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We study the properties of the intensity profiles scattered from the self-affine fractal random surfaces. We use the mathematical decay function to approximate the duple negative exponent function in the rigorous theory of scattering, by letting them have the same maximum value and half-width, and the expression for the half-widths of the intensity profiles in the whole range of the perpendicular wave vector component is obtained. The previous results in the two extreme cases are included in the results of this paper. In the simulational verification, we propose a method for the generation of self-affine fractal random surfaces, using the square-root of Fourier transform of the correlation function of the surface height. The simulated results conform well with the theory.

Theoretical studies and analytical scalings were carried out to find the optimized laser parameters and target conditions so that ultrashort hard x-ray pulses and high x-ray power could be achieved. The dependence of laser intensity and wavelength on the yield of K-shell x-ray emission was studied. We propose an optimal design for a foil target for producing high-yield hard x-ray pulses of customizing duration.

The Problems of resonant absorption in laser-plasma interactions are analyzed by means of a new method. First, we obtain an analytical expression for the electromagnetic field structure of resonant absorption, which is valid for all regions of the coronal plasma and correctly reflects various fundamental features. Then, we derive the absorption coefficient in the form of an elementary function. The results are in excellent agreement with numerical calculations for all angles of incidence. This work extends previous results obtained by solving the wave equation.

The hydrodynamic modification of an expanding plasma near the reflection point of an electron plasma wave is investigated by simultaneously solving the wave equation together with the steady-state hydrodynamic equations. The electric field and electron density fluctuation of the plasma wave are derived in a self-consistently steepened density profile while the density jump and its dependence on the wave amplitude are also determined.