Resonance Phenomena in Extended Mathieu Equation

Student: Semenov Vladimir

Faculty: HSE Tikhonov Moscow Institute of Electronics and Mathematics (MIEM HSE)

Educational Programme: Mathematical Methods of Natural Sciences and Computer Technologies (Master)

Year of Graduation: 2016

Dynamics of dusty particles motion is studied analytically and numerically. Model of dusty plasma system is formulated. Mechanism of energy transfer between degrees of freedom based on parametric resonance is described by extended Mathieu equation. Resonance regions and growth rates of dust particles energy are obtained by analysis of this equation. The condition of parametric resonance in dusty plasma is evaluated from obtained results. First stages of energy transfer between degrees of freedom are described more precisely. It is shown that a wide spectrum of oscillations participates in a system heating. Obtained results are compared with experimental data.

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