Related papers: Mathematical and Numerical Methods for Non-linear …
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…
Nonlinear effects in emission and absorption spectra of gaseous systems are considered. It is shown that level splitting can be detected spectroscopically even if it is below the Doppler width. Conditions for distinguishing interference…
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.
Particle acceleration at astrophysical shocks may be very efficient if magnetic scattering is self-generated by the same particles. This nonlinear process adds to the nonlinear modification of the shock due to the dynamical reaction of the…
We provide a both qualitative and quantitative comparison among different approaches aimed to solve the problem of non-linear diffusive acceleration of particles at shocks. In particular, we show that state-of-the-art models (numerical,…
The interaction of the two beams in a collider leads to a variety of effects that may limit the performance of the machine. This lecture introduces the basic aspects necessary to understand the design of modern colliders.
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.
One of the most severe limitations in high-intensity particle colliders is the beam-beam interaction, i.e. the perturbation of the beams as they cross the opposing beams. This introduction to beam-beam effects concentrates on a description…
A fundamental problem in plasma physics, space science, and astrophysics is the transport of energetic particles interacting with stochastic magnetic fields. In particular the motion of particles across a large scale magnetic field is…
The limits of linear electrodynamics are reviewed, and possible directions of nonlinear extension are explored. The central theme is that the qualitative character of the empirical successes of quantum electrodynamics must be used as a…
In this contribution we will discuss the non-linear effects in the baryon acoustic oscillations and present a systematic and controllable way to account for them within time-sliced perturbation theory.
We discuss some common misconceptions in Unruh effect and Unruh radiation for the cases of linear and circular uniform acceleration of a charged particle or detector moving in a quantum field. We point to the need to go beyond Unruh effect…
Approximate dynamic programming has been investigated and used as a method to approximately solve optimal regulation problems. However, the extension of this technique to optimal tracking problems for continuous time nonlinear systems has…
Of the tens of thousands of particle accelerators in operation worldwide, the vast majority are not used for particle physics, but instead for applications. Some applications such as radiotherapy for cancer treatment are well-known, while…
When a beam propagates in an accelerator, it interacts with both the external fields and the self-generated electromagnetic fields. If the latter are strong enough, the interplay between them and a perturbation in the beam distribution…
A brief review is given of topics relating to dynamical processes arising in nonlinear interactions between light and resonant systems (atoms or molecules) in the presence of a magnetic field.
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…
This Chapter contains an overview of the effects of nonlinear interactions in selected problems of non-equilibrium statistical mechanics. Most of the emphasis is put on open setups, where energy is exchanged with the environment. With…
Fully describing light propagation in a rotating, anisotropic medium with thermal nonlinearity requires modeling the interplay between nonlinear refraction, birefringence, and the nonlinear group index. Incorporating these factors into a…
The consideration of dynamics of relativistic beams/particles is based on variational approach to rational (in dynamical variables) approximation for equations of motions. It allows to control contribution from each scale of underlying…