A Two-Dimensional Intense Relativistic Beam Equilibrium

The behavior of an intense relativistic charged particle beam is studied by determining a two-dimensional equilibrium solution of the laminar flow, monoenergetic particle dynamics equations. With these relations formulated in azimuthally symmetric cylindrical coordinates, the free parameter method is used to derive the most general similarity variable nf(r,z) appropriate to the equations and an exact solution is found in terms of this unknown. The solution is interpreted as a force-free converging or diverging particle beam propagating in the z direction within a conical drift chamber.