Self-excited Regime Research Articles

Intermittency route to self-excited chaotic thermoacoustic oscillations

In nonlinear dynamics, there are three classic routes to chaos, namely the period-doubling route, the Ruelle–Takens–Newhouse route and the intermittency route. The first two routes have previously been observed in self-excited thermoacoustic systems, but the third has not. In this experimental study, we present evidence of the intermittency route to chaos in the self-excited regime of a prototypical thermoacoustic system – a laminar flame-driven Rijke tube. We identify the intermittency to be of type II from the Pomeau–Manneville scenario through an analysis of (i) the probability distribution of the quiescent epochs between successive bursts of chaos, (ii) the first return map, and (iii) the recurrence plot. By establishing the last of the three classic routes to chaos, this study strengthens the universality of how strange attractors arise in self-excited thermoacoustic systems, paving the way for the application of generic suppression strategies based on chaos control.

Transit-time diodes and transistors with variable injection for generation and detection of THz radiation

The non-linear model of THz generation in variable injection transit-time structures coupled with antenna is proposed. The simulation demonstrates the crossover from the initial harmonic regime of selfexcitation to non-harmonic generation in the developed stage.

Possible gyrotron operation in the “no start current” zone caused by the axial dependence of the phase of the resonator field

It is known that gyrotrons (as well as other electron beam driven microwave and millimeter-wave oscillators) can operate in the regime of either soft or hard self-excitation. In the regime of soft self-excitation, the beam current exceeds its starting value; thus, the oscillations can start to grow from the noise produced by electrons. In the regime of hard self-excitation, the beam current is less than its starting value. Therefore, for exciting the oscillations, a certain start-up scenario is required, which may include the variation of the mod-anode and/or beam voltage or the guiding magnetic field. It was found recently [O. Dumbrajs and G. S. Nusinovich, Phys. Plasmas 25, 013121 (2018)] that some gyrotrons can also operate in the region of magnetic fields where there is no start current at all. In the present paper, it is shown that this sort of operation can be attributed to the presence of the axial dependence of the phase of the resonator field.

A Nonlinear Relaxation Mechanism of the Filtering Noise Generation in Porous Media

We propose a model that explains the microscopic origin of the nonstationarity and related filtering noise generation in porous media. The noise is not determined by hydrodynamic sources, and the transition to a turbulent flow regime in pores is not required for its occurrence. The physical mechanism of a nonstationary flow is connected with the development of instability at contacts inside cracks or grains, as well as with the presence of relaxation phenomena in voids and channels always available in rocks. It has been shown that the structural elements in rocks provide a self-excited oscillation regime. The proposed model is in good agreement with known experimental data.

Efficiency of gyrotrons with a tapered magnetic field in the regime of soft self-excitation

As a rule, gyrotron operation with high efficiency is realized in the regime of hard self-excitation that requires a special start-up scenario: either a tuning of the external magnetic field or providing certain relations between mod-anode and beam voltages. This paper describes a study of gyrotron operation in slightly tapered external magnetic fields. It is shown how the use of tapered magnetic fields affects the maximum efficiency realizable in hard and soft excitation regimes. First, a model of gyrotron with the Gaussian axial profile of the resonator field is studied. Then, a similar treatment is done for a realistic resonator designed for a 140 GHz Karlsruhe Institute for Technology gyrotron.

The Use of Piezoelectric Structures for the Purpose of Creating a String Transducer Based on an Self-Vibratory System

Structures based on piezoelectric materials are now fi nding applications in different fi elds related to monitoring and control of vibratory and periodic motions of different structures [1, 2]. Such structures may be used not only for vibration damping or control of given deformation regimes. The use of piezoelectric materials is critical for the creation of new sensing elements of sensors of physical quantities based on monocrystalline silicon, silicon carbide, and other materials. In the present article we will be giving a preliminary analysis of a string (frequency) sensing element made of crystalline silicon possessing a piezoelectric structure based on fi lms of lead zirconate-titanate PbZr 0.48 Ti 0.52 O 3 and functioning in a self-excited oscillator regime.

