  The Helmholtz wave scattering problem by screens in 2D can be recast into
first-kind integral equations which lead to ill-conditioned linear systems
after discretization. We introduce two new preconditioners, in the form of
square-roots of local operators respectively for the corresponding problems
with Dirichlet and Neumann conditions on the arc. They generalize the so-called
"analytical" preconditioners available for Lipschitz scatterers. We introduce a
functional setting adapted to the singularity of the problem and enabling the
analysis of those preconditioners. The efficiency of the method is demonstrated
on several numerical examples.
