Context. 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. Aims. We investigate how non-ideal magnetohydrodynamic (MHD) effects, combined with a simplified chemical model affect the evolution and accretion of a star-forming filament. Methods. 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. Results. 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). Conclusions. 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.
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