Threshold Of Parametric Instability Research Articles

Wave-vortex interaction

We present an experimental study of the effect of an electromagnetically generated vortex flow on parametrically amplified waves at the surface of a vertically vibrated fluid layer. The underlying vortex flow, generated by a periodic Lorentz force, creates spatiotemporal fluctuations that nonlinearly interact with the standing surface waves. We measure the power spectral density of the surface wave amplitude and we characterize the bifurcation diagram by recording the subharmonic response of the surface to the external vibration. We show that the parametric instability is delayed in the presence of spatiotemporal fluctuations due to the vortex flow. In addition, the dependence of the amplitude of the subharmonic response on the distance to the instability threshold is modified. This shows that the nonlinear saturation mechanism of the waves is modified by the vortex flow.

Spinning down newborn neutron stars: Nonlinear development of ther-mode instability

We model the nonlinear saturation of the r-mode instability via three-mode couplings and the effects of the instability on the spin evolution of young neutron stars. We include one mode triplet consisting of the r-mode and two near-resonant inertial modes that couple to it. We find that the spectrum of evolutions is more diverse than previously thought. We start our evolutions with a star of temperature {approx}10{sup 10} K and a spin frequency close to the Kepler break-up frequency. We assume that hyperon bulk viscosity dominates at high temperatures (T{approx}10{sup 9}-10{sup 10} K) and boundary layer viscosity dominates at lower temperatures ({approx}a fewx10{sup 8} K). To explore possible nonlinear behavior, we vary properties of the star such as the hyperon superfluid transition temperature, the strength of the boundary layer viscosity, and the fraction of the star that cools via direct URCA reactions. The evolution of the star is dynamic and initially dominated by fast neutrino cooling. Nonlinear effects become important when the r-mode amplitude grows above its first parametric instability threshold. The balance between neutrino cooling and viscous heating plays an important role in the evolution. Depending on the initial r-mode amplitude, and on the strength of the viscosity and more » of the cooling this balance can occur at different temperatures. If thermal equilibrium occurs on the r-mode stability curve, where gravitational driving equals viscous damping, the evolution may be adequately described by a one-mode model. Otherwise, nonlinear effects are important and lead to various more complicated scenarios. Once thermal balance occurs, the star spins down oscillating between thermal equilibrium states until the instability is no longer active. The average evolution of the mode amplitudes can be approximated by quasistationary states that are determined algebraically. For lower viscosity we observe runaway behavior in which the r-mode amplitude passes several parametric instability thresholds. In this case more modes need to be included to model the evolution accurately. In the most optimistic case, we find that gravitational radiation from the r-mode instability in a very young, fast spinning neutron star within about 1 Mpc of Earth may be detectable by advanced LIGO for years, and perhaps decades, after formation. Details regarding the amplitude and duration of the emission depend on the internal dissipation of the modes of the star, which would be probed by such detections. « less

Estimation of dynamic parameters of overthreshold parametric phase conjugation of ultrasound in magnetostrictive ferrites according to data of quasi-static measurements

A simple method for testing ferrite samples intended to be active elements of parametric phase conjugator of ultrasound was proposed and experimentally approved. The method allows one to estimate such dynamic parameters of parametric phase conjugator of ultrasound as the parametric amplification increment, threshold of absolute parametric instability, and optimum operating point position for a particular sample using results of measurements in a dc magnetic field. Results for two ferrite samples of different compositions and properties were compared to direct measurement data; their satisfactory agreement was obtained.

Spin evolution of accreting neutron stars: Nonlinear development of ther-mode instability

