Transfer in cylindrical fluxtubes, with 1 or 2 dimensions

This is a review of methods for the solution of non-LTE radiative transfer equations in long cylinders. The principal goal of these methods is the modelling of elongated structures imbedded in the solar corona, such as loops or prominence threads. These objects are submitted to the solar radiation, which determines the boundary conditions of the problem. Different cases are examined. Concerning the geometry, one-dimension and two-dimension cases are treated. The two-dimension case itself is subdivided into (radius, altitude) and (radius, azimuth) problems, which are treated by quite different methods. Another distinction concerns the method of resolution: semi-analytical, Monte-Carlo and finite-difference methods are examined. Some methods are restricted to a two-level atom, others allow the treatment of realistic multilevel cases. Some recent results, obtained with finite-difference, accelerated Λ-iteration methods, are presented