Lecture

Recap from classical mechanics and accelerator physics

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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 recap of classical mechanics and accelerator physics, focusing on topics such as relative transverse coordinates, canonical conjugate momenta, action and angle variables, beam size, emittance, divergence, and correlation.

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.

Official source

Related concepts (32)

Action-angle coordinates

In classical mechanics, action-angle variables are a set of canonical coordinates that are useful in characterizing the nature of commuting flows in integrable systems when the conserved energy level set is compact, and the commuting flows are complete. Action-angle variables are also important in obtaining the frequencies of oscillatory or rotational motion without solving the equations of motion. They only exist, providing a key characterization of the dynamics, when the system is completely integrable, i.

Canonical coordinates

In mathematics and classical mechanics, canonical coordinates are sets of coordinates on phase space which can be used to describe a physical system at any given point in time. Canonical coordinates are used in the Hamiltonian formulation of classical mechanics. A closely related concept also appears in quantum mechanics; see the Stone–von Neumann theorem and canonical commutation relations for details.

Analytical mechanics

In theoretical physics and mathematical physics, analytical mechanics, or theoretical mechanics is a collection of closely related alternative formulations of classical mechanics. It was developed by many scientists and mathematicians during the 18th century and onward, after Newtonian mechanics. Since Newtonian mechanics considers vector quantities of motion, particularly accelerations, momenta, forces, of the constituents of the system, an alternative name for the mechanics governed by Newton's laws and Euler's laws is vectorial mechanics.

Classical mechanics

Classical mechanics is a physical theory describing the motion of macroscopic objects, from projectiles to parts of machinery and astronomical objects, such as spacecraft, planets, stars, and galaxies. For objects governed by classical mechanics, if the present state is known, it is possible to predict how it will move in the future (determinism), and how it has moved in the past (reversibility). The "classical" in "classical mechanics" does not refer classical antiquity, as it might in, say, classical architecture.

Canonical transformation

In Hamiltonian mechanics, a canonical transformation is a change of canonical coordinates (q, p, t) → (Q, P, t) that preserves the form of Hamilton's equations. This is sometimes known as form invariance. It need not preserve the form of the Hamiltonian itself. Canonical transformations are useful in their own right, and also form the basis for the Hamilton–Jacobi equations (a useful method for calculating conserved quantities) and Liouville's theorem (itself the basis for classical statistical mechanics).

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