We present here the five numerical simulation codes and models used by the contributors to model the line-shapes of the C

ii 723-nm line for four cases sharing the same electron density of n

_{e} = 10

^{17} cm

^{−3} but for two distinct values of the electron temperature T

_{e} = 2 eV and T

_{e} = 4 eV, without and with a magnetic field (B = 4 T). Note that the electron and ion temperatures were assumed equal. Even though there are differences in the treatment of the Stark effect by the various codes, they can be separated into two groups, according to the adopted approach to treat the Zeeman effect. Indeed, the line-shape codes used here can be divided into two groups. Those of the first group treat the Zeeman effect within the weak-field approximation [

4,

5] in which the magnetic field is a perturbation of the emitter fine-structure energy levels, shown in

Figure 2a. This approximation is valid when the fine structure splitting exceeds the Zeeman splitting (Δ

E_{FS} >> Δ

E_{Z}). Three methods belong to this group: SCRAM (Sandia National Laboratory), PPP-B and WEAKZEE (CNRS/ Aix-Marseille Université). The PPP-B code [

6] is an extension of the PPP standard Stark line-shape code [

7,

8], which accounts for ion dynamics. In PPP-B, the Zeeman effect is described in either the weak-field approximation or the opposite one,

i.e., the strong-field approximation [

4,

5]. The latter is valid when the Zeeman splitting is higher than the fine structure one (Δ

E_{Z} >> Δ

E_{FS}). Note that, when input MCDF atomic data are used, an asterisk is added to the code name PPP-B which becomes PPP-B *. WEAKZEE is a very simple version of PPP-B where only the electron Stark broadening is accounted for, the ion Stark broadening being neglected. In WEAKZEE, the Zeeman components are dressed by a Lorentzian shape with a given width. The later can be obtained from the Stark-B database [

9,

10]. In [

9], one can find Stark broadening parameters (FWHM: Full Width at Half Maximum) by electrons and ions for few values of the electron density and the electron temperature. For all other temperatures, the Stark widths w (in Å units) can be obtained using the following fit formula [

11]:

where

a_{0},

a_{1}, and

a_{2} are fitting parameters depending on the line, perturbers (ions or electrons) and the electron density. In this relation, the electron temperature is expressed in Kelvin. For the present calculations, the Lorentzian width w used by WEAKZEE was calculated using Equation (1). SCRAM [

12,

13], which is primarily used for non-LTE diagnostics of emission spectra that cover a wide range of energies and access many charge states, satellites,

etc., uses the electron impact approximation for collisional broadening (based on allowed distorted wave transitions among fine structure states), the quasi-static approximation for the ionic Stark broadening, and can interpolate between the weak and strong field limits. Including forbidden collisional transitions increases the widths by about 10%. The second group of codes contains two models: SIMU [

14,

15] and INTDPH [

16] (Weizmann Institute of Science). In these codes, the Zeeman effect is treated non-perturbatively, via a numerical solution of the static (INTDPH) or time-dependent (SIMU) Schrödinger equation. The initial atomic system is that shown on

Figure 2a (see also

Table 1). More precisely, SIMU is a combination of two codes: a molecular dynamics (MD) simulation of variable complexity and a solver for evolution of an atomic system with the MD field history used as a time-dependent perturbation. INTDPH is another Stark–Zeeman line-shape code using the quasi-static approximation for the ions. In order to account for the electron broadening, the output is convolved with a shifted Lorentzian at the post-processing step. The width and shift of the Lorentzian should be obtained separately from another code or a database. This is a very fast and accurate procedure (when electrons are strictly impact, e.g., for isolated lines). An application of INTDPH to diagnostics of magnetized plasmas can be found in [

17]. For the calculations presented here, the impact broadening parameters were inferred from the SIMU line shapes obtained assuming B = 0.

**Figure 2.**
Schematic energy diagrams of the radiator considered for the present study without (**a**) and with (**b**) the fine structure effect. Energy splitting between the 1s^{2}2s^{2}3p ^{2}P° and 1s^{2}2s^{2}3d ^{2}D doublets is exaggerated (magnified by a factor of 500) for both of levels. Arrows represent radiative dipolar transitions with solid ones representing those transitions considered for the present study.