  Filaments have been studied in detail through observations and simulations. A
range of numerical works have separately investigated how chemistry and
diffusion effects, as well as magnetic fields and their structure impact the
gas dynamics of the filament. However, non-ideal effects have hardly been
explored thus far. We investigate how non-ideal magnetohydrodynamic (MHD)
effects, combined with a simplified chemical model affect the evolution and
accretion of a star-forming filament. We modeled an accreting self-gravitating
turbulent filament using lemongrab, a one-dimensional (1D) non-ideal MHD code
that includes chemistry. We explore the influence of non-ideal MHD, the
orientation and strength of the magnetic field, and the cosmic ray ionization
rate, on the evolution of the filament, with particular focus on the width and
accretion rate. We find that the filament width and the accretion rate are
determined by the magnetic field properties, including the initial strength,
the coupling with the gas controlled by the cosmic ray ionization rate, and the
orientation of the magnetic field with respect to the accretion flow direction.
Increasing the cosmic-ray ionization rate leads to a behavior closer to that of
ideal MHD, reducing the magnetic pressure support and, hence, damping the
accretion efficiency with a consequent broadening of the filament width. For
the same reason, we obtained a narrower width and a larger accretion rate when
we reduced the initial magnetic field strength. Overall, while these factors
affect the final results by approximately a factor of~2, removing the non-ideal
MHD effects results in a much greater variation (up to a factor of~7). The
inclusion of non-ideal MHD effects and the cosmic-ray ionization is crucial for
the study of self-gravitating filaments and in determining critical observable
quantities, such as the filament width and accretion rate.
