Gaussian wave formalism model for propagation of charged-particle beam through a first-order optical system

An elliptical Gaussian wave formalism model of a charged-particle beam is proposed by analogy with an elliptical Gaussian light beam. In the paraxial approximation, the charged-particle beam can be described as a whole by a complex radius of curvature in the real space domains. Therefore, the propagation and transform of charged-particle beam passing through a first-order optical system is represented by the ABCD-like law.As an example of the application of this model, the relation between the beam waist and the minimum beam spot at a fixed target is discussed. The result, well matches that from conventional phase space model, and proves that the Gaussian wave formalism model is highly effective and reasonable.