  The ultrafast and ultracold electron source, based on near-threshold
photoionisation of a laser-cooled and trapped atomic gas, offers a unique
combination of low transverse beam emittance and high bunch charge. Its use is
however still limited because of the required cold-atom laser-cooling
techniques. Here we present a compact ultracold electron source based on a
grating magneto-optical trap (GMOT), which only requires one trapping laser
beam that passes through a transparent accelerator module. This makes the
technique more widely accessible and increases its applicability. We show the
GMOT can be operated with a hole in the center of the grating and with large
electric fields applied across the trapping region, which is required for
extracting electron bunches. The calculated values of the applied electric
field were found to agree well with measured Stark shifts of the laser cooling
transition. The electron beams extracted from the GMOT have been characterised.
Beam energies up to 10 keV were measured using a time-of-flight method. The
normalised root-mean-squared transverse beam emittance was determined using a
waist scan method, resulting in $\epsilon = 1.9 \rm{nm}$. The root-mean-squared
transverse size of the ionisation volume is $30 \mu\rm{m}$ or larger, implying
an electron source temperature in the few-10K range, $2-3$ orders of magnitude
lower than conventional electron sources, based on photoemission or thermionic
emission from solid state surfaces.
