Rigorous Error Bounds on Position and Velocity in Satellite Orbit Theories

Error bounds on position and velocity in satellite orbit theorie

Propagation of a laser beam in a plasma

This paper shows that for a nonabsorbing medium with a prescribed index of refraction, the effects of beam stability, line focusing, and beam distortion can be predicted from simple ray optics. When the paraxial approximation is used, diffraction effects are examined for Gaussian, Lorentzian, and square beams. Most importantly, it is shown that for a Gaussian beam, diffraction effects can be included simply by adding imaginary solutions to the paraxial ray equations. Also presented are several procedures to extend the paraxial approximation so that the solution will have a domain of validity of greater extent

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