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 (γJ/Δγ_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 (γ-1)mc² cannot exceed (Jγπec)^1/2λ_c ^-3/2, where λ_c is the Compton wavelength. The normalized brightness cannot exceed 2Δγeccλ_c^-3, where Δγmc² is the electron energy spread, and will be 1/π 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