introduction, it explains different methods of injecting the beam for hadron and lepton machines. It describes single- and…
The design luminosity for the future linear colliders is very demanding and challenging. Beam-based feedback systems will be required to achieve the necessary beam-beam stability and steer the two beams into collision. In particular we have…
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…
We consider the motion of a particle on a surface which is a small perturbation of the standard sphere. One may qualitatively describe the motion by means of a precessing great circle of the sphere. The observation is employed to derive a…
This work addresses the Hamiltonian dynamics of the Kepler problem in a deformed phase space, by considering the equatorial orbit. The recursion operators are constructed and used to compute the integrals of motion. The same investigation…
The rarely used Hamilton-Jacobi equation has been utilized as an elegant way to find the trajectories of mechanical systems and to derive symplectic maps. Further, the exact solution in kick approximation of Hamilton's equations of motion…
The performance of various systems of the Next Linear Collider (NLC) have been studied in terms of ground motion using recently developed models. In particular, the performance of the beam delivery system is discussed. Plans to evaluate the…
Hamilton's equations of motion are local differential equations and boundary conditions are required to determine the solution uniquely. Depending on the choice of boundary conditions, a Hamiltonian may thereby describe several different…
The constants of motion of the following systems are deduced: a relativistic particle with linear dissipation, a no-relativistic particle with a time explicitly depending force, a no-relativistic particle with a constant force and time…
We introduce a practical approach to extract the symplectic transfer maps for arbitrary magnetic beam-line elements. Beam motion in particle accelerators depends on linear and nonlinear magnetic fields of the beam-line elements. These…
We briefly go through the problem of the quantum description of Brownian motion, concentrating on recent results about the connection between dynamics of the particle and dynamic structure factor of the medium.
A general formalism for obtaining the Lagrangian and Hamiltonian for a one dimensional dissipative system is developed. The formalism is illustrated by applying it to the case of a relativistic particle with linear dissipation. The…
A techniques, describing electron dynamics for magnetic models closed to cyclical accelerators, is developed and applied to the analysis of electromagnetic radiation emitted by charged particles. Formulas for the angular characteristics of…
This lecture provides an overview of the principles and methodologies involved in linear optics design. It aims to introduce key concepts such as the matrix formalism, the symplecticity, the quantities that are preserved in the single…
Axial-symmetric magnetic field is often used in focusing of particle beams. Most existing ion Low Energy Beam Transport lines are based on solenoid focusing. Modern accelerator projects utilize superconducting solenoids in combination with…
This lecture introduces major physics and technology aspects of accelerator vacuum systems. Following an introduction, in the second section generic vacuum quantities such as pressure, gas density, the gas equation, pumping speed,…
Transverse breathing mode oscillations in a particle beam can couple energy into longitudinal oscillations in a bunch of finite length and cause significant losses. We develop a model that illustrates this effect and explore the dependence…
The challenges in beam instrumentation and diagnostics for present and future particle accelerator projects are presented. A few examples for advanced hadron and lepton beam diagnostics are given.