Related papers: Longitudinal Beam Dynamics -- Recap
We present the basic formulation of Hamilton dynamics in complex phase space. We extend the Hamilton's function by including the imaginary part and find out the corresponding Hamilton's canonical equation of motion. Example of simple…
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…
We determine the phase portrait of a Hamiltonian system of equations describing the motion of the particles in linear deep-water waves. The particles experience in each period a forward drift which decreases with greater depth.
In this lecture we discuss the intensity limitations in hadron LINACs. First, we will detail what are the two main meanings of intensity limitations as they differ substantially between high power LINACs and high brightness LINACs. Then we…
We study the longitudinal motion of beam particles under the action of a single resonator wave induced by the beam itself. Based on the method of multiple scales we derive a system of coupled amplitude equations for the slowly varying part…
To study the characteristics of synchrotron radiation in magnetic fields of accelerators first the author was necessary to obtain a continuous solutions of Hill's equation. For this purpose the gradient or the components of magnetic field…
The dynamics of several light filaments (spatial optical solitons) propagating in an optically nonlinear and non-local random medium is investigated using the paradigms of the physics of complexity. Cluster formation is interpreted as a…
This paper describes the beam dynamic simulation with transfer matrix method for cyclotron. Starting from a description on the equation of motion in the cyclotron, lattice functions were determined from transfer matrix method and the…
The investigation of single-particle dynamics in circular particle accelerators can be traced back to pioneering works in the 1950s. Traditionally, the design of new circular accelerators has focused on optimising linear dynamics, striving…
This paper reviews the important physical and technological aspects of cyclotrons for the acceleration of high-intensity beams. Special emphasis is given to the discussion of beam loss mechanisms and extraction schemes.
When a charged particle travels across the vacuum chamber of an accelerator, it induces electromagnetic fields, which are left mainly behind the generating particle. These electromagnetic fields act back on the beam and influence its…
The low-level RF system (LLRF) generates the drive sent to the high-power equipment. In synchrotrons, it uses signals from beam pick-ups (radial and longitudinal) to minimize the beam losses and provide a beam with reproducible parameters…
We report the discovery of an envelope Hamiltonian describing the charged-particle dynamics in general linear coupled lattices.
One of the most severe limitations in particle accelerators and beam transport are non-linear effects. Techniques to study and possibly suppress some of these detrimental effects exist, the most popular are based on particle tracking and…
It has long been known that the ellipse normally used to model the phase space extension of a beam in linear dynamics may be represented by a complex number which can be interpreted similarly to a complex impedance in electrical circuits,…
Motivated by the desire to understand the longitudinal effects of beam-beam forces, we study the longitudinal dynamics of protons and anti-protons at injection and top energy in the Tevatron. Multi-turn data of the longitudinal profiles are…
Motion of an ensemble of particles in a space-periodic potential well with a weak wave-like perturbation imposed is considered. We found that slow oscillations of wavenumber of the perturbation lead to occurrence of directed particle…
The goal of this manuscript is to give an introduction into the design of the magnet lattice and as a consequence into the transverse dynamics of the particles in a synchrotron or storage ring. Starting from the basic principles of how to…
Kinetic approaches provide an effective description of the process of particle acceleration at shock fronts and allow to take into account the dynamical reaction of the accelerated particles as well as the amplification of the turbulent…
The operation of high-energy and high-intensity particle accelerators inevitably leads to the loss of a fraction of beam particles, either through controlled processes or accidental events. This article builds on a first lecture on…