# Материалы очередной ЦЕРНовской школы по ускорителям. На сей раз - компьютерные методы

CAS - CERN Accelerator School: Numerical Methods for Analysis, Design and Modelling of Particle Accelerators, 11-23 November 2018, Thessaloniki, Greece

Simulation of Particle-Material Interactions: https://arxiv.org/abs/2006.09866
Nikolai Mokhov
This paper gives an overview of the particle transport theory essentials, the basics of particle-material interaction simulation, physical quantities needed to simulate particle transport and interactions in materials, Monte Carlo simulation flow, response of additive detectors, statistical weights and other techniques to minimize statistical errors. Effects in materials under irradiation, materials response related to component lifetime and performance are considered with a focus on high-energy and high-power accelerator applications. Implementation of simulation of particle-material interactions in the modern Monte Carlo codes along with the code s main features and results of recent benchmarking are described.

Finite-Element Simulation of an Accelerator Magnet: an Exercise: https://arxiv.org/abs/2006.10463
H. De Gersem, I. Kulchytska-Ruchka, S. Schöps
This note describes an extended exercise on the finite-element (FE) simulation of an accelerator magnet. The students construct and simulate a magnet model using the FEMM freeware. They get the opportunity to exercise on the theory of FEs, including Maxwell equations, magnetoquasistatic formulation, weighted residual approach, choice of appropriate FE shape functions and algebraic system of equations, thereby guided by fill-in sheets. They are invited to implement the most crucial parts of a simple FE solver. Finally, the own software is used to simulate the magnet once more and to develop some problem-dedicated post-processing routines. The exercise educates students in accelerator physics and electrical engineering on the construction and simulation of accurate and manageable FE models, the algorithms behind a standard FE solver and some ideas to extend a FE solver for own purposes. All necessary files to carry out the exercise are freely available.

Dynamical Systems, Representation of Particle Beams: https://arxiv.org/abs/2006.14332
Alex Chao
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.

Monte Carlo Simulation Techniques: https://arxiv.org/abs/2006.10506
Ji Qiang
Monte Carlo simulations are widely used in many areas including particle accelerators. In this lecture, after a short introduction and reviewing of some statistical backgrounds, we will discuss methods such as direct inversion, rejection method, and Markov chain Monte Carlo to sample a probability distribution function, and methods for variance reduction to evaluate numerical integrals using the Monte Carlo simulation. We will also briefly introduce the quasi-Monte Carlo sampling at the end of this lecture.

Direct Vlasov solvers: https://arxiv.org/abs/2006.09080
Nicolas Mounet
In these proceedings we will describe the theory and practical steps required to build Vlasov solvers such as those commonly used to compute coherent instabilities in synchrotrons. Thanks to a Hamiltonian formalism, we will derive a compact and general form of the linearized Vlasov equation, written using Poisson brackets. This in turn will be the basis of a procedure to build Vlasov solvers, applied to the specific example of transverse instabilities arising from beam coupling impedance.

Measuring the Field Quality in Accelerator Magnets with the Oscillating-Wire Method -- a Case Study for Solving Partial Differential Equations: https://arxiv.org/abs/2006.09828
Stephan Russenschuck
The single stretched-wire method is commonly used to measure the magnetic field strength and magnetic axis in an accelerator magnet. The integrated voltage at the connection terminals of the wire is a measure for the flux linked with the surface traced out by the displaced wire. The stretched wire can also be excited with an alternating current well below the resonance frequency. It is thus possible to measure multipole field errors by making use of the linear relationship between the wire-oscillation amplitude, integrated field, and current amplitude. This technique is a good example for solving partial differential equations, or more precisely, boundary value problems in one and two dimensions. In particular, the field in the aperture of accelerator magnets is governed by the Laplace equation, which leads to a boundary-value problem that is solved by determining the coefficients in the series of eigenfunctions from measurements of the field components or wire-oscillation amplitudes on the domain boundary. The oscillation of the taut string is an example of a one-dimensional, in-homogenous wave equation. The metrological characterization of the oscillating-wire system yield the feedback on the uncertainties (and limitations) of the method, as only the linearized equations of the wire motion and the integrated field harmonics of the magnet are considered.

Simple Linear and Nonlinear Examples of Truncated Power Series Algebra: https://arxiv.org/abs/2006.09686
Étienne Forest
The paper displays calculations of linear systems as explained by Dr. Guido Sterbini. We also show a simple nonlinear calculation involving a rotation followed by an octupole kick. Some analytical calculations are compared to the Truncated Power Series Algebra (TPSA) results. The examples use the library PTC which is in MAD-X of CERN and BMAD of Cornell (see Ref. ).

Mathematical and Numerical Methods for Non-linear Beam Dynamics: https://arxiv.org/abs/2006.09052
Werner Herr
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 its analysis. This lecture is an introduction to the topic, shows some of the problems and presents several contemporary tools to treat them using a systematic and consistent approach.

Multi-Particle Simulation Techniques: https://arxiv.org/abs/2006.09057
Ji Qiang
The nonlinear space-charge effects play an important role in high intensity/high brightness accelerators. These effects can be self-consistently studied using multi-particle simulations. In this lecture, we will discuss the particle-in-cell method and the symplectic tracking model for self-consistent multi-particle simulations.

Introduction to Machine Learning for Accelerator Physics: https://arxiv.org/abs/2006.09913
Daniel Ratner
This pair of CAS lectures gives an introduction for accelerator physics students to the framework and terminology of machine learning (ML). We start by introducing the language of ML through a simple example of linear regression, including a probabilistic perspective to introduce the concepts of maximum likelihood estimation (MLE) and maximum a priori (MAP) estimation. We then apply the concepts to examples of neural networks and logistic regression. Next we introduce non-parametric models and the kernel method and give a brief introduction to two other machine learning paradigms, unsupervised and reinforcement learning. Finally we close with example applications of ML at a free-electron laser.

Imperfections and corrections: https://arxiv.org/abs/2006.10661
R. Tomás, X. Buffat, J. Coello, E. Fol, L. Malina
The measurement and correction of optics parameters has been a major concern since the advent of strong focusing synchrotron accelerators. A review of typical imperfections in accelerator optics together with measurement and correction algorithms is given with emphasis on numerical implementations. Python examples are shown using existing libraries when possible.

Computing techniques: https://arxiv.org/abs/2006.10664
X. Buffat
This lecture aims at providing a user's perspective on the main concepts used nowadays for the implementation of numerical algorithm on common computing architecture. In particular, the concepts and applications of Central Processing Units (CPUs), vectorisation, multithreading, hyperthreading and Graphical Processing Units (GPUs), as well as computer clusters and grid computing will be discussed. Few examples of source codes illustrating the usage of these technologies are provided.

Linear Optics Computations: https://arxiv.org/abs/2006.14340
Guido Sterbini
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 elements to write a linear optics code. To this aim, we complement the text with few practical examples and code listings.

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Его страхолюдную личинку я видел в жизни дважды, а его самого - сегодня впервые в жизни! Заметил случайно и снял кое-как: он весьма ловко и шустро…

• #### На морковке дикой я Марусю встретил...

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