Quantum-mechanical constraints on electron-beam brightness

Bounds on the brightness and quality of fermion beams are derived from Pauli's exclusion principle and the finite density of quantum eigenstates for free fermions. These bounds are applied to electron-beam sources to derive limitations on the quality ( gamma J/ Delta gamma /sub z/) of the electron beams they generate. In the absence of electromagnetic fields, the quality of a relativistic electron beam of current density J and kinetic energy ( gamma -1)mc/sup 2/ cannot exceed (J gamma pi ec)/sup 1/2/ lambda /sub c//sup -3/2/, where lambda /sub c/ is the Compton wavelength. The normalized brightness cannot exceed 2 Delta gamma ecc lambda /sub c//sup -3/, where Delta gamma mc/sup 2/ is the electron energy spread, and will be 1/ pi times the beam quality for a beam of maximal quality. It is concluded that the qualities of electron beams produced by existing linear accelerators for free-electron lasers could be increased by six to eight orders of magnitude before reaching the quality limit.<
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