Optimal Laser Heating of Plasmas with Constant Density

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 determining 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.