Stability and evolution of wave packets in strongly coupled degenerate plasmas

Abstract

We study the nonlinear propagation of electrostatic wave packets in a collisional plasma composed of strongly coupled ions and relativistically degenerate electrons. The equilibrium of ions is maintained by an effective temperature associated with their strong coupling, whereas that of electrons is provided by the relativistic degeneracy pressure. Using a multiple scale technique, a (3+1)-dimensional coupled set of nonlinear Schrödinger-like equations with nonlocal nonlinearity is derived from a generalized viscoelastic hydrodynamic model. These coupled equations, which govern the dynamics of wave packets, are used to study the oblique modulational instability of a Stoke's wave train to a small plane wave perturbation. We show that the wave packets, though stable to the parallel modulation, becomes unstable against oblique modulations. In contrast to the long-wavelength carrier modes, the wave packets with short-wavelengths are shown to be stable in the weakly relativistic case, whereas they can be stable or unstable in the ultra-relativistic limit. Numerical simulation of the coupled equations reveals that a steady state solution of the wave amplitude exists together with the formation of a localized structure in (2+1) dimensions. However, in the (3+1)-dimensional evolution, a Gaussian wave beam self-focuses after interaction and blows up in a finite time. The latter is, however, arrested when the dispersion predominates over the nonlinearities. This occurs when the Coulomb coupling strength is higher or a choice of obliqueness of modulation, or a wavelength of excitation is different. Possible application of our results to the interior as well as in an outer mantle of white dwarfs are discussed.

Nano breathers and molecular dynamics simulations in hydrogen-bonded chains

“…The results of the modulational instability suggest that when plane waves are highly unstable, it leads to the formation of spatially localized structures. This MI-induced energy localization has been proposed to be the mechanism responsible for the formation of intrinsic localization by many authors [63][64][65][66][67][68][69]. The normalized energy density distribution is represented by…”

Characteristics of solitary waves in a relativistic degenerate ion beam driven magneto plasma

“…al. and Misra and Shukla [46,47]. Here since we have used the pressure equation in full form, so we have the freedom of choosing any density corresponding to S0<1 or S0>1 for the case of weakly (or non-relativistic) and relativistic case respectively.…”

Relativistically modulational instability by strong Langmuir waves

“…Misra and Shukla investigated the multidimensional modulation of electrostatic wave packets propagating in ultra-relativistic degenerate dense plasma. 18,19 Chakraborty and Das obtained the MI condition for a uniform electromagnetic wave train due to inclusion of the weak relativistic effect. 20 Shivamoggi investigated the relativistic MI of an intense circularly polarized electromagnetic wave propagating along a constant external magnetic field in the plasma.…”