  The neutron's permanent electric dipole moment $d_n$ is constrained to below
$3\times10^{-26} e~\text{cm}$ (90% C.L.) [ arXiv:hep-ex/0602020,
arXiv:1509.04411 ], by experiments using ultracold neutrons (UCN). We plan to
improve this limit by an order of magnitude or more with PanEDM, the first
experiment exploiting the ILL's new UCN source SuperSUN. SuperSUN is expected
to provide a high density of UCN with energies below 80 neV, implying extended
statistical reach with respect to existing sources, for experiments that rely
on long storage or spin-precession times. Systematic errors in PanEDM are
strongly suppressed by passive magnetic shielding, with magnetic field and
gradient drifts at the single fT level. A holding-field homogeneity on the
order of $10^{-4}$ is achieved in low residual fields, via a high static
damping factor and built-in coil system. No comagnetometer is needed for the
first order-of-magnitude improvement in $d_n$, thanks to high magnetic
stability and an assortment of sensors outside the UCN storage volumes. PanEDM
will be commissioned and upgraded in parallel with SuperSUN, to take full
advantage of the source's output in each phase. Commissioning is ongoing in
2019, and a new limit in the mid $10^{-27} e~\text{cm}$ range should be
possible with two full reactor cycles of data in the commissioned apparatus.
