  A magnetic coil operated at cryogenic temperatures is used to produce
spatial, relative field gradients below 6 ppm/cm, stable for several hours. The
apparatus is a prototype of the magnetic components for a neutron electric
dipole moment (nEDM) search, which will take place at the Spallation Neutron
Source (SNS) at Oak Ridge National Laboratory using ultra-cold neutrons (UCN).
That search requires a uniform magnetic field to mitigate systematic effects
and obtain long polarization lifetimes for neutron spin precession
measurements. This paper details upgrades to a previously described apparatus,
particularly the introduction of super-conducting magnetic shielding and the
associated cryogenic apparatus. The magnetic gradients observed are
sufficiently low for the nEDM search at SNS.
