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 coefficients, 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.Based on a thesis submitted as partial fulfillment for a Ph.D. degree at the University of Michigan. Financial support, provided to the first author by Consejo Nacional de Ciencia y Tecnología, Universidad Nacional Autónoma de México, by the National Science Foundation, and by the Michigan Memorial Phoenix Project, is deeply appreciated.