  Amongst the hydrogen-deficient accreting binaries known as the "AM~CVn stars"
are three systems with the shortest known orbital periods: HM Cnc (321 s), V407
Vul (569 s) and ES Cet (620 s). These compact binaries are predicted to be
strong sources of persistent gravitational wave radiation. HM Cnc and V407 Vul
are undergoing direct impact accretion in which matter transferred from their
donor hits the accreting white dwarfs directly. ES Cet, is the longest period
of the three and is amongst the most luminous AM CVn stars, but it is not known
whether it accretes via a disk or direct impact. ES Cet displays strong HeII
4686 line emission, which is sometimes a sign of magnetically-controlled
accretion. Peculiarly, although around one third of hydrogen accreting white
dwarfs show evidence for magnetism, none have been found amongst helium
accretors. We present the results of Magellan and VLT spectroscopic and
spectropolarimetric observing campaigns dedicated to ES Cet with the aim of
understanding its accretion structure. We find strong variability in our
spectra on the 620 s period. The lines show evidence for double-peaked
emission, characteristic for an accretion disc, with an additional component
associated with the outermost disc, rather than a direct impact, that is
broadly consistent with "S"-wave emission from the gas stream/disc impact
region. This confirms beyond any doubt that 620\,s is the orbital period of ES
Cet. We find no significant circular polarisation (below 0.1 %). The trailed
spectra show that ES Cet's outer disc is eclipsed by the mass donor, revealing
at the same time that the photometric minimum coincides with the hitherto
unrecognised eclipse. ES Cet shows spectroscopic behaviour consistent with
accretion via a disc, and is the shortest orbital period eclipsing AM CVn star
known.
