  We have modelled the X-ray emission from the young rapid rotator AB Doradus
(P = 0.514 days) using as a basis Zeeman-Doppler maps of the surface magnetic
field. This allows us to reconcile the apparently conflicting observations of a
high X-ray emission measure and coronal density with a low rotational
modulation in X-rays. The technique is to extrapolate the coronal field from
the surface maps by assuming the field to be potential. We then determine the
coronal density for an isothermal corona by solving hydrostatic equilibrium
along each field line and scaling the plasma pressure at the loop footpoints
with the magnetic pressure. We set the density to zero along those field lines
that are open and those where at any point along their length the plasma
pressure exceeds the magnetic pressure. We then calculate the optically thin
X-ray emission measure and rotational modulation for models with a range of
coronal densities. Although the corona can be very extended, much of the
emission comes from high-latitude regions close to the stellar surface. Since
these are always in view as the star rotates, there is little rotational
modulation. We find that emission measures in the observed range of 10^52.8 -
10^53.3 per cubic centimetre can be reproduced with densities in the range 10^9
- 10^10.7 per cubic centimetre for coronae at temperatures of 10^6-10^7 K.
