Analysis of 3-D phase space dynamics of pencil-to-sheet-electron-beam transformation in highly-non-paraxial quadrupole lens system

Summary form only given, as follows. Sheet electron beams have the potential to make possible higher power-sources of microwave radiation due to their ability to transport high currents, at reduced current densities, through a single narrow RF interaction structure. Previous investigations have indicated the feasibility for laboratory formation of an elliptical sheet beam using magnetic quadrupoles and a Pierce gun pencil-beam source. The configuration exhibits several unique physical features of phase space evolution not observed in more conventional, paraxial beam transport systems. Previous numerical simulations using MAGIC3-D indicate the r.m.s. phase space volume occupied by the sheetbeam increased longitudinally, which contradicts the principle of phase space conservation for a conservative system (Liouville´s theorem). The explanation is that is Liouville´s theorem does not strictly apply to r.m.s. emittance calculations and some alternative phase space measure might provide closer agreement with Liouville´s theorem. The developed phase space measure is non-statistical and uses principles from mathematical morphology. We discuss and compare the results of numerical simulations using the TRACE3-D and MAGIC3-D codes. In addition, we discuss the morphological algorithm for computing phase space area and compare its results with that of the r.m.s. formalism for calculating phase space area.