The nonlinear saturation of the $r$-mode instability and its effects on the spin evolution of low mass x-ray binaries (LMXBs) are modeled using the triplet of modes at the lowest parametric instability threshold. We solve numerically the coupled equations for the three modes in conjunction with the spin and temperature evolution equations. We observe that very quickly the mode amplitudes settle into quasistationary states that change slowly as the temperature and spin of the star evolve. Once these states are reached, the mode amplitudes can be found algebraically and the system of equations is reduced from eight to two equations: spin and temperature evolution. The evolution of the neutron star angular velocity and temperature follow easily calculated trajectories along these sequences of quasistationary states. The outcome depends on whether or not the star will reach thermal equilibrium, where the viscous heating by the three modes is equal to the neutrino cooling ($H=C$ curve). If, when the $r$-mode becomes unstable, the star spins at a frequency below the maximum of the $H=C$ curve, then it will reach a state of thermal equilibrium. It can then either (1) undergo a cyclic evolution with a small cycle size with a frequency change of at most 10%, (2) evolve toward a full equilibrium state in which the accretion torque balances the gravitational radiation emission, or (3) enter a thermogravitational runaway on a very long time scale of $\ensuremath{\approx}{10}^{6}\text{ }\text{ }\mathrm{years}$. If the star does not reach a state of thermal equilibrium, then a faster thermal runaway (time scale of $\ensuremath{\approx}100\text{ }\text{ }\mathrm{years}$) occurs and the $r$-mode amplitude increases above the second parametric instability threshold. Following this evolution requires more inertial modes to be included. The sources of damping considered are shear viscosity, hyperon bulk viscosity, and viscosity within the core-crust boundary layer. We vary proprieties of the star such as the hyperon superfluid transition temperature ${T}_{c}$, the fraction of the star that is above the threshold for direct URCA reactions, and slippage factor, and map the different scenarios we obtain to ranges of these parameters. We focus on ${T}_{c}\ensuremath{\gtrsim}5\ifmmode\times\else\texttimes\fi{}{10}^{9}\text{ }\text{ }\mathrm{K}$ where nonlinear effects are important. Wagoner [R. Wagoner, Astrophys. J. 578, L63 (2002).] has shown that a very low $r$-mode amplitude arises at smaller ${T}_{c}$. For all our bounded evolutions the $r$-mode amplitude remains small $\ensuremath{\sim}{10}^{\ensuremath{-}5}$. The spin frequency of accreting neutron stars is limited by boundary layer viscosity to ${\ensuremath{\nu}}_{\mathrm{max}}\ensuremath{\approx}800\text{ }\text{ }\mathrm{Hz}[{S}_{\mathrm{ns}}/({M}_{1.4}{R}_{6}){]}^{4/11}{T}_{8}^{\ensuremath{-}2/11}$. Fast rotators are allowed for $[{S}_{\mathrm{ns}}/({M}_{1.4}{R}_{6}){]}^{4/11}{T}_{8}^{\ensuremath{-}2/11}\ensuremath{\sim}1$ and we find that in this case the $r$-mode instability would be active for about 1 in 1000 LMXBs and that only the gravitational waves from LMXBs in the local group of galaxies could be detected by advanced LIGO interferometers.

Quantum Monte Carlo study of ring-shaped polariton parametric luminescence in a semiconductor microcavity

We present a quantum Monte Carlo study of the quantum correlations in the parametric luminescence from semiconductor microcavities in the strong exciton-photon coupling regime. As already demonstrated in recent experiments, a ring-shaped emission is obtained by applying two identical pump beams with opposite in-plane wavevectors, providing symmetrical signal and idler beams with opposite in-plane wavevectors on the ring. We study the squeezing of the signal-idler difference noise across the parametric instability threshold, accounting for the radiative and non-radiative losses, multiple scattering and static disorder. We compare the results of the complete multimode Monte Carlo simulations with a simplified linearized quantum Langevin analytical model.

Absolute measurement of laser frequency-shifted optical feedback by pump modulation

The dynamical response of a laser simultaneously subject to frequency-shifted optical feedback and pump modulation is investigated both theoretically and experimentally. We show that the amount of light reinjected in the intra-cavity laser can be determined by the pump modulation contrast, either for a destructive interference condition between the optical feedback and the pump modulation, or near the parametric instability threshold.

Nonlinear coupling network to simulate the development of thermode instability in neutron stars. II. Dynamics

Two mechanisms for nonlinear mode saturation of the $r$ mode in neutron stars have been suggested: the parametric instability mechanism involving a small number of modes and the formation of a nearly continuous Kolmogorov-type cascade. Using a network of oscillators constructed from the eigenmodes of a perfect fluid incompressible star, we investigate the transition between the two regimes numerically. Our network includes the 4995 inertial modes up to $n\ensuremath{\le}30$ with 146 998 direct couplings to the $r$ mode and 1 306 999 couplings with detuning $<0.002$ (out of a total of approximately ${10}^{9}$ possible couplings). The lowest parametric instability thresholds for a range of temperatures are calculated and it is found that the $r$ mode becomes unstable to modes with $13<n<15$. In the undriven, undamped, Hamiltonian version of the network the rate to achieve equipartition is found to be amplitude dependent, reminiscent of the Fermi-Pasta-Ulam problem. More realistic models driven unstable by gravitational radiation and damped by shear viscosity are explored next. A range of damping rates, corresponding to temperatures ${10}^{6}\text{ }\text{ }\mathrm{K}$ to ${10}^{9}\text{ }\text{ }\mathrm{K}$, is considered. Exponential growth of the $r$ mode is found to cease at small amplitudes $\ensuremath{\approx}{10}^{\ensuremath{-}4}$. For strongly damped, low temperature models, a few modes dominate the dynamics. The behavior of the $r$ mode is complicated, but its amplitude is still no larger than about ${10}^{\ensuremath{-}4}$ on average. For high temperature, weakly damped models the $r$ mode feeds energy into a sea of oscillators that achieve approximate equipartition. In this case the $r$-mode amplitude settles to a value for which the rate to achieve equipartition is approximately the linear instability growth rate.

