Related Experiment Video
Updated: Apr 25, 2026

Finite Element Modelling of a Cellular Electric Microenvironment
Published on: May 18, 2021
Generalized Courant-Snyder theory for charged-particle dynamics in general focusing lattices
Hong Qin1, Ronald C Davidson2, Moses Chung3
1Plasma Physics Laboratory, Princeton University, Princeton, New Jersey 08543, USA and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China.
Abstract:
The Courant-Snyder (CS) theory for one degree of freedom is generalized to the case of coupled transverse dynamics in general linear focusing lattices with quadrupole, skew-quadrupole, dipole, and solenoidal components, as well as torsion of the fiducial orbit and variation of beam energy. The envelope function is generalized into an envelope matrix, and the phase advance is generalized into a 4D sympletic rotation. The envelope equation, the transfer matrix, and the CS invariant of the original CS theory all have their counterparts, with remarkably similar expressions, in the generalized theory.
More Related Videos
08:54Vibrational Spectra of a N719-Chromophore/Titania Interface from Empirical-Potential Molecular-Dynamics Simulation, Solvated by a Room Temperature Ionic Liquid
Published on: January 25, 2020
11:03An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
Related Concept Videos
Motion Of A Charged Particle In A Magnetic Field
The de Broglie Wavelength
Energy Associated With a Charge Distribution
Electric Field of a Non Uniformly Charged Sphere
Consider a non-uniformly charged sphere, for which the density of charge depends only on the distance from a point in space and not on the direction. Such a sphere has a spherically symmetrical charge distribution. Here, the electric...
Electric Field of a Charged Disk
The system's symmetry is in the cylindrical directions across the plane of the charge. As a result, the electric fields created by various surface charge elements nullify each other in the direction parallel to the surface. Thereby, the resulting electric field is perpendicular to the plane. Since the disk is...
Continuous Charge Distributions
The electric charge can also be subjected to an analogical...