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In this paper, we provide a more accurate description of the evolution of themagnetic flux redistribution during prestellar core collapse by includingresistive terms in the magnetohydrodynamics (MHD) equations. We focus moreparticularly on the impact of ambipolar diffusion. We use the adaptive meshrefinement code RAMSES to carry out such calculations. The resistivitiesrequired to calculate the ambipolar diffusion terms were computed using areduced chemical network of charged, neutral and grain species. The inclusionof ambipolar diffusion leads to the formation of a magnetic diffusion barrierin the vicinity of the core, preventing accumulation of magnetic flux in andaround the core and amplification of the field above 0.1G. The mass and radiusof the first Larson core remain similar between ideal and non-ideal MHD models.This diffusion plateau has crucial consequences on magnetic braking processes,allowing the formation of disk structures. Magnetically supported outflowslaunched in ideal MHD models are weakened when using non-ideal MHD. Contrary toideal MHD misalignment between the initial rotation axis and the magnetic fielddirection does not significantly affect the results for a given mu, showingthat the physical dissipation truly dominate over numerical diffusion. Wedemonstrate severe limits of the ideal MHD formalism, which yield unphysicalbehaviours in the long-term evolution of the system. This includes counterrotation inside the outflow, interchange instabilities, and flux redistributiontriggered by numerical diffusion, none observed in non-ideal MHD. Disks withKeplerian velocity profiles form in all our non-ideal MHD simulations, withfinal mass and size which depend on the initial magnetisation. This ranges froma few 0.01 solar masses and 20-30 au for the most magnetised case (mu=2) to 0.2solar masses and 40-80 au for a lower magnetisation (mu=5).

Ambipolar diffusion in low-mass star formation. I. General comparison with the ideal MHD case