ABSTRACT
This chapter deals with cylindrical one-dimensional relativistic and non-relativistic electron oscillations. The focus is on a simpler model. Regardless of the relativism, the cylindrical electron oscillations end in a rollover. The formal formulation of the problem in the Eulerian variables, allows us to generally characterize the qualitative scenario of the dynamics of axially symmetric plasma oscillations. The chapter aims to study the process of oscillations, which is similar to the dynamics of wake waves excited by a laser pulse, so the first scenario is of priority importance. It also deals with finding axial solutions for two problems associated with cylindrical plasma oscillations. The chapter provides the dynamics of the development and destruction of oscillations. For cylindrical oscillations, ‘truncated’ problems are obtained that describe the behaviour of the solution on the axis of symmetry. These dedicated solutions are called, for convenience, axial.
