  A control theory for Hamiltonian systems, based on KAM theory, was introduced
in \cite{ciraolo_control_2004} and applied to a model of magnetic field in
\cite{chandre_control_2006}. By a combination of Frequency Analysis and of a
rigorous (Computer Assisted) KAM algorithm we show that in the phase space of
the magnetic field, due to the control term, a set of invariant tori appear,
and it acts as a transport barrier. Our analysis, which is common (but often
also limited) to celestial mechanics, is very general and can be applied to
quasi-integrable Hamiltonian systems satisfying a few additional mild
assumptions.
