Emittanz

Emittanz, commonly referred to in English as emittance, is a property of a particle beam in accelerators that characterizes the spread of particle positions and momenta in phase space. In a transverse plane, it describes the area occupied by the beam in the x-x’ plane, where x is the transverse position and x’ is the angle relative to the beam direction. Emittance thus quantifies beam quality and brightness: a beam with small emittance can be focused to a small spot and achieve high luminosity.

There are several related measures. The geometric (or classical) emittance ε is defined in phase space. The normalized emittance ε_n = γβ ε is invariant under acceleration for relativistic beams, because γ and β change while ε_geo decreases accordingly.

Common variants include rms emittance, defined from second moments, and slice emittance, describing emittance for a short segment of the bunch; six-dimensional emittance combines all transverse and longitudinal planes. In practice, for linear beam dynamics and in the absence of damping, emittance is approximately conserved (Liouville’s theorem). Damping or cooling mechanisms can reduce emittance.

Measurement: Emittance is inferred from measurements such as quadrupole-scan methods, pepper-pot or slit techniques, and beam-profile monitors, often reporting rms or projected emittance values.

Importance: Emittance sets the ultimate spot size at focusing, affects luminosity in colliders, brightness of light sources, and the performance of medical accelerators; it is a central figure of merit in beam-physics design.