The link between turbulence, magnetic fields, filaments, and star
  formation in the Central Molecular Zone cloud G0.253+0.016
  Star formation is primarily controlled by the interplay between gravity,
turbulence, and magnetic fields. However, the turbulence and magnetic fields in
molecular clouds near the Galactic Center may differ substantially from
spiral-arm clouds. Here we determine the physical parameters of the central
molecular zone (CMZ) cloud G0.253+0.016, its turbulence, magnetic field and
filamentary structure. Using column-density maps based on dust-continuum
emission observations with ALMA+Herschel, we identify filaments and show that
at least one dense core is located along them. We measure the filament width
W_fil=0.17$\pm$0.08pc and the sonic scale {\lambda}_sonic=0.15$\pm$0.11pc of
the turbulence, and find W_fil~{\lambda}_sonic. A strong velocity gradient is
seen in the HNCO intensity-weighted velocity maps obtained with ALMA+Mopra,
which is likely caused by large-scale shearing of G0.253+0.016, producing a
wide double-peaked velocity PDF. After subtracting the gradient to isolate the
turbulent motions, we find a nearly Gaussian velocity PDF typical for
turbulence. We measure the total and turbulent velocity dispersion,
8.8$\pm$0.2km/s and 3.9$\pm$0.1km/s, respectively. Using magnetohydrodynamical
simulations, we find that G0.253+0.016's turbulent magnetic field
B_turb=130$\pm$50$\mu$G is only ~1/10 of the ordered field component. Combining
these measurements, we reconstruct the dominant turbulence driving mode in
G0.253+0.016 and find a driving parameter b=0.22$\pm$0.12, indicating
solenoidal (divergence-free) driving. We compare this to spiral-arm clouds,
which typically have a significant compressive (curl-free) driving component
(b>0.4). Motivated by previous reports of strong shearing motions in the CMZ,
we speculate that shear causes the solenoidal driving in G0.253+0.016 and show
that this reduces the star formation rate (SFR) by a factor of 6.9 compared to
typical nearby clouds.
