We present the POL-2 850 $mu$m linear polarization map of the Barnard 1 clump in the Perseus molecular cloud complex from the B-fields In STar-forming Region Observations (BISTRO) survey at the James Clerk Maxwell Telescope. We find a trend of decreasing polarization fraction as a function of total intensity, which we link to depolarization effects towards higher density regions of the cloud. We then use the polarization data at 850 $mu$m to infer the plane-of-sky orientation of the large-scale magnetic field in Barnard 1. This magnetic field runs North-South across most of the cloud, with the exception of B1-c where it turns more East-West. From the dispersion of polarization angles, we calculate a turbulence correlation length of $5.0 pm 2.5$ arcsec ($1500$ au), and a turbulent-to-total magnetic energy ratio of $0.5 pm 0.3$ inside the cloud. We combine this turbulent-to-total magnetic energy ratio with observations of NH$_3$ molecular lines from the Green Bank Ammonia Survey (GAS) to estimate the strength of the plane-of-sky component of the magnetic field through the Davis-Chandrasekhar-Fermi method. With a plane-of-sky amplitude of $120 pm 60$ $mu$G and a criticality criterion $lambda_c = 3.0 pm 1.5$, we find that Barnard 1 is a supercritical molecular cloud with a magnetic field nearly dominated by its turbulent component.
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