Lecture

Linear Dynamics: Hamiltonians and Machine Elements

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In course

PHYS-751: Advanced concepts in particle accelerators

Accelerator physics covers a wide range of very exciting topics. This course presents basic physics ideas and the technologies underlying the workings of modern accelerators. An overview of the new ideas and challenges of the possible paths towards the nex ...

Description

This lecture covers the formulation of Hamiltonians for machine elements in 3D, focusing on multipoles of different orders. It explains the Hamiltonians for drift space, dipole, quadrupole, and sextupole magnets, emphasizing the paraxial approximation for linear maps. The lecture also discusses the matrix representation of linear maps, particle motion in phase space, and the concept of thin lens approximation for focusing. Furthermore, it explores the construction of FODO lattice configurations, stability conditions, and the transfer matrix approach for beamline calculations.

Instructors (3)

Tatiana Pieloni

Expertise Beam dynamics in accelerators.Colliders luminosity and beam-beam interactions.Collective effects. Teaching & PhD PhD Students Yi Wu, Lode Vanhecke Past EPFL PhD Students as codirector Xavier Buffat, Claudia Tambasco Courses Advanced concepts in particle accelerators PHYS-751 Accelerator physics covers a wide range of very exciting topics. This course presents basic physics ideas and the technologies underlying the workings of modern accelerators. An overview of the new ideas and

Rasmus Ischebeck

Teaching & PhD PhD Students Maria Paula Rey Barrera, Raziyeh Dadashi Motlagh, Evan James Ericson Past EPFL PhD Students as codirector Bennie Smit, Ishkhan Gorgisyan

Werner Friedrich Herr

Teaching & PhD Courses Advanced concepts in particle accelerators PHYS-751 Accelerator physics covers a wide range of very exciting topics. This course presents basic physics ideas and the technologies underlying the workings of modern accelerators. An overview of the new ideas and challenges of the possible paths towards the next generation of accelerators will be given.

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Related concepts (32)

Storage ring

A storage ring is a type of circular particle accelerator in which a continuous or pulsed particle beam may be kept circulating typically for many hours. Storage of a particular particle depends upon the mass, momentum and usually the charge of the particle to be stored. Storage rings most commonly store electrons, positrons, or protons. Storage rings are most often used to store electrons that radiate synchrotron radiation. Over 50 facilities based on electron storage rings exist and are used for a variety of studies in chemistry and biology.

Machine

A machine is a physical system using power to apply forces and control movement to perform an action. The term is commonly applied to artificial devices, such as those employing engines or motors, but also to natural biological macromolecules, such as molecular machines. Machines can be driven by animals and people, by natural forces such as wind and water, and by chemical, thermal, or electrical power, and include a system of mechanisms that shape the actuator input to achieve a specific application of output forces and movement.

Thin lens

In optics, a thin lens is a lens with a thickness (distance along the optical axis between the two surfaces of the lens) that is negligible compared to the radii of curvature of the lens surfaces. Lenses whose thickness is not negligible are sometimes called thick lenses. The thin lens approximation ignores optical effects due to the thickness of lenses and simplifies ray tracing calculations. It is often combined with the paraxial approximation in techniques such as ray transfer matrix analysis.

Simple machine

A simple machine is a mechanical device that changes the direction or magnitude of a force. In general, they can be defined as the simplest mechanisms that use mechanical advantage (also called leverage) to multiply force. Usually the term refers to the six classical simple machines that were defined by Renaissance scientists: Lever Wheel and axle Pulley Inclined plane Wedge Screw A simple machine uses a single applied force to do work against a single load force.

Machine element

Machine element or hardware refers to an elementary component of a machine. These elements consist of three basic types: structural components such as frame members, bearings, axles, splines, fasteners, seals, and lubricants, mechanisms that control movement in various ways such as gear trains, belt or chain drives, linkages, cam and follower systems, including brakes and clutches, and control components such as buttons, switches, indicators, sensors, actuators and computer controllers.

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