Analysis of the data on the electronic avalanche obtained from numerical solutions of differential-difference and diffusion-type equations (Abstract Only)

Vladimir N. Strekalov; A. V. Voronenko

doi:10.1117/12.344373

7 April 1999 Analysis of the data on the electronic avalanche obtained from numerical solutions of differential-difference and diffusion-type equations (Abstract Only)

Vladimir N. Strekalov, A. V. Voronenko

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Proceedings Volume 3578, Laser-Induced Damage in Optical Materials: 1998; (1999) https://doi.org/10.1117/12.344373
Event: Laser-Induced Damage in Optical Materials: 1998, 1998, Boulder, CO, United States

Abstract

Heating of electrons by light and impact ionization of the crystal valence band are described by a complicated differential-difference equation. An analytical solution to this equation is not so far found. To simplify the problem, the unknown solution of the exact equation is presented in a form of Taylor series. Then the initial equation is replaced by an approximate differential equation. Usually, it is a diffusion type of equation. Such approach is the most common for theoretical studies of optical damage. But this step has no real grounds. Consequently we need some possibilities for verification ofthe approximate equations. We suggest using of a numerical method for solving of this equation which is suitable for all equations. It allows us to compare different descriptions of the same phenomenon. If the results are similar then we can suppose that the Taylor's method can be used, and the analytical expressions based on this method are corrected. However we have shown that there is no such similarity of the results (in optical range of frequencies). So, using of Taylor's series and the diffi.ision-like type of equations is not correct. We must look for other methods for exact solving of the initial equation.

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Vladimir N. Strekalov and A. V. Voronenko "Analysis of the data on the electronic avalanche obtained from numerical solutions of differential-difference and diffusion-type equations (Abstract Only)", Proc. SPIE 3578, Laser-Induced Damage in Optical Materials: 1998, (7 April 1999); https://doi.org/10.1117/12.344373

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KEYWORDS

Numerical analysis

Crystals

Differential equations

Diffusion

Electrons

Ionization

Laser optics

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