Self-excited regime of sedimentation of partially molten rocks

We consider the phenomenon of sedimentation of partially molten rocks in intrusions. During the sedimentation of the suspension, a stratified structure consisting of zones with different degree of compaction of the solid phase appears. The highest degree of compaction corresponds to a poroviscous medium. With a critical porosity at the boundary, this medium is overlaid by a thin intermediate layer. The supercritical porosity values correspond to the violation in the skeleton’s connectivity. Within the thin layer, the skeleton of the poroviscous medium generally retains its properties, although in a strongly reduced form. The grains bounded by strong hydrodynamical bonds form the structures characterized by instability. During the sedimentation, these structures periodically collapse and recover, which is perceived as periodic self-excited oscillations on the macroscopic level. The self-excited sedimentation regime leads to the formation of a periodical layered structure in the cumulates, which is detectable many millions of years after the solidification of the intrusive chamber. This process is studied in the present paper.

Surface stress on three-terminal vibrational nanomechanical transistor

The impact of the surface effect induced stress on a nanomechanical transistor (NMT) is investigated. It is shown that the surface stress of the doubly clamped beam in the NMT causes an increased resonant frequency, whereas a fluctuated average electrical current. The self-excitation regime of the NMT is studied through bifurcation calculation, which is extended with the surface stress considered.

Dependence of the gyrotron efficiency on the azimuthal index of non-symmetric modes

Development of MW-class gyrotrons for future controlled fusion reactors requires careful analysis of the stability of high efficiency operation in very high-order modes. In the present paper, this problem is analyzed in the framework of the non-stationary self-consistent theory of gyrotrons. Two approaches are used: the one based on the wave envelope representation of the resonator field and the second one based on representation of this field as a superposition of eigenmodes, whose fields are determined by a self-consistent set of equations. It is shown that at relatively low beam currents, when the maximum efficiency can be realized in the regime of soft self-excitation, the operation in the desired mode is stable even in the case of a very dense spectrum of competing modes. At higher currents, the maximum efficiency can be realized in the regimes with hard self-excitation; here the operation in the desired mode can be unstable because of the presence of some competing modes with low start currents. Two 170 GHz European gyrotrons for the international thermonuclear experimental reactor are considered as examples. In the first one, which is the 2 MW gyrotron with a coaxial resonator, the stability of operation in a chosen TE34,19-mode in the presence of two sideband modes with almost equidistant spectrum is analyzed and the region of magnetic fields in which the oscillations of the central mode are stable is determined. The operation of the second gyrotron, which is the 1 MW gyrotron with a cylindrical cavity currently under development in Europe, is studied by using the wave envelope approach. It is shown that high efficiency operation of this gyrotron in the TE32,9-mode should be stable.

Internal wave radiation by a turbulent fountain in a stratified fluid

Large eddy simulation is applied to model a fountain in a density-stratified fluid. The fountain is formed, as a vertical turbulent jet penetrates through a pycnocline. The jet flow is initiated by the formulation of a boundary condition in the form of an upward neutral-buoyancy fluid flow with the Gaussian axisymmetric mean-velocity profile and a given fluctuation level. It is shown that at a Froude number Fr higher than a certain critical value the fountain executes self-oscillations accompanied by internal wave generation within the pycnocline. The predominant self-oscillation mode is axisymmetric, when the fountain top periodically breaks down generating internal wave packets traveling toward the periphery of the computation domain. The characteristic frequency of the internal waves coincides with that of the fountain top oscillations and monotonically decreases with increase in Fr. The Fr-dependence of the fountain top oscillation amplitude obtained in the numerical solution is in good agreement with the predictions of the theoretical Landau model for the instability mode in the soft self-excitation regime.

Investigation on a nanomechanical transistor

In this paper, we propose the mathematical model of a novel device, the nanomechanical transistor, able to control a current through a small drive voltage. The novelty of the device relies in its mechanical working principle where nanopillars vibrate between electrodes under a self-excitation regime which provides a continuative electric charge transportation. The dynamics of the investigated system involves electromechanical phenomena with the addition of quantum effects due to the electron tunneling of charges from pillars to electrodes. The theory here presented is an attempt to build a general model for those multiphysics phenomena (electrical-mechanical with presence of quantum effects) frequently met in nanotechnology that do not fit yet into a systematic frame.

