AN OPERATOR PERTURBATION METHOD FOR POLARIZED LINE TRANSFER .1. NONMAGNETIC REGIME IN 1D MEDIA

In this paper we generalize an Approximate Lambda Iteration (ALI) tech nique developed for scalar transfer problems to a vectorial transfer p roblem for polarized radiation. Scalar ALI techniques are based on a s uitable decomposition of the Lambda operator governing the integral fo rm of the transfer equation. Lambda operators for scalar transfer equa tions are diagonally dominant, offering thus the possibility to use it erative methods of the Jacobi type where the iteration process is base d on the diagonal of the Lambda operator (Olson et al. 1986). Here we consider resonance polarization, created by the scattering of an aniso tropic radiation field, or spectral lines formed with complete frequen cy redistribution in a 1D axisymmetric medium. The problem can be form ulated as an integral equation for a 2-component vector (Rees 1978) or , as shown by Ivanov (1995), as an integral equation for a (2 x 2) mat rix source function which involves the same generalized Lambda operato r as the vector integral equation. We find that this equation holds al so in the presence of a weak; turbulent magnetic field. The generalize d Lambda operator is a (2 x 2) matrix operator. The element {11} descr ibes the propagation of the intensity and is identical to the Lambda o perator of non-polarized problems. The element {22} describes the prop agation of the polarization. The off-diagonal terms weakly couple the intensity and the polarization. We propose a block Jacobi iterative me thod and show that its convergence properties are controlled by the pr opagator for the intensity. We also show that convergence can be accel erated by an Ng acceleration method applied to each element of the sou rce matrix. We extend to polarized transfer a convergence criterion in troduced by Auer el al. (1994) based on the grid truncation error of t he converged solution.