We present test results on the simultaneous inversion of the Stokes profiles
of the He I lines at 587.6 nm (D_3) and 1083.0 nm in prominences (90-deg
scattering). We created datasets of synthetic Stokes profiles for the case of
quiescent prominences (B<200 G), assuming a conservative value of 10^-3 of the
peak intensity for the polarimetric sensitivity of the simulated observations.
In this work, we focus on the error analysis for the inference of the magnetic
field vector, under the usual assumption that the prominence can be assimilated
to a slab of finite optical thickness with uniform magnetic and thermodynamic
properties. We find that the simultaneous inversion of the two lines
significantly reduces the errors on the inference of the magnetic field vector,
with respect to the case of single-line inversion. These results provide a
solid justification for current and future instrumental efforts with multi-line
capabilities for the observations of solar prominences and filaments.Comment: 14 pages, 5 figures, 1 tabl