Nonlinear couplings of R-modes: Energy transfer and saturation amplitudes at realistic timescales

Non-linear interactions among the inertial modes of a rotating fluid can be described by a network of coupled oscillators. We use such a description for an incompressible fluid to study the development of the r-mode instability of rotating neutron stars. A previous hydrodynamical simulation of the r-mode reported the catastrophic decay of large amplitude r-modes. We explain the dynamics and timescale of this decay analytically by means of a single three mode coupling. We argue that at realistic driving and damping rates such large amplitudes will never actually be reached. By numerically integrating a network of nearly 5000 coupled modes, we find that the linear growth of the r-mode ceases before it reaches an amplitude of around 10^(-4). The lowest parametric instability thresholds for the r-mode are calculated and it is found that the r-mode becomes unstable to modes with 13<n<15 if modes up to n=30 are included. Using the network of coupled oscillators, integration times of 10^6 rotational periods are attainable for realistic values of driving and damping rates. Complicated dynamics of the modal amplitudes are observed. The initial development is governed by the three mode coupling with the lowest parametric instability. Subsequently a large number of modes are excited, which greatly decreases the linear growth rate of the r-mode.

Dual pumping of magnetostatic and spin-wave modes in yttrium–iron–garnet spheres

In ferrimagnetic materials subjected to a static magnetic field H, a parallel rf magnetic field h gives rise to nonlinear absorption due to the unstable growth of certain spin waves when exceeding a parametric instability threshold (PIT), h=hc. The excited spin waves have half the pumping frequency and a wave number k that depends on H, such that the curve hc vs H resembles the Greek symbol ν and is thus called a “butterfly curve.” Recent experiments in a yttrium–iron–garnet sphere have shown that the PIT is resonantly reduced in the presence of a simultaneous perpendicular rf field at half the parallel-pumping frequency only on the right wing of the butterfly curve, where “volume” magnetostatic modes (k∼0) are primarily excited. Here, dual pumping experiments are reported at lower frequencies (8.882 and 4.441 GHz), allowing the presence of “surface” magnetostatic modes on the left wing and corresponding resonant PIT reduction in that region, where spin waves with k∼105 cm−1 are primarily excited by the parallel-pumping field. The results qualitatively agree with a model that put no restriction on the pumping frequency, thus extending earlier calculations by White and Schlömann [R. M. White and Schlömann, J. Appl. Phys. 33, 2437 (1962)].

Scattering of electromagnetic waves in a magnetized plasma with an HF pump

The scattering of transverse electromagnetic waves by turbulent density fluctuations in a magnetized plasma in the presence of external pump fields is investigated. The case where a lower-hybrid pump wave decays into daughter and ion-cyclotron waves in a plasma with ion-temperature anisotropy is considered. The situation where an upper-hybrid pump wave parametrically excites modified convective cells and electron drift waves is also analyzed. The differential scattering cross-sections in the region above the parametric instability thresholds for these three cases are calculated.

Multi-frequency parametric phase conjugation of ultrasound beams in magnetic ceramics.

A new operation mode of a parametric phase conjugation of ultrasound waves above the threshold of absolute parametric instability of phonons is reported. A deviation of the carrier frequency in a sequence of incident ultrasound bursts and in a proper sequence of electromagnetic pumping is applied. The deviation avoids amplification of the reverberation noise in the active medium when the repetition time of the conjugation is short enough to be comparable with the relaxation time of acoustic reverberations. As a result, a decrease of repetition time and a correspondent increase of the average output power of a phase conjugator becomes available. The advantage of the new operation mode is demonstrated on an example of supercritical phase conjugation in magnetoacoustic ceramics.

Numerical simulation of acoustic wave phase conjugation in active media

Godunov-type computation schemes are applied to numerical simulations of wave propagations in time-dependent heterogeneous media (solids and liquids). The parametric phase conjugation of a wide band ultrasound pulse is considered. The supercritical dynamics of the acoustic field is described for one-dimensional systems containing a parametrically active solid. The impulse response function, numerically calculated for a finite active zone in an infinite medium above the threshold of absolute parametric instability, is in a good agreement with the analytical asymptotic theory. The supercritical evolution of the acoustic field spatial distribution is studied in detail for parametric excitations in an active zone of a solid layer, loaded by a semi-infinite liquid on one side and free on the other.

Observation of Nonlinear Coupled Photon-Magnon Oscillations in YIG

Nonequilibrium spin waves excited by the parallel pumping in an yttrium iron garnet placed in a microwave cavity was studied by means of additional weak microwave signal. The response of the probe signal represented a two-hump spectrum just above the threshold of parametric instability. It corresponds to mixed oscillations of photons and magnons and demonstrates that the parametric spin-wave pair behaves as a single-mode oscillator nonlinearly coupled with the electromagnetic mode of microwave cavity. We observed another splitting in the spectrum before the onset of auto-oscillations. It is assumed to indicate that this steady state of parametric system consists of two different parametric spin-wave pairs. Theoretical calculations which consider coupled systems of resonator mode and magnetic sample are found to be in good agreement with the experimental data.

Spin-wave experiments: Simultaneous pumping revisited

Confirming theoretical predictions more than 30 years old, we show that the parametric instability threshold of microwave parallel-pumped spin waves in YIG spheres is reduced by the simultaneous application of an orthogonal RF field at half the pumping frequency. As a function of the orthogonal field, the reduction first increases with the square of the field, as predicted, and saturation is critically reached at the second-order Suhl instability threshold. In addition, we show that the auto-oscillation threshold is also affected by the orthogonal field, but not its amplitude nor its frequency.

Resonant decrease of the parametric instability threshold by pump frequency modulation

The pump wave frequency modulation, as well as the plasma non-stationarity, are well known to stabilize the parametric decay instabilities due to violation of the decay condition for wave frequencies. The plasma inhomogeneity has a similar effect associated with the decay condition for the wavenumbers. In the present paper the simultaneous influence of these two factors on the decay instability of the Trivelpiece-Gould wave in a magnetized plasma is studied. A strong increase of the amplitude of decay waves is observed in a narrow range of pump frequency modulation rates. The decay point motion due to the pump frequency modulation is shown to be responsible for this effect, which occurs when the decay point velocity is equal to the group velocity of one of the parametrically driven waves. Elimination of convective losses is proved to occur under these conditions. The dependence of the decay wave amplitude on pump power and on the pump frequency modulation time is studied for this resonance.

Parametric excitation of nonlinear waves in a one-dimensional system of interacting magnons.

We consider the parametric excitation of nonlinear magnetic waves by a uniform high-frequency magnetic field in the one-dimensional easy-plane (EP) and easy-axis (EA) ferromagnets. The problem is reduced to a perturbed nonlinear Schr\odinger equation for the wave function of the Bose-condensed magnons. It is shown that close to the threshold of parametric instability a rotating localized distribution of longitudinal magnetization can be maintained in the form of a kink for EP and soliton for EA ferromagnets. The moving magnetic soliton can also be excited in EA ferromagnets. The conditions on intensity for generation within the transverse plane of a rotating domain wall are discussed. The results can also be applied to the Ni(${\mathrm{C}}_{2}$${\mathrm{H}}_{8}$${\mathrm{N}}_{2}$${)}_{2}$${\mathrm{NO}}_{2}$${\mathrm{ClO}}_{4}$ one-dimensional antiferromagnet. Information about the Haldane gap may be obtained from the conditions of kink generation.

Observation of parametric decay correlated with edge heating using an ion Bernstein wave antenna on DIII-D

Significant levels of parametric decay activity and correlated edge ion heating were observed during injection of high power ion Bernstein waves (IBWs) in DIII-D. Both minority hydrogen ions and majority deuterium ions showed the formation of a high energy perpendicular tail; no parallel heating was observed. The edge ion heating and the parametric decay activity were both strongest when an ion cyclotron harmonic was present at the plasma edge. Ion tail formation had a power threshold of several hundred kilowatts, above which the tail size increased with antenna power; a comparable power threshold for parametric decay instability (PDI) was observed. Both the PDI and the associated edge deuterium heating were found to be sensitive to the hydrogen-to-deuterium ratio

Overthreshold Nonlinearity of Parametric Sound Wave Phase Conjugation in Solids

The nonlinear stage of acoustic wave phase conjugation over the threshold of absolute parametric instability is considered with respect to magnetic active media. The common case of nonlinear, nonstationary and spatially inhomogeneous