When no radiation is present, the emittances remain constant (apart from impedance effects and intrabeam scattering). In this case, the emittance is determined by the initial particle distribution. In particular if one injects a "small" emittance, it remains small, whereas if one injects a "large" emittance, it remains large. Acceptance The acceptance, also called admittance, is the maximum emittance that a beam transport system or analyzing system is able to transmit. This is the size of the chamber transformed into phase space and does not suffer from the ambiguities of the definition of beam emittance. Conservation of emittance Lenses can focus a beam, reducing its size in one transverse dimension while increasing its angular spread, but cannot change the total emittance. This is a result of Liouville's theorem. Ways of reducing the beam emittance include radiation damping, stochastic cooling, and electron cooling. Emittance and brightness Emittance is also related to the brightness of the beam. In microscopy brightness is very often used, because it includes the current in the beam and most systems are circularly symmetric. Consider the brightness of the incident beam at the sample, where indicates the beam current and represents the total emittance of the incident beam and the wavelength of the incident electron. The intrinsic emittance , describing a normal distribution in the initial phase space, is diffused by the emittance introduced by aberrations . The total emittance is approximately the sum in quadrature. Under the assumption of uniform illumination of the aperture with current per unit angle , we have the following emittance-brightness relation, See also Accelerator Physics Thermal Emittance / Mean Transverse Energy Etendue References Accelerator physics