Wave theories of non-laminar charged particle beams: from quantum to thermal regime

摘要

The standard classical description of non-laminar charge particle beams inparaxial approximation is extended to the context of two wave theories. Thefirst theory is the so-called Thermal Wave Model (TWM) that interprets theparaxial thermal spreading of the beam particles as the analog of the quantumdiffraction. The other theory, hereafter called Quantum Wave Model (QWM), thattakes into account the individual quantum nature of the single beam particle(uncertainty principle and spin) and provides the collective description of thebeam transport in the presence of the quantum paraxial diffraction. QWM can beapplied to beams that are sufficiently cold to allow the particles to manifesttheir individual quantum nature but sufficiently warm to make overlapping-lessthe single-particle wave functions. In both theories, the propagation of thebeam transport in plasmas or in vacuo is provided by fully similar set ofnonlinear and nonlocal governing equations, where in the case of TWM theCompton wavelength (fundamental emittance) is replaced by the beam thermalemittance. In both models, the beam transport in the presence of theself-fields (space charge and inductive effects) is governed by a suitablenonlinear nonlocal 2D Schroedinger equation that is used to obtain the envelopebeam equation in quantum and quantum-like regimes, respectively. An envelopeequation is derived for both TWM and QWM regimes. In TWM we recover the wellknown Sacherer equation whilst, in QWM we obtain the evolution equation of thesingle-particle spot size, i.e., single quantum ray spot in the transverseplane (Compton regime). We show that such a quantum evolution equation containsthe same information carried out by an evolution equation for the beam spotsize (description of the beam as a whole). This is done by defining the lowestQWM state reachable by a system of overlapping-less Fermions.