Mixed-mode oscillations (MMOs) are trajectories of a dynamical system in which there is an alternation between oscillations of distinct large and small amplitudes. MMOs have been observed and studied for over thirty years in chemical, physical, and biological systems. Few attempts have been made thus far to classify different patterns of MMOs, in contrast to the classification of the related phenomena of bursting oscillations. This paper gives a survey of different types of MMOs, concentrating its analysis on MMOs whose small-amplitude oscillations are produced by a local, multiple-time-scale “mechanism.” Recent work gives substantially improved insight into the mathematical properties of these mechanisms. In this survey, we unify diverse observations about MMOs and establish a systematic framework for studying their properties. Numerical methods for computing different types of invariant manifolds and their intersections are an important aspect of the analysis described in this paper.

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Mixed-Mode Oscillations with Multiple Time Scales

Dusty plasmas are ubiquitous in low-temperature laboratory discharges as well as in the near-earth environment, planetary rings, and interstellar spaces. In this paper, updated knowledge of fundamentals of collective dust-plasma interactions and several novel phenomena are presented that have been observed in laboratories and in space dusty plasmas. Mechanisms that are responsible for the charging of dust grains are discussed, and the fact that the dust charge perturbation is a new dynamical variable in a dusty plasma. The underlying physics of different forces that act on a charged dust grain is reviewed. In dusty plasmas, there are new attractive forces (e.g., due to wakefield and ion focusing effects and dipole-dipole interactions between unevenly charged dust rods). Furthermore, in the presence of an ensemble of charged dust grains, there are collective dust-plasma interactions featuring new waves (e.g., the dust acoustic wave, the dust ion-acoustic wave, the dust lattice wave, etc.), new instabilities, and coherent nonlinear structures (dust acoustic and dust ion-acoustic shocks, dust voids, and dust vortices), which are also discussed. Theoretical models for numerous collective dust-plasma interactions are compared with existing observations from laboratories and space environments.

Colloquium : Fundamentals of dust-plasma interactions

Oscillation quenching mechanisms: Amplitude vs. oscillation death

The evolution of silicon cryoetching is reported in this topical review, from its very first introduction by a Japanese team to today's advanced technologies. The main advances in terms of the performance and comprehension of the mechanisms are chronologically presented. After presenting the principle of silicon cryoetching, the main defects encountered in cryoetching (such as undercut, bowing and crystal orientation dependent etching) are presented and discussed. Mechanisms involved in SiOxFy passivation layer growth in standard cryoetching are investigated through several in situ characterization experiments. The STiGer process and alternative cryoetching processes for high-aspect-ratio structures are also proposed to enhance the process robustness. The over-passivation regime, which can provide self-organized columnar microstructures, is presented and discussed. Finally, advanced technologies, such as the cryoetching of sub-20 nm features and porous OSG low-k cryoetching, are described.

https://iopscience.iop.org/article/10.1088/0022-3727/47/12/123001/pdf

Plasma cryogenic etching of silicon: from the early days to today's advanced technologies

Dedicated experiments on melting of two-dimensional plasma crystals were carried out. The melting was always accompanied by spontaneous growth of the particle kinetic energy, suggesting a universal plasma-driven mechanism underlying the process. By measuring three principal dust-lattice wave modes simultaneously, it is unambiguously demonstrated that the melting occurs due to the resonance coupling between two of the dust-lattice modes. The variation of the wave modes with the experimental conditions, including the emergence of the resonant (hybrid) branch, reveals exceptionally good agreement with the theory of mode-coupling instability.

Direct observation of mode-coupling instability in two-dimensional plasma crystals.

An on-ground measurement of dust-particle residual charges in the afterglow of a dusty plasma was performed in a rf discharge. An upward thermophoretic force was used to balance the gravitational force. It was found that positively charged, negatively charged, and neutral dust particles coexisted for more than 1 min after the discharge was switched off. The mean residual charge for 200-nm-radius particles was measured. The dust particle mean charge is about -5e at a pressure of 1.2 mbar and about -3e at a pressure of 0.4 mbar.

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Residual dust charges in discharge afterglow.

Instabilities in dusty plasmas are frequent phenomena. We show that some instabilities can be described by mixed-mode oscillations often encountered in chemical systems or neuronal dynamics and studied through dynamical system theories. The time evolution of these instabilities is studied through the change in the associated waveform. Frequency and interspike interval are analyzed and compared to results obtained in other scientific fields concerned by mixed-mode oscillations.

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Mixed-mode oscillations in complex-plasma instabilities.

When a three-dimensional dust cloud is present in a plasma, a dust-free region, called a void, is usually obtained in the plasma centre. Under certain conditions, this region exhibits a self-excited unstable behaviour consisting of successive contractions and expansions of its size. In this paper, this low frequency instability (few Hz), called a 'heartbeat', is characterised by various diagnostics. Electrical and optical measurements both correlated with high speed imaging brought to the fore the main features of this instability. Forces involved in the void existence are an inward electrostatic force and an outward ion drag one. The force balance ensures an open void but this equilibrium can be disturbed, leading to the observed instabilities. As these forces are strongly dependent on local ionisation conditions, correlations between physical processes in the plasma volume and the dust cloud motion are investigated through experimental results.

https://iopscience.iop.org/article/10.1088/1367-2630/9/8/268/pdf

Self-excited void instability in dusty plasmas: plasma and dust cloud dynamics during the heartbeat instability

Experiments with two-dimensional (2D) plasma crystals are usually carried out in rf plasma sheaths, where the interparticle interactions are modified due to the presence of plasma wakes. The wake-mediated interactions result in the coupling between wave modes in 2D crystals, which can trigger the mode-coupling instability and cause melting. The theory predicts a number of distinct fingerprints to be observed upon the instability onset, such as the emergence of a new hybrid mode, a critical angular dependence, a mixed polarization, and distinct thresholds. In this paper we summarize these key features and provide their detailed discussion, analyze the critical dependence on experimental parameters, and highlight the outstanding issues.

Lénaïc Couëdel

Papers

Direct observation of mode-coupling instability in two-dimensional plasma crystals.

Residual dust charges in discharge afterglow.

Mixed-mode oscillations in complex-plasma instabilities.

Self-excited void instability in dusty plasmas: plasma and dust cloud dynamics during the heartbeat instability

Wave mode coupling due to plasma wakes in two-dimensional plasma crystals: in-depth view