Related papers: Complex formalism of the linear beam dynamics
The subject of this introductory course is transverse dynamics of charged particle beams in linear approximation. Starting with a discussion of the most important types of magnets and defining their multipole strengths, the linearized…
A novel technique to determine invariant curves in nonlinear beam dynamics based on the method of formal series has been developed. It is first shown how the solution of the Hamilton equations of motion describing nonlinear betatron…
The definitions and some basic properties of the linear transports along paths in vector bundles and the normal frames for them are recalled. The formalism is specified on line bundles and applied to a geometrical description of the…
The goal of this contribution is to introduce the Hamiltonian formalism of theoretical mechanics for analysing motion in generic linear and non-linear dynamical systems, including particle accelerators. This framework allows the derivation…
We formalise the teleparallel version of extended geometry (including gravity) by the introduction of a complex, the differential of which provides the linearised dynamics. The main point is the natural replacement of the two-derivative…
Using a two-dimensional fluid description, we investigate the nonlinear radial-longitudinal dynamics of intense beams in storage rings and cyclotrons. With a multiscale analysis separating the time scale associated with the betatron motion…
In this paper, we study transport features of a one-dimensional beam-plasma system in the presence of multiple resonances. As a model description of the general problem of a warm energetic particle beam, we assume $n$ cold supra-thermal…
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…
We describe a generalized formalism, addressing the fundamental problem of reflection and transmission of complex optical waves at a plane dielectric interface. Our formalism involves the application of generalized operator matrices to the…
Presenting systems of differential equations in the form of diagrams has become common in certain parts of physics, especially electromagnetism and computational physics. In this work, we aim to put such use of diagrams on a firm…
The control of structured waves has recently opened innovative scenarios in the perspective of radiation propagation and light-matter interaction. In particular, the transmission of customized electromagnetic fields is investigated for…
While linear systems are well-understood, no explicit solution for general nonlinear systems exists. A classical approach to make the understanding of linear system available in the nonlinear setting is to represent a nonlinear system by a…
General formalism for describing dynamics of modulated beams along linear beamlines is developed. We describe modulated beams with spectral distribution function which represents Fourier transform of the conventional beam distribution…
Besides being one of the most fundamental basic issues of plasma physics, the stability analysis of an electron beam-plasma system is of critical relevance in many areas of physics. Surprisingly, decades of extensive investigation had not…
An analysis of classical mechanics in a complex extension of phase space shows that a particle in such a space can behave in a way redolant of quantum mechanics; additional degrees of freedom permit 'tunnelling' without recourse to…
These are notes for the lecture on Transport Theory in a one-week intensive course, "Techniques of Proton Radiotherapy". Topics are: Phase space diagrams: model beam line-effect of a scatterer-effect of a drift-the beam ellipse-phase space…
We describe theoretically the process of multi-beam reflection in a two-dimensional electron system with a lateral potential barrier. Due to spin-orbital interaction, the reflection process leads to the formation of three beams with…
The recently proposed effective potential theory [Phys. Rev. Lett. 110, 235001 (2013)] allows evaluating transport in coupled plasmas with the well-developed formalisms for systems with binary collisions. To facilitate practical…
The propagation of stable coherent entities of an electromagnetic field in nonlinear media with parameters varying in space can be described in the framework of iterations of nonlinear integral transformations. It is shown that for a set of…
In the first part of this paper, we introduce the notion of "cyclic stratum" of a Frobenius manifold $M$. This is the set of points of the extended manifold $\mathbb C^*\times M$ at which the unit vector field is a cyclic vector for the…