Representative sketch of our set-up. The code evolves a vector variable with three components (x, y, z,) along one coordinate (x); hence, y and z have periodic boundary conditions. The x coordinate traverses the filament (shaded gradient) and the initial density distribution along this component follows a Plummer-like profile with maximum density, ρ_ridge, and background density, ρ₀, see Eq. (1). The gas accretes along the same axis, as indicated by the arrows. The magnetic field is inclined by an angle θ with respect to the x-axis, where θ = arctan B_y/B_x. We note that the color palette employed for the filament is only included for illustration purposes.