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Modulation instability; nonlinear dispersion relation; nonlinear governing equation; electron–positron–ion plasma.

The modulation instability of an intense circularly polarized laser beam propagating in an unmagnetized, cold electron–positron–ion plasma is investigated. Adopting a generalized Karpman method, a three-dimensional nonlinear equation is shown to govern the laser field. Then the conditions for modulation instability and the temporal growth rate are obtained analytically. In order to compare with the usual electron–ion plasmas, the effect of positron concentration is considered. It is found that the increase in positron-to-electron density ratio shifts the instability region towards higher vertical wave numbers but does not cause displacement along the parallel wave number direction, and the growth rate increases as the positron-to-electron density ratio increases.

San Qiu Liu¹ Wei Tang¹ Xiao Qing Li^{1 2}

1. Department of Physics, Nanchang University, Nanchang 330047, People’s Republic of China
2. Department of Physics, Nanjing Normal University, Nanjing 210097, People’s Republic of China

Manuscript received

18 May 2011

Manuscript revised

2 July 2011

Accepted

26 August 2011