The area occupied by a beam in transverse position-momentum or position-angle phase space, with a stated area or rms convention. Geometric emittance uses trajectory angle, while normalized emittance removes the ideal kinematic damping due to acceleration.
The phase-space area measure in the vertical transverse plane. If coupling is described by , changing the coupling and changing the natural emittance both alter its equilibrium value.
The phase-space area measure of the horizontal transverse beam distribution. With negligible dispersion and a specified optical function, it determines beam size and angular spread.
The equilibrium horizontal beam emittance set by synchrotron-radiation excitation and damping in an uncoupled storage ring. The radiation-integral relation is ; similar cell optics give a cubic dependence on bending angle.
The geometric emittance multiplied by the relativistic velocity and Lorentz factor. For paraxial acceleration without dilution, this is proportional to transverse canonical phase-space area and remains constant. Thus geometric emittance decreases approximately as inverse beam momentum.
For a centered beam, the displayed rms area in coordinates. A matched beam has , where is one of the Courant-Snyder parameters. Under ideal acceleration, adiabatic damping of geometric emittance decreases this area even when the canonical phase-space area is preserved.
For slowly accelerated paraxial motion, decreases as longitudinal momentum grows while transverse canonical phase-space area is conserved. The normalized emittance stays constant in the ideal limit, so the geometric emittance scales inversely with longitudinal momentum. This is kinematic damping rather than dissipation of canonical area.
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Beam emittance is a fundamental property in accelerator physics and related fields, describing the spread of particles in a beam with respect to their position and momentum. It quantifies how "focused" or "spread out" the beam is in both spatial and momentum dimensions, and it plays a crucial role in determining the quality and performance of particle beams in accelerators, such as those used in synchrotrons and colliders. Emittance is often expressed in units of area (e.g.