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This lecture is a brief introduction to charged particle accelerators. The aim is to provide the reader with basic concepts and tools needed to describe the motion of charged particles under the action of guiding and focussing fields, with an emphasis on those aspects that are relevant to understanding and quantifying how accelerator vacuum systems affect accelerator performance. Even though the f

A basic training in VHDL with emphasis on FPGA implementation

Krein strings appear in the study of the motion of a vibrating string where an irregular density is allowed. This thesis presents the theory from the perspective of integral equations and operator theory. It will be shown that each Krein string gives rise to a unique Stieltjes function, by utilizing the compactness of the resolvent operators for short strings and then approximating any long string

The PYTHIA program is a standard tool for the generation of events in high-energy collisions, comprising a coherent set of physics models for the evolution from a few-body hard process to a complex multiparticle final state. It contains a library of hard processes, models for initial- and final-state parton showers, matching and merging methods between hard processes and parton showers, multiparto

In 2007, the European Commission (EC) commissioned a group of experts to undertake the revision of Report Radiation Protection (RP 91) oCriteria for acceptability of radiological (including radiotherapy) and nuclear medicine installations' written in 1997(( 1)). The revised draft report was submitted to the EC in 2010, who issued it for public consultation. The EC has commissioned the same group o

We establish the central convergence properties of ordinary Dirichlet series, including the classical result by Bohr, providing uniform convergence of the series where it has a bounded analytic continuation. We also derive a lower bound for the supremum of Dirichlet polynomials using Kronecker's theorem, of which we see one proof. With this knowledge and some probability theory we can follow t

This thesis aims to introduce the tools that are needed to understand — and historically led to the inception of — Hitchin systems. We lay out a basic theory of Hamiltonian systems on symplectic manifolds, and prove the Liouville-Arnold theorem, which states that integrable Hamiltonian systems admit coordinates in which their solution is basically linear. We then introduce a theory of holomorphic

This thesis introduces the theory of quasiconformal mappings on the plane. We give three different definitions of quasiconformal mappings: Differentiable quasiconformal map and two geometric definitions, one based on boundedness of the modulus of quadrilaterals and the other on ring domains. We also showcase when these definitions are equivalent. Then we prove that the geometric definition for qua