Different ways of thinking about beams

Some of the characteristics of particle beams used in various fields such as electron microscopy, microwave tubes, particle accelerators and various aspects of fusion research, are contrasted and compared. Starting with a discussion of the very simplest type of beam in paraxial approximation, the concepts of emittance and perveance are introduced. These characterize respectively the degree of disorder of the beam, and the effect of the smoothed out self electric and magnetic fields of the particles. Simple models illustrate some of the types of behaviour encountered in more complex systems. Alternative descriptions of some of these phenomena are discussed, and some effects associated with "negative mass" instability in annular systems are described.