  This paper proposes a new fast and stable algorithm for the reconstruction of
the plasma boundary from discrete magnetic measurements taken at several
locations surrounding the vacuum vessel. The resolution of this inverse problem
takes two steps. In the first one we transform the set of measurements into
Cauchy conditions on a fixed contour $\Gamma\_O$ close to the measurement
points. This is done by least square fitting a truncated series of toroidal
harmonic functions to the measurements. The second step consists in solving a
Cauchy problem for the elliptic equation satisfied by the flux in the vacuum
and for the overdetermined boundary conditions on $\Gamma\_O$ previously
obtained with the help of toroidal harmonics. It is reformulated as an optimal
control problem on a fixed annular domain of external boundary $\Gamma\_O$ and
fictitious inner boundary $\Gamma\_I$. A regularized Kohn-Vogelius cost
function depending on the value of the flux on $\Gamma\_I$ and measuring the
discrepency between the solution to the equation satisfied by the flux obtained
using Dirichlet conditions on $\Gamma\_O$ and the one obtained using Neumann
conditions is minimized. The method presented here has led to the development
of a software, called VacTH-KV, which enables plasma boundary reconstruction in
any Tokamak.
