  We present high-resolution (0.3'') ALMA 870um imaging of 52 sub-millimeter
galaxies (SMGs) in the Ultra Deep Survey (UDS) field and investigate the size
and morphology of the sub-millimeter (sub-mm) emission on 2-10kpc scales. We
derive a median intrinsic angular size of FWHM=0.30$\pm$0.04'' for the 23 SMGs
in the sample detected at a signal-to-noise ratio (SNR) >10. Using the
photometric redshifts of the SMGs we show that this corresponds to a median
physical half-light diameter of 2.4$\pm$0.2kpc. A stacking analysis of the SMGs
detected at an SNR <10 shows they have sizes consistent with the 870um-bright
SMGs in the sample. We compare our results to the sizes of SMGs derived from
other multi-wavelength studies, and show that the rest-frame ~250um sizes of
SMGs are consistent with studies of resolved 12CO (J=3-2 to 7-6) emission
lines, but that sizes derived from 1.4GHz imaging appear to be approximately
two times larger on average, which we attribute to cosmic ray diffusion. The
rest-frame optical sizes of SMGs are around four times larger than the
sub-millimeter sizes, indicating that the star formation in these galaxies is
compact relative to the pre-existing stellar distribution. The size of the
starburst region in SMGs is consistent with the majority of the star formation
occurring in a central region, a few kpc in extent, with a median star
formation rate surface density of 90$\pm$30Msol/yr/kpc$^2$, which may suggest
that we are witnessing an intense period of bulge growth in these galaxies.
