Influence of wake field inhomogeneity on the vibrational spectra of two dust particles in a plasma with an ion flow

A charged colloidal (dust) particle immersed in a plasma with an ion flow creates a disturbed region behind it, known as a wake. The paper considers a system of two charged and strongly coupled microparticles aligned along the ion flow in a weakly ionized plasma (e.g., in the plasma sheath of a ground-based RF discharge) and confined vertically by an external electric field. Using the OpenDust code, a fully self-consistent numerical simulation of the dynamics of dust particles and the ionic component is carried out. It is demonstrated that the inhomogeneity of the wake field from the upstream particle can significantly change the spectrum of vertical (longitudinal) vibrations of both particles in the system and has a negligible effect on their horizontal (transverse) vibrations. In particular, a relationship exists between horizontal and vertical particle oscillations, manifested as an additional mode of vertical vibrations of particles corresponding to the doubled frequency of their relative horizontal vibrations. In accordance with the model of nonreciprocally coupled stochastically driven oscillators, analytical expressions are derived for the vibrational spectra of particles taking into account the spatial variations in particle charges caused by inhomogeneities in the surrounding plasma. The proposed theory improves the experimental method of spectral response to stochastic processes, enabling the measurement of effective forces, particle friction coefficients, and temperatures of their heat sources, as well as the horizontal charge gradient of the lower particle oscillating in the wake field of the upper one.