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Lecture

Linear Beam Dynamics

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 basics of particle accelerators, focusing on the dynamics of charged particle beams in electromagnetic fields. Topics include transfer maps, Hamiltonian equations, symplecticity, and the conservation of phase space. The instructor explains how to compute maps for beamline elements, the importance of canonical transformations, and the use of electric and magnetic fields in particle acceleration.

Instructors (3)

Werner Friedrich Herr

Tatiana Pieloni

Rasmus Ischebeck

Official source

Related concepts (32)

Particle beam

A particle beam is a stream of charged or neutral particles. In particle accelerators, these particles can move with a velocity close to the speed of light. There is a difference between the creation and control of charged particle beams and neutral particle beams, as only the first type can be manipulated to a sufficient extent by devices based on electromagnetism. The manipulation and diagnostics of charged particle beams at high kinetic energies using particle accelerators are main topics of accelerator physics.

Accelerator physics

Accelerator physics is a branch of applied physics, concerned with designing, building and operating particle accelerators. As such, it can be described as the study of motion, manipulation and observation of relativistic charged particle beams and their interaction with accelerator structures by electromagnetic fields. It is also related to other fields: Microwave engineering (for acceleration/deflection structures in the radio frequency range). Optics with an emphasis on geometrical optics (beam focusing and bending) and laser physics (laser-particle interaction).

Particle accelerator

A particle accelerator is a machine that uses electromagnetic fields to propel charged particles to very high speeds and energies, and to contain them in well-defined beams. Large accelerators are used for fundamental research in particle physics. The largest accelerator currently active is the Large Hadron Collider (LHC) near Geneva, Switzerland, operated by the CERN. It is a collider accelerator, which can accelerate two beams of protons to an energy of 6.5 TeV and cause them to collide head-on, creating center-of-mass energies of 13 TeV.

Linear particle accelerator

A linear particle accelerator (often shortened to linac) is a type of particle accelerator that accelerates charged subatomic particles or ions to a high speed by subjecting them to a series of oscillating electric potentials along a linear beamline. The principles for such machines were proposed by Gustav Ising in 1924, while the first machine that worked was constructed by Rolf Widerøe in 1928 at the RWTH Aachen University.

Electromagnetic tensor

In electromagnetism, the electromagnetic tensor or electromagnetic field tensor (sometimes called the field strength tensor, Faraday tensor or Maxwell bivector) is a mathematical object that describes the electromagnetic field in spacetime. The field tensor was first used after the four-dimensional tensor formulation of special relativity was introduced by Hermann Minkowski. The tensor allows related physical laws to be written very concisely, and allows for the quantization of the electromagnetic field by Lagrangian formulation described below.

Related lectures (31)

Interaction with External Electromagnetic Field

Explores classical and quantum physics concepts related to the interaction with an external electromagnetic field.

Particle in EM Field

Explores the interaction of particles with external electromagnetic fields and the quantum behavior in magnetic fields.

Non-linear dynamics

Explores practical applications in nonlinear dynamics, emphasizing symplectic integration methods and thin lens approximations for accurate computations in accelerator physics.

Collective Effects: Basics and Mitigation

Explores collective effects in accelerators, discussing instabilities, mitigation techniques, and impedance reduction.

Non-linear dynamics: phenomenology, tools and methods