Escape factors in zero-dimensional radiation-transfer codes

Several zero-dimensional non-LTE radiation-transfer codes are in common use within the laser-plasma community (for example, RATION, FLY, FLYCHK and GALAXY). These codes are capable of generating calculated emission spectra for a plasma of given density and temperature in the presence of a radiation field. Although dimensionless in nature, these codes can take into account the coupling of radiation and populations by use of the escape factor method, and in this sense the codes incorporate the finite size of the plasma of interest in two ways – firstly in the calculation of the effect of the radiation on the populations and secondly when using these populations to generate a spectrum. Different lengths can be used within these two distinct operations, though it has not been made clear what these lengths should be. We submit that the appropriate length to use for the calculation of populations in such zero-dimensional codes is the mean chord of the system, whilst when calculating the spectrum the appropriate length is the size of the plasma along the line of sight. Indeed, for specific plasma shapes using the appropriate escape factors it can be shown that this interpretation agrees with analytic results. However, this is only the case if the correct escape factor is employed: use of the Holstein escape factor (which is in widely distributed versions of the codes mentioned above) is found to be significantly in error under most conditions. We also note that for the case where a plasma is close to coronal equilibrium, some limited information concerning the shape of the plasma can be extracted merely from the ratio of optically thick to optically thin lines, without the need for any explicit spatial resolution.