Self - Excited Vibration Arising from Tribology - Dynamic Interaction

An elastic contact model of a pad/disc system is developed which can give some explanations on self-excited vibration induced during continuous dry friction. Based on this model, it is possible to show that establishement and sustainability of self-excited vibration in disc brake system are linked to the interface properties as well as the physical properties of the disc brake components. It is shown using theoretical and experimental analysis that the regime of self-excited vibrations can be triggered when approaching any of the modified resonant frequencies of either pad or disc system. These frequencies are dependant upon contact stiffness value during self-excitation regime. Experimental investigations have also shown that contact stiffness during sustained self-excitation may increase monotonically upto 35% of its initial value due to continuous wear and sliding. One of the main findings in this work, is that the resonance of any of the system frequencies is linked mainly to the established value of contact stiffness due to wear, load and speed. Also, for each self-excited regime, there is a limiting frequency after which the self-excited regime either sustains at this frequency or change to another regime. Sudden changing of load or speed at this limiting frequency may cause the transition from one regime of self-excitation to another.

Observation of Dynamic Interactions between Fundamental and Second-Harmonic Modes in a High-Power Sub-Terahertz Gyrotron Operating in Regimes of Soft and Hard Self-Excitation

Dynamic mode interaction between fundamental and second-harmonic modes has been observed in high-power sub-terahertz gyrotrons [T. Notake et al., Phys. Rev. Lett. 103, 225002 (2009); T. Saito et al. Phys. Plasmas 19, 063106 (2012)]. Interaction takes place between a parasitic fundamental or first-harmonic (FH) mode and an operating second-harmonic (SH) mode, as well as among SH modes. In particular, nonlinear excitation of the parasitic FH mode in the hard self-excitation regime with assistance of a SH mode in the soft self-excitation regime was clearly observed. Moreover, both cases of stable two-mode oscillation and oscillation of the FH mode only were observed. These observations and theoretical analyses of the dynamic behavior of the mode interaction verify the nonlinear hard self-excitation of the FH mode.

Internal wave generation by a fountain in a stratified fluid

The purpose of the study is the direct numerical and theoretical modeling of fountain dynamics in a fluid with density stratification in the form of a pycnocline. The fountain is formed as a vertical jet penetrates through the pycnocline. In numerical simulation the jet flow is initiated by means of preassigning a boundary condition in the form of an upward-directed laminar flow of a neutral-buoyancy fluid with an axisymmetric Gaussian velocity profile. The calculations show that at a Froude number Fr greater than a certain critical value the flow becomes unstable and the fountain executes self-oscillations accompanied by internal wave generation in the pycnocline. Depending on Fr, two self-oscillation modes can be distinguished. At fairly low Fr the fountain executes circular motion in the horizontal plane, in the vicinity of the center of jet, its shape remaining almost invariant. In this case, internal waves in the form of unwinding spirals are radiated. At fairly high Fr another mode predominates, when the fountain top chaotically “strays” in the vicinity of the center of the jet and, periodically breaking down, generates wave packets propagating toward the periphery of the computation domain. In both cases, the main peak in the frequency spectrum of the internal waves coincides with the fountain top oscillation frequency which monotonically decreases with increase in Fr. In numerical simulation the Fr-dependence of the fountain top oscillation amplitude is in good agreement with that predicted by the theoretical model of the concurrence of the interacting modes in the soft self-excitation regime.

Vortex shedding in high Reynolds number axisymmetric bluff-body wakes: Local linear instability and global bleed control

In the present work we study the large-scale helical vortex shedding regime in the wake of an axisymmetric body with a blunt trailing edge at high Reynolds numbers, both experimentally and by means of local, linear, and spatiotemporal stability analysis. In the instability analysis we take into account the detailed downstream evolution of the basic flow behind the body base. The study confirms the existence of a finite region of absolute instability for the first azimuthal number in the near field of the wake. Such instability is believed to trigger the large-scale helical vortex shedding downstream of the recirculating zone. Inhibition of vortex shedding is examined by blowing a given flow rate of fluid through the base of the slender body. The extent of the locally absolute region of the flow is calculated as a function of the bleed coefficient, Cb=qb/(πR2u∞), where qb is the bleed flow rate, R is the radius of the base, and u∞ is the incident free-stream velocity. It is shown that the basic flow becomes convectively unstable everywhere for a critical value of the bleed coefficient of Cb*∼0.13, such that no self-excited regime is expected for Cb>Cb*. In addition, we report experimental results of flow visualizations and hot-wire measurements for increasing values of the bleed coefficient. When a sufficient amount of base bleed is applied, flow visualizations indicate that vortex shedding is suppressed and that the mean flow becomes axisymmetric. The critical bleed coefficient predicted by linear instability analysis is shown to fall within the experimental values in the range of Reynolds numbers analyzed here.

Self-excitation and operational characteristics of the crossed-field secondary emission electron source

We have investigated the crossed-field secondary emission (CFSE) electron source which is of a magnetron type with smooth cylindrical electrodes and axial applied magnetic field. It initiates at the negative slope d|U|/dt<0 of the high voltage pulse U∼10–40 kV, but further current production is maintained by a self-sustained secondary electron emission regardless to the voltage pulse shape. The output electron beam is tubular with a thin ∼1 mm wall. This article is concerned mainly with the identification of the mechanisms governing the excitation and generation of the electron beam and with the determination of the principles upon which the “optimal” CFSE electron source should be designed. We have demonstrated that the CFSE diode starts operation in a self-excitation regime (i.e., without application of the primary current) provided there is a partial trapping of the multiplying electrons inside the diode boundaries. The required axial decelerating force can be established with the use of either axial electric or nonuniform magnetic fields. Amongst all of the practical methods tested (shifting of the anode with respect to the cathode, double diode, diodes with ferromagnetic parts, use of the nonuniform external magnetic field), the diode with a ferromagnetic ring insert inside the cathode cylinder has been shown to be the most successful. It has generated an ∼240 A electron beam with a perveance of ∼85 μA/V3/2. The operating range of the CFSE diode is limited by both low and high magnetic fields. The lower limit arises from a necessity to comply with a Hull cutoff condition. The upper limit is determined by the time required for development of an electron avalanche. A secondary electron emission mechanism of current production in the CFSE diode allows the diode to operate in an oscillating regime when the applied magnetic field is higher but close to the Hull cutoff value. It has thus been possible to generate 100% density modulated electron beams at a modulation frequency of ∼107 Hz in our present experiments with the possibility of further increases up to ∼108 Hz. A geometrical scaling law for the CFSE diodes has been deduced empirically. It states that the perveance of the output electron beam is proportional to the geometrical factor X=(Dk/de)(Ld/de−0.8), where Dk is the cathode diameter, de is an effective diode gap, and Ld is the diode length. The scaling law provides a tool for designing the CFSE diodes and predicting the ultimate beam currents. For a practical size of device, this electron current could be as high as ∼1 kA.

Self-excited oscillatory regimes in the growth of thin films from a multicomponent vapor: Dynamics and control

A model system describing the nucleation of films from a multicomponent vapor with allowance for chemical reactions between different components in the initial phase is investigated in detail. It is shown that the condensation of thin films can proceed by different avenues, depending on the values of external parameters such as the temperature or the precipitation rate of particles of the component that limits the chemical reaction. In particular, low precipitation rates are characterized by a stable condensation regime, in which any deviations from equilibrium die out. At medium precipitation rates the phase transition takes place in a self-excited oscillatory regime corresponding to a stable limit cycle. Finally, at high precipitation rates the stable limit cycle breaks up, and the new phase usually condenses in a sawtooth (accretion) regime. A procedure is developed for controlling the given oscillatory processing by judicious time variation of the external parameters. The investigated system is found to have a special kind of memory in that for external parameters with identical values but different histories the films condense differently; even a slight difference in the past behavior of the external parameters can lead to different precipitation regimes. It is concluded that these memory effects are in fact responsible for the poor reproducibility encountered in some cases of experiments on film growth utilizing chemical reactions.