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Solutions of the nonlinear paraxial equation due to laser plasma–interactions

Published online by Cambridge University Press:  01 March 2004

F. OSMAN ,
R. BEECH  and
H. HORA
F. OSMAN
Affiliation:
School of Quantitative Methods & Mathematical Sciences, University of Western Sydney, Penrith South, Australia
R. BEECH
Affiliation:
School of Quantitative Methods & Mathematical Sciences, University of Western Sydney, Penrith South, Australia
H. HORA
Affiliation:
Department of Theoretical Physics, University of New South Wales, Sydney, Australia
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Abstract

This article presents a numerical and theoretical study of the generation and propagation of oscillation in the semiclassical limit ħ → 0 of the nonlinear paraxial equation. In a general setting of both dimension and nonlinearity, the essential differences between the “defocusing” and “focusing” cases are observed. Numerical comparisons of the oscillations are made between the linear (“free”) and the cubic (defocusing and focusing) cases in one dimension. The integrability of the one-dimensional cubic nonlinear paraxial equation is exploited to give a complete global characterization of the weak limits of the oscillations in the defocusing case.

Keywords

Laser-plasma interactionsNonlinear paraxial equationOscillationsWave propagation
Type
Research Article
Information
Laser and Particle Beams , Volume 22 , Issue 1 , March 2004 , pp. 69 - 74
Copyright
2004 Cambridge University Press

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References

REFERENCES

Boreham, B., Bolton, P.R., Newman, D.S., Obolu, S., Hora, H., Aydin, M., Azechi, H., Cicchiellit, L., Eliezer, S., Goldsworthy, M.P., Häuser, T., Kasotakis, G., Kitagawa, Y., Martinez-Val, J.M., Mima, K., Murakami, M., Nishihara, K., Piera, M., Ray, P.S., Schied, W., Sarris, E., Stening, R.J., Takabe, H., Velarded, G., Yamanaka, M., Yamanaka, T., Castillo, R. & Osman, F. (1998). Beam matter interaction physics for fast ignitors. Fusion Eng. Design. 44, 215.CrossRefGoogle Scholar
Esarey, E., Sprangle, P., Kroll, N.M. & Ting, A. (1997). IEEE J. Quantum Electron. QE-33, 1879.
Fornberg, B. & Whitman, G.B. (1978). A numerical and theoretical study of certain nonlinear wave phenomena. Phil. Trans. Roy. Soc. A 289, 373–404.CrossRefGoogle Scholar
Häuser, T., Scheid, W. & Hora, H. (1992). Phys. Rev. A 45, 1278.
Hora, H. (1991). Plasmas at High Temperature & Density: Applications & Implications of Laser-Plasma Interaction. Heidelberg, New York: Springer-Verlag.
Hora, H. (2000). Laser Plasma Physics: Forces and the Nonlinearity Principle. Bellingham, WA: SPIE Press.
Osman, F. (1998). Nonlinear Paraxial Equation at Laser Plasma Interaction. PhD Thesis, University of Western Sydney, Australia.
Tabak, M., Hammer, J., Glimsky, M.E., Kruer, W.L., Wilks, S.C., Woodworth, J., Campbell, E.M., Perry, M.D. & Mason, R.J. (1993). Plasma Phys. 1, 1626.
Wang, J.X., Ho, Y.K., Kong, Q., Zhu, L.J., Feng, L., Scheid, W. & Hora, H. (1998). Phys. Rev. E 58, 6575.
Zakharov, V.E. & Shabat, A.B. (1973). Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media. Sov. Phys. JETP 34, 62–69.Google Scholar