  We use a numerical nonlinear multigrid magnetic relaxation technique to
investigate the generation of current sheets in three-dimensional magnetic flux
braiding experiments. We are able to catalogue the relaxed nonlinear force-free
equilibria resulting from the application of deformations to an initially
undisturbed region of plasma containing a uniform, vertical magnetic field. The
deformations are manifested by imposing motions on the bounding planes to which
the magnetic field is anchored. Once imposed the new distribution of magnetic
footpoints are then taken to be fixed, so that the rest of the plasma must then
relax to a new equilibrium configuration. For the class of footpoint motions we
have examined, we find that singular and nonsingular equilibria can be
generated. By singular we mean that within the limits imposed by numerical
resolution we find that there is no convergence to a well-defined equilibrium
as the number of grid points in the numerical domain is increased. These
singular equilibria contain current "sheets" of ever-increasing current
intensity and decreasing width; they occur when the footpoint motions exceed a
certain threshold, and must include both twist and shear to be effective. On
the basis of these results we contend that flux braiding will indeed result in
significant current generation. We discuss the implications of our results for
coronal heating.
