Abstract
In this paper, the effect of charge gradient in a one-dimensional dusty plasma crystal is considered to investigate shock structure. Under the continuum limit, the nonlinear Korteweg–de Vries (KdV)–Burgers equation with a charge gradient effect is derived using the reductive perturbation method. Then, the shock solution based on the KdV–Burgers equation is obtained. The influence of the parameter ε, which measures the effect of charge gradient on the dynamic of the shock wave, is discussed in detail. It is found that the shock amplitude and strength increase with the increase in the parameter ε. Furthermore, it is also found that charge gradient effect makes oscillatory shock more easily converted to monotonic shock.
Highlights
Over the last few decades, dust crystal has been the most interesting discovery in dusty plasma.1,2 Ikezi3 first theoretically predicted in 1986 that when dust particle potential energy exceeds its kinetic energy, i.e., the coupling parameter Γ ≫ 1, dusty plasma can spontaneously form ordered structure, which is called a dusty plasma crystal
Since the coefficients α and β are related to the dispersion term Ω∥, which is modified by charge gradient effect, we focus on studying the effect of the parameter ε of charge gradient on shock structure and shock strength in Sec
Due to the fact that the dynamic damping causes a dissipative effect of the dust lattice, an oscillatory shock is generated when the dissipative effect is weak, while a monotonic shock wave is formed when the dissipative effect is strong
Summary
Over the last few decades, dust crystal has been the most interesting discovery in dusty (complex) plasma. Ikezi first theoretically predicted in 1986 that when dust particle potential energy exceeds its kinetic energy, i.e., the coupling parameter Γ ≫ 1, dusty plasma can spontaneously form ordered structure, which is called a dusty plasma crystal. Dust lattice waves (DLWs) are one of the most important aspects of dust crystal research, which have been extensively studied by a simple one-dimensional (1D) infinite straight dust chain mode.. Weakly coupled dusty plasmas only support dust acoustic wave (i.e., longitudinal wave) propagation. Strongly coupled dusty plasmas can support both longitudinal and transverse mode propagation. Melandsø first introduced the method of solid-state physics to study the linear and non-linear wave propagation in a 1D dusty plasma lattice and found that the results of analytical expressions and particle simulations are consistent. The dispersion relation of longitudinal waves in a 1D dusty plasma lattice was obtained by Otani et al.. Liu et al. observed a transverse optical mode and calculated the dispersion relation of transverse waves The dispersion relation of longitudinal waves in a 1D dusty plasma lattice was obtained by Otani et al. Soon after, Liu et al. observed a transverse optical mode and calculated the dispersion relation of transverse waves
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