Procedure to Solve the One-Dimensional Radiative Transfer Equation (1D-RTE) of an Ionized Medium Using Spatial Discretization and an Iterative Process

A new solution procedure for the one-dimensional radiation transfer equation, which describes the radiation propagation in semi-transparent media, is proposed. The resolution proposed, in this work for the first time, is based on spatial discretization and an iterative method. The emitter medium is subdivided into several layers and each layer is considered homogeneous and at the local thermodynamic equilibrium. The emission intensity of each layer is deduced from that of the previous layer. Comparisons are made between our method and other methods described in the literature. This solution is then used to model the line profiles of the Balmer Hα line emitted by a plasma created by the breakdown of a pulsed laser in water.