Geodesic
Mathematical modeling of femtosecond pulse propagation
Matematičeskoe modelirovanie, Tome 18 (2006) no. 4, pp. 3-18

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This paper is devoted to the investigation of the femtosecond pulse propagation in the air by means of numerical methods. The phenomenon behavior is determined by the relation between the multiphoton ionization and small-scale self-focusing (filamentation). A sharp decrease of the problem actual size during self-focusing and necessity need of the accuracy for the approximation of calculations result in the numerical meshes of small-scale with number of steps about of 1012. These calculations were made by means of the cluster with using of parallel programming algorithms. The step-by-step behaviour of this process was established, where the evolution of filamentation takes place without energy losses till the intensity reaches the threshold value. Then the dissipation for ionization comes into play and the intensity starts to decrease under defocusing influence of electron plasma. The conditions for repeated self-focusing can be formed after the intensity is below the ionization threshold. 
@article{MM_2006_18_4_a0,
     author = {A. D. Balashov and A. Kh. Pergament},
     title = {Mathematical modeling of femtosecond pulse propagation},
     journal = {Matemati\v{c}eskoe modelirovanie},
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     publisher = {mathdoc},
     volume = {18},
     number = {4},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2006_18_4_a0/}
}
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A. D. Balashov; A. Kh. Pergament. Mathematical modeling of femtosecond pulse propagation. Matematičeskoe modelirovanie, Tome 18 (2006) no. 4, pp. 3-18. http://geodesic.mathdoc.fr/item/MM_2006_18_4_a0/