Optimal transport of nonstationary high intensity beams

The problem to determine focusing field configuration that provides the minimal transverse emittance growth of an intense continuous beam at the end of the transport channel is considered. The nonlinear terminal Mayer problem of optimal control related with nonstationary space charge dominated beam transport by fringe magnetic quadrupoles was formulated. Then it was reduced to the quadrupole parameters optimization. Squared transverse RMS emittance of a beam was casted as the quality criteria. Matrix differential equations for the transfer map factors together with the integral equations for space charge potentials were evaluated. The solutions of the optimization problem were received by the Nelder-Mead method combined with the penalty functions. The computer code was carried out and verified. Test results are represented.