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.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45228/1/10957_2004_Article_BF00938468.pd

Second-order necessary conditions in optimal control: Accessory-problem results without normality conditions

An optimal control problem, which includes restrictions on the controls and equality/inequality constraints on the terminal states, is formulated. Second-order necessary conditions of the accessory-problem type are obtained in the absence of normality conditions. It is shown that the necessary conditions generalize and simplify prior results due to Hestenes (Ref. 5) and Warga (Refs. 6 and 7).Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45219/1/10957_2004_Article_BF00934437.pd