Excitation Of Parametric Instability Research Articles

Parametric excitation of plane waves and traveling nonlinear surface charge structures by an oscillating electric field at the plasma boundary

With the help of a single equation, to which it was possible to reduce the original system of equations, it turned out to be possible to describe the excitation of parametric instability on plane surface waves in an alternating electric field, its saturation due to the nonlinearity of the surface charge and the generation of nonlinear structures of this charge propagating along the boundary and depending on the parameters of external influence. The amplitude of saturation of the increasing plane waves was found as a result of stabilization of parametric instability by the nonlinear effect of the surface charge. An example of a nonlinear wave structure propagating along the surface of the boundary as a result of the interaction of an external electric field with a nonlinear surface charge is presented.

An interview with Vladimir Tikhonchuk

Vladimir Tikhonchuk, Professor Emeritus at Centre Lasers Intenses et Applications, University of Bordeaux, France, and senior researcher at the Extreme Light Infrastructure ERIC, ELI-Beamlines Facility, Czech Republic. His research is in the domain of high energy density physics and nonlinear optics, including inertial confinement fusion (ICF), dynamic processes in laboratory astrophysics, laser–plasma interactions, excitation of parametric instabilities, generation of magnetic and electric fields, acceleration of charged particles and energy transport.

Studies of laser-plasma interaction physics with low-density targets for direct-drive inertial confinement fusion on the Shenguang III prototype

The physics of laser-plasma interaction is studied on the Shenguang III prototype laser facility under conditions relevant to inertial confinement fusion designs. A sub-millimeter-size underdense hot plasma is created by ionization of a low-density plastic foam by four high-energy (3.2 kJ) laser beams. An interaction beam is fired with a delay permitting evaluation of the excitation of parametric instabilities at different stages of plasma evolution. Multiple diagnostics are used for plasma characterization, scattered radiation, and accelerated electrons. The experimental results are analyzed with radiation hydrodynamic simulations that take account of foam ionization and homogenization. The measured level of stimulated Raman scattering is almost one order of magnitude larger than that measured in experiments with gasbags and hohlraums on the same installation, possibly because of a greater plasma density. Notable amplification is achieved in high-intensity speckles, indicating the importance of implementing laser temporal smoothing techniques with a large bandwidth for controlling laser propagation and absorption.

Anharmonic oscillations of the single dust particle trapped in a standing striation

The nonlinear features of the vibrational motion of a single dust particle trapped in a standing strip are investigated. The excitation of the nonlinear oscillations with the large amplitude of the order of 1.5 mm is due to the periodic movement of the standing striation caused by the square-wave modulation of the discharge current. The frequency responses are investigated depending on value of the modulation depth. The anharmonic effects of the dust particle oscillations such as parametric instabilities and hysteresis are obtained. The theory of the anharmonic oscillator provides a good quantitative description of the experimental data. The values of the thresholds of excitation of parametric instabilities, the anharmonic coefficients and the critical values of the oscillation amplitude for the hysteresis are calculated. The potential energy curve of the single dust particle trapped in the striation is calculated using the values of anharmonic coefficients.

Threshold of parametric instability in the ionospheric heating experiments

Many observations in the ionospheric heating experiment, by a powerful high frequency electromagnetic wave with ordinary polarization launched from a ground-based facility, is attributed to parametric instability (PI). In this paper, the general dispersion relation and the threshold of the PI excitation in the heating experiment are derived by considering the inhomogeneous spatial distribution of pump wave field. It is shown that the threshold of PI is influenced by the effective electron and ion collision frequencies and the pump wave frequency. Both collision and Landau damping should be considered in the PI calculation. The derived threshold expression has been used to calculate the required threshold for excitation of PI for several ionospheric conditions during heating experiments conducted employing EISCAT high frequency transmitter in Tromsø, Norway, on 2nd October 1998, 8th November 2001, 19th October 2012 and 7th July 2014. The results indicate that the calculated threshold is in good agreement with the experimental observations.

On mathematical models for describing parametric and modulation instabilities

The development of modulation instability of a finite amplitude wave is considered. A modified S-theory, previously developed in the works of V. Ye. Zakharov, was used to describe unstable modes. It is noted that near the instability threshold a self-similar spatial wave structure can form at different scales. The dynamics of the instability is analyzed in a model of a high intensity practically undamped oceanic wave, the mechanism of the formation of anomalous amplitude waves is shown. The modes of excitation of parametric instabilities are discussed. It is noted, that there is a similarity in the development of modulation and parametric instabilities, however there are also differences related to the nature of the dynamics of the wave packets of unstable perturbations. The nature of parametric instabilities is associated with the presence of a high-frequency, spatially homogeneous component of one or more parameters of the medium. Since the wave number of such HF oscillations is zero, or extremely small, in comparison with the characteristic lengths of the system, the spectrum of unstable disturbances is also located symmetrically, resembling the unstable spectrum of modulation instability. However, the growing perturbations practically do not move in space. Far from the threshold of parametric instability, a strong small-scale modulation of environmental parameters can form, which often takes on the character of a process with aggravation. The formation of self-similar spatial structures in the developed convection of a thin liquid or gas layer due to the development of modulation instability. The toroidal convection vortices generate poloidal vortices of large scale - the effect of a hydrodynamic dynamo and the experimental results of the investigation self-similar structures on the graphite are presented. The nature of self-consistent parametric instabilities is similar to the processes of modulation instability.

Aspect dependence of Langmuir parametric instability excitation observed by EISCAT

AbstractRecent studies of X‐mode wave heating experiments observed by EISCAT (European Incoherent Scatter Scientific Association UHF radar indicate that parametric instability (PI) can be excited unexpectedly. In this paper, we reinvestigate the ionospheric heating experiment on 21 and 22 October 2012 in details. The observed HF‐enhanced ion lines (HFILs) and HF‐enhanced plasma lines (HFPLs) observed during the experiments present dependence on the heating incidence angles. The observational evidence and numerical calculation that the parallel electric field of X‐mode heating wave can exceed the PI excitation threshold at certain angles indicate the decisive role of parallel electric field for the PI excitation. The excited HFPLs and HFILs during X‐mode heating cycles also present the evidence for the non‐Maxwellian distribution of the electrons in the heated region.

Parametric instability induced byX‐mode wave heating at EISCAT

AbstractIn this paper, we present results of parametric instability induced byX‐mode wave heating observed by EISCAT (European Incoherent Scatter Scientific Association) radar at Tromsø, Norway. Three typicalX‐mode ionospheric heating experiments on 22 October 2013, 19 October 2012, and 21 February 2013 are investigated in details. Both parametric decay instability (PDI) and oscillating two‐stream instability are observed during theX‐mode heating period. We suggest that the full dispersion relationship of the Langmuir wave can be employed to analyze theX‐mode parametric instability excitation. A modified kinetic electron distribution is proposed and analyzed, which is able to satisfy the matching condition of parametric instability excitation. Parallel electric field component ofX‐mode heating wave can also exceed the parametric instability excitation threshold under certain conditions.

A theoretical investigation on the parametric instability excited by X‐mode polarized electromagnetic wave at Tromsø

AbstractRecent ionospheric modification experiments performed at Tromsø, Norway, have indicated that X‐mode pump wave is capable of stimulating high‐frequency enhanced plasma lines, which manifests the excitation of parametric instability. This paper investigates theoretically how the observation can be explained by the excitation of parametric instability driven by X‐mode pump wave. The threshold of the parametric instability has been calculated for several recent experimental observations at Tromsø, illustrating that our derived equations for the excitation of parametric instability for X‐mode heating can explain the experimental observations. According to our theoretical calculation, a minimum fraction of pump wave electric field needs to be directed along the geomagnetic field direction in order for the parametric instability threshold to be met. A full‐wave finite difference time domain simulation has been performed to demonstrate that a small parallel component of pump wave electric field can be achieved during X‐mode heating in the presence of inhomogeneous plasma.

Ionospheric modifications in high frequency heating experiments

Featured observations in high-frequency (HF) heating experiments conducted at Arecibo, EISCAT, and high frequency active auroral research program are discussed. These phenomena appearing in the F region of the ionosphere include high-frequency heater enhanced plasma lines, airglow enhancement, energetic electron flux, artificial ionization layers, artificial spread-F, ionization enhancement, artificial cusp, wideband absorption, short-scale (meters) density irregularities, and stimulated electromagnetic emissions, which were observed when the O-mode HF heater waves with frequencies below foF2 were applied. The implication and associated physical mechanism of each observation are discussed and explained. It is shown that these phenomena caused by the HF heating are all ascribed directly or indirectly to the excitation of parametric instabilities which instigate anomalous heating. Formulation and analysis of parametric instabilities are presented. The results show that oscillating two stream instability and parametric decay instability can be excited by the O-mode HF heater waves, transmitted from all three heating facilities, in the regions near the HF reflection height and near the upper hybrid resonance layer. The excited Langmuir waves, upper hybrid waves, ion acoustic waves, lower hybrid waves, and field-aligned density irregularities set off subsequent wave-wave and wave-electron interactions, giving rise to the observed phenomena.

Parametric resonances revisited: comparison with kinetic description

A previous paper, McKenzie and Hagfors (1996 J. Plasma Phys . 55 (3), 539–585) henceforth referred to as P1, discussed the excitation of parametric instability in a homogeneous plasma pumped by an external electrostatic field. The discussion was carried out in the fluid approximation, and growth rates and resonance frequencies for several different modes were calculated, some of which had previously been overlooked because of inconsistent cut-off of certain series expansions. In this brief note we show that the fluid treatment gives growth rates and resonance frequencies that agree well with the kinetic treatment.

Anomalous absorption of a radio wave in the ionosphere

A radio wave transmitted into the ionosphere in the presence of a lower-hybrid drift wave excites a Langmuir wave, which is then damped by electrons, thereby heating them. This constitutes an important absorption mechanism. We evaluate the potential of the Langmuir wave and obtain an expression for the ratio Pr of the power of the Langmuir wave to that of the incident radio wave in the inhomogeneous ionosphere. It is found that the radio wave suffers an absorption of about 8% for a density fluctuation n1/n0 = 5%, but the electric field of the Langmuir wave becomes about 11.7 times that of the radio wave, which can lead to the excitation of parametric instabilities in the ionosphere.

Criteria for excitation of parametric instability in the ionosphere by an obliquely incident high-frequency heater

Parametric excitation of lower-hybrid decay mode together with upper-hybrid sideband in the ionosphere by an obliquely incident high-frequency pump is studied. The conditions for the instability, including the frequency range, the elevation angle, and the threshold field intensity of the pump are determined.

Vibration and parametric excitation in asymmetric circular plates under moving loads

The natural frequencies and modes of transverse vibration of circular plates containing small imperfections are determined through a perturbation method. Incision of equally spaced, equal-size radial slots at the rim of the plate creates asymmetry in some, but not all, of the vibration modes, and it causes the repeated natural frequencies of these modes in the symmetric plate to split into two distinct values. These vibration modes are called the split modes, and those associated with the repeated natural frequencies are called the repeated modes. A relationship identifying the split and repeated modes for any configuration of slots is presented. The vibration of a plate containing any number of thin slots cut into it at the rim and with any number of rotating linear springs is analyzed. Parametric instability can be excited in the split modes of the plate by the springs rotating below critical speed, but it cannot be excited in the repeated modes. The response of the plate in forms such as traveling or standing waves at parametric resonance is discussed. The theoretical predictions of split and repeated vibration modes and of the excitation of parametric instability are confirmed by experiments.

Vibration of circular saws containing slots

The natural modes of transverse vibration of circular saws containing radial slots are analyzed in this paper. Incision of equally-spaced asymmetry, equally sized, radial slots at the rim of a saw creates in some, but surprisingly not all, of the vibration modes of the circular saw. It causes the repeated natural frequencies in these asymmetric modes to split into two distinct values. These vibration modes are called the split modes. The vibration modes associated with the repeated natural frequencies, typical of the axisymmetric saw plate, are called the repeated modes. A relationship predicting which vibration modes are split and which are repeated for any configuration of slots on the saw is presented in this paper. Further, it is shown that parametric, transverse vibration instability can be excited in the split modes of the slotted saw by the saw guides and the workpiece. These parametric vibrations can not be excited in the repeated modes. The theoretical predictions of split and repeated vibration modes and the excitation of parametric instability are confirmed by experiments.

Russian Text Ignored.

AbstractThe nonlinear penetration of an electromagnetic wave through an overdense plasma layer due to the excitation of parametric instabilities is studied. The quasistatic h.f. surface wave and the ionacoustic wave, both parametrically growing, generate a nonlinear current which also exist beyound the linear skin length of the incident electromagnetic wave. This current leads to an exponential amplification of the electromagnetic wave amplitude in the layer. The growth rate of this process depends on the overthreshold value of the external wave intensity and the thickness of the layer. The saturation level of the transmitted wave amplitude is estimated for the case, when the instabilities are stabilized by generation of ion‐acoustic harmonics.

Theory of electron cyclotron resonance heating of tokamak plasmas

A theoretical study of tokamak plasma heating by electron cyclotron resonance is presented. The density limitations imposed by accessibility are first reviewed. Then, the predictions of linear theory (including relativistic effects on the wave absorption) are examined via solutions of the ray equations in a toroidal tokamak equilibrium. These solutions indicate quite favorable characteristics for large tokamaks. Finally, the possibilities of scattering of the incident heating wave by existing drift-wave-type fluctuations and excitation of parametric instability are examined; it is tentatively concluded that parametric instabilities should not be important in typical situations of interest.

The Thermic Excitation of Parametric Instability in a Plasma

The new possibility of controlled excitation of parametric instability in a partially ionized collisional plasma is suggested. This possibility is based on a special type of the interaction two radiowaves in a plasma, when the threshold amplitude value of parametric instability of plasma-wave resonant interaction, connected with one radiowave, is governed by electron heating, produced by another radiowave. The possibilities of utilization of such effects are connected with temperature excitation or attenuation of parametrical instabilities and separate determination of frequencies of electron-ion and electron-neutral elastic collisions in a local plasma region.

Excitation of parametric instabilities by electron cyclotron waves in a plasma column

Experimental results are presented illustrating parametric instabilities with thresholds as low as a fraction of a watt. Two types of instabilities are observed under different plasma conditions. The type I instability has broad sideband below the pump and a corresponding low frequency acoustic component. The type II instability occurs at higher neutral pressures, where a 30% dip in density on the column axis is created and has an upper sideband with harmonic structure and no observable low frequency components. Wave length measurements of each wave component are made to compare with parametric theory. The time domain evolution of the sidebands in the form of an RF burst is observed and discussed.

Excitation of parametric instabilities in statically stable and unstable fluid interfaces

By enforcing an oscillatory motion on superimposed fluids perpendicular to their interface, one can excite parametric instabilities, i.e., the unstable growth of interface or surface modes. Both the oscillation parameters and the wavelengths of the excited parametric instabilities depend on the viscosity and the surface tension of the fluids. This has been measured for the interface between air and various liquids and compared with theoretical predictions from Troyon and Gruber. The position of the liquids was either normal (air upon liquid) or inverted (liquid superimposed upon air). In the latter case the oscillation parameters had to be limited to those beyond the threshold for dynamic stabilization of the Rayleigh-Taylor instability. The applied frequencies were in the range between 30 and 4000 Hz, the surface tension was varied between 10 and 100 dyn/cm, and the viscosity between 10−2 and 10 P. Typical liquids were mineral oils, water, and gasoline.