Open Journal Systems

Weibel instability in Weakly Relativistic Laser Fusion Plasma

slimen belghit


In this work, we used the MATLAB code to calculate the growth rate of the Weibel instability (WI) in weakly relativistic parameters of laser-plasma interaction in the inertial thermonuclear fusion. In this study, the basic equation is the relativistic Fokker-Planck equation (FPE). However in our paper, the distribution function is not supposed but it is calculated from FPE by considering the fusion plasma heating by the laser source and the collisions term which corresponds to the laser fusion experiments. The main obtained result is a decrease in the spectral range of Weibel unstable modes. This decreasing is accompanied by a reduction of two orders in the growth rate spectrum of instability, this spectrum presents a maximum, which can be in terpreted by the competition between the loss effects (collisions and Landau damping) and the inverse bremsstrahlung absorption (IBA) with parameters of laser-plasma interactions.


relativistic Weibel instability, laser fusion plasma, static magnetic field, stabilization, Relativistic laser plasma interaction.

Full Text:



E. S. Weibel , Phys. Rev. Lett. 2, 83 (1959).

K. Bendib, A. Bendib and A. Sid, Laser and Particle Beams 16, 3 (1998).

L. Bhatanagar,E.P.Gross,M.Krook,phys,rev,94,511(1954)

Slimen Belghit and Abdelaziz Sid, PHYSICS OF PLASMAS 23, 063104 (2016)

I. P. Shkarofsky, T.W. Johnston and M.P. Bachynski, The particule Kinetic of Plasmas, (Addison-Wesley) 1966.

M. Abramowitz and I. Stegun, Handbook of Mathematical Functions, (Dover, New York 1970).

T. M. Macrobert. Spherical harmonics an elementary treatise on harmonic functions with applications second edition, revised. 1947.

A. B. Langdon, Phys. Rev. Lett. 44, 575 (1980).

A. Bendib, K. Bendib and A. Sid, Phys. Rev. E55, 7522 (1997).

A. Bendib and J. F. Luciani, Phys. Fluids 30, 1353 (1987).

A. Sid, S. Belghit and A. Ghezal ,25th IAEA Fusion Energy Conference IAEA CN-221-IFE/P6-8,2014.

Wright, T. P. & Hadley, G. R. (1975).. Phys. Rev. A 12, no. 2, p. 686.697

D. Pesme, La fusion thermonucléaire contrôlée par laser, Ed. R. Dautrey et J. P. Watteau (Eyrolles, Paris 1993).

J. D. Lindl, R. L. McCroy and E. M. Campbell, Progress towards and burn propagation in inertiel confinement fusion, Phys. Today, 34, (1992).

P. Alaterre, J. P. Matte and M. Lamoureux, Phys. Rev. A 34, 1578 (1986).

J. P. Matte and all, Plasma Phys. Controlled Fusion 30, 1665 (1988).

A. Sid, Physics of Plasmas, 1, 214 (2003).

(84 Abstract Views, 57 PDF Downloads)


  • There are currently no refbacks.

Copyright (c) 2019 slimen belghit

Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.