Cartoon of electron-beam phase-space emittance

This animation creates a cartoon of the relationship between real- and phase-space in representing the emittance of an electron beam. The lefthand side shows an ensemble of noninteracting electrons passing through a focal minimum in real space. On the right, the same beam is represented in phase space (abscissa: position, ordinate: angle) as the sampling semitransparent bar moves over the real-space representation on the left. Note that the angles never change (as the electrons are assumed to be noninteracting), while the position away from the propagating axis changes according to the position relative to the minimum focus. As a result, the ensemble in phase space transforms from a skewed ellipse in one direction, through a symmetric ellipse, to an ellipse skewed in the opposite direction. The area of the ellipse remains constant, as this represents the electron emittance, which is invariant in a storage ring.