Reflection and transmission of an incident solitary wave at an interface of a binary complex plasma in a microgravity condition

Theoretical results are given in the present paper, which can well explain the experimental observations performed under microgravity conditions in the PK-3 Plus Laboratory on board the International Space Station about the propagation of a solitary wave across an interface in a binary complex plasma. By using the traditional reductive perturbation method and the continuity conditions of both the electric potential and the momentum at the interface, we obtain the equivalent “initial conditions” for both the transmitted wave and the reflected waves from the incident wave. Then we obtain the numbers of the reflected and the transmitted solitary waves as well as all the wave amplitudes by using the inverse scattering method. The ripples of both reflection and transmission have also been given by using the Fourier series. The number of the reflected and the transmitted solitary waves produced by interface, as well as all the solitary wave amplitudes, depend on the system parameters such as the number density, electric charge, mass of the dust particles, and the effective temperature in both regions. The analytical results agree with observations in the experiments.

Figure 1

Propagation of a solitary wave in a phase-separated binary complex plasma in the experiment performed in the PK-3 Plus laboratory on board ISS under microgravity conditions [23]. In each panel, three consecutive recorded images with a interval of 0.02 s are filtered and overlayedand are in blue, green, and red, respectively. The approximate locations of the solitary wave are highlighted by the yellow boxes. Gas pressure is 10 Pa.

Figure 2

Propagation of a solitary wave in a phase-separated binary complex plasma in the Langevin dynamics simulation [23]. Gas pressure is 5 Pa. The vertical velocity $v_z$ is exhibited by the color. The interface is marked by a gray square sheet.

Figure 3

Propagation characteristics of solitary waves in terms of particle $z$ velocity $v_z$ [(a)–(e)] and number density $n$ [(f)–(j)] in phased-separated binary complex plasmas. The analytical results are shown in columns 1 and 2. The results obtained from Langevin dynamics simulations are shown in columns 3 and 4. The experimental results are shown in column 5.

Figure 4

Particle $z$ velocity $v_z$ in the solitary waves. For the experiments and simulations, $v_z$ in the incident and transmitted waves are shown in square and triangle symbols, respectively, while that in the reflected waves is shown in circle symbols. The analytical results are shown by lines.