Entropy and emittance of particle and photon beams

Abstract

The emittance as the available phase space area is defined as the product of the elementary cell area /spl delta//spl Omega/ and exp(S), where S is the normalized entropy of a particle beam. The definition is based on the fact that the factor exp(S) can be interpreted as the number of the occupied cells. For particle beams, a closed expression for the emittance in terms of the phase space distribution function is obtained which is independent of /spl delta//spl Omega/. To compute the emittance of the radiation beam, it is necessary to find the eigenvalues of the correlation operator. An explicit solution is found for the case of a partially coherent radiation beam which is a stochastic superposition of coherent Gaussian beams with a Gaussian probability distribution. Such a beam is a reasonable model for undulator radiation by beam of electrons. From the requirement that the radiation emittance reproduces the particle beam emittance in the incoherent limit, the elementary cell area /spl delta//spl Omega/ is determined unambiguously to be /spl lambda/, the radiation wavelength. The emittance in the coherent limit then becomes /spl lambda/.