  We simulate Lattice QED in a constant external magnetic field using the RHMC
algorithm. We seek evidence for chiral symmetry breaking predicted by truncated
Schwinger-Dyson methods. Since the predicted values of the dynamical electron
mass and chiral condensate at the physical fine structure constant are too
small to be measured, we simulate at a larger value $\alpha=1/5$. This requires
using electron masses as low as $m=0.001$ to extrapolate to $m=0$. At a large
magnetic field, the electrons occupy the lowest Landau level which has a small
profile in the plane orthogonal to the magnetic field, so that we are able to
use a lattice with small extent in these 2 directions. If chiral symmetry is
unbroken at $m=0$ the chiral condensate is dominated by large momenta and
should be insensitive to the lattice extent in the direction of the magnetic
field and the time direction. When chiral symmetry is broken at $m=0$, the
chiral condensate should be sensitive to the lattice size in these directions
as $m \rightarrow 0$. We search for this behaviour by increasing the lattice
extent in these 2 directions. Preliminary simulations show strong dependence of
the chiral condensate on the lattice extent in these 2 directions for the
smallest masses, and these increased condensates appear to be approaching a
non-zero limit as $m \rightarrow 0$.
