ABSTRACT

The chapter deals with plane one-dimensional relativistic electron oscillations described by the P1RE system of equations. First, it explains the background of breaking: the shift of the fundamental oscillation frequency and the violation of the property of invariance. Then, a basic numerical algorithm is built on the basis of the ‘leapfrog’ scheme and the Lagrangian variables, with the help of which the development and completion of oscillations is determined by numerical simulation. Further, in order to study more complex problems (for the future!), an approximate method is constructed based on the Eulerian variables and the idea of splitting along physical processes. Finally, using asymptotic formulas describing the dynamics of relativistic oscillations, the artificial boundary conditions of various orders of accuracy with respect to amplitude and grid parameters are derived.