Phase-space area occupied by a bunch: ε_x = √⟨x²⟩⟨x'²⟩–⟨xx'⟩². Liouville-preserved under Hamiltonian dynamics, reduced by stochastic cooling, radiation damping, or laser cooling. Brightness ~ N/εxεyεz is the key figure of merit.
Phase-space area occupied by a bunch: ε_x = √⟨x²⟩⟨x'²⟩–⟨xx'⟩². Liouville-preserved under Hamiltonian dynamics, reduced by stochastic cooling, radiation damping, or laser cooling. Brightness ~ N/εxεyεz is the key figure of merit.