Optimal Laser Heating of Plasmas with Constant Density I

Abstract. The laser heating of a plasma with constant density is analyzed using optimal control theory. Heating strategies that minimize the total energy spent, the heating time, or a linear combination of the two, for several values of weighting coelficients, are obtained by deter-mining the optimal laser intensity associated with each point of the phase plane. A numerical example is used to illustrate the application of the theory. In this particular example, savings in the energy spent up to 75%, compared with the energy required using a constant laser pulse, are obtained when minimum energy trajectories are implemented. Strategies that minimize the heating time, however, did not yield a significant reduction in the heating time. Numerical results may depend strongly on the initial state of the system as well as on the final ion temperature of the plasma. Key Words. Optimal control theory, plasmas, laser heating, singular controls