A Thermal Wave Model for relativistic-charged-particle beam propagation

We show that the well-known analogy between electromagnetic beam optics (EBO) and relativistic-charged-particle beam optics (RCPBO) in paraxial approximation is deeper than it would usually appear in the literature. This analogy is understood by suggesting a wave model of thermal nature for particle-beam propagation. This is done using a parabolic equation for a wave function whose modulus squared is proportional to the number of particles per unitary transverse section, and the emittance represents the diffraction parameter as the wavelength in monochromatic EBO. Since the particle beam is described by a Schrodinger-like equation, we get a further formal analogy between RCPBO and nonrelativistic quantum mechanics (NQM). The emittance plays now the role corresponding to Planck's constant. The wave model for RCPBO is completely new and gives a formal unified description of RCPBO, EBO and NQM. This equivalence allows us, using quantum mechanics, to obtain in a simple way all the already known results of RCPBO. Furthermore, it provides in perspective a useful framework for a more accurate study of several applications, such as those in particle accelerators, in FEL and particle beam-plasma interaction.