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Independently of the debate on the importance of magnetic fields in large scales and in the cloud and core formation process, magnetic effects are crucial in the evolution of collapsing low-mass cores. We show this by following the formation and collapse of a low-mass core all the way until the formation of a hydrostatic protostar at its center. We simulate the evolution of the core using an adaptive-grid numerical code, which follows the nonideal six-fluid MHD equations, and accounts explicitly and self-consistently for gravity, thermal pressure, the magnetic field, cosmic-ray and radioactivity-induced ionization, and the chemical and dynamical effects of dust grains. We evaluate the relative importance of different magnetic flux-loss mechanisms (ambipolar diffusion and Ohmic dissipation) in the resolution of the magnetic flux problem of star formation, and we model the spatial structure of the density, magnetic, and velocity fields inside the collapsing core. At this stage, we see the onset of magnetically driven radial shocks, which we then continue to follow after a hydrostatic protostellar object is formed, by isolating and studying the isothermal envelope surrounding the protostar and supplying it with accreting matter. We find that the magnetic shocks are controlled by ambipolar diffusion and occur in a quasi-periodic fashion, resulting in episodic accretion from the envelope onto the protostellar accretion disc.
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