Emittance calculation using Liouville´s theorem for a diagonalized Hamiltonian

It is demonstrated that in a special electrostatic arrangement, the z-dependence (direction of beam) of the Hamiltonian can be neglected. The Hamiltonian separates into two parts describing the degrees of freedom of the perpendicular motion of the particles. This allows one to use Liouville´s theorem to calculate emittance. A formula is easily derived by taking into account the additive structure of the Hamiltonian (constant partial phase space). A simple method is presented for measuring the emittance.<>