A quantum-like approach to the interaction of relativistic charged particle beams with plasmas

It is shown that particle beam dynamics can be described in terms of a Schrodinger-like equation for a complex function, the so- called beam wave function (BWF), whose squared modulus yields the density distribution of the particles in the configuration space. The role of Planck's constant is here played by the beam emittance (transverse or longitudinal). In this framework, we describe the interaction of a relativistic charged particle beam with an unmagnetized, collisionless plasma in terms of nonlinear Schrodinger-like equations fully similar to the ones are describing the nonlinear electromagnetic beam-plasma interaction. This way, both longitudinal and transverse particle dynamics in plasmas can be naturally described, and new insights are obtained readily.