  Non-ideal magnetohydrodynamic effects that rule the coupling of the magnetic
field to the circumstellar gas during the low-mass star formation process
depend heavily on the local physical conditions, such as the ionization
fraction of the gas. The purpose of this work is to observationally
characterize the level of ionization of the circumstellar gas at small envelope
radii and investigate its relation to the efficiency of the coupling between
the star-forming gas and the magnetic field in the Class 0 protostar B335. We
have obtained molecular line emission maps of B335 with ALMA, which we use to
measure the deuteration fraction of the gas, its ionization fraction, and the
cosmic-ray ionization rate, at envelope radii $\lesssim$1000 au. We find large
fractions of ionized gas, $\chi_{e} \simeq 1-8 \times 10^{-6}$. Our
observations also reveal an enhanced ionization that increases at small
envelope radii, reaching values up to $\zeta_{CR} \simeq 10^{-14}$~s$^{-1}$ at
a few hundred au from the central protostellar object. We show that this
extreme ionization rate can be attributed to the presence of cosmic rays
accelerated close to the protostar. We report the first resolved map of the
cosmic-ray ionization rate at scales $\lesssim 1000$~au in a solar-type Class 0
protostar, finding remarkably high values. Our observations suggest that local
acceleration of cosmic rays, and not the penetration of interstellar Galactic
cosmic rays, may be responsible for the gas ionization in the inner envelope,
potentially down to disk forming scales. If confirmed, our findings imply that
protostellar disk properties may also be determined by local processes setting
the coupling between the gas and the magnetic field, and not only by the amount
of angular momentum available at large envelope scales and the magnetic field
strength in protostellar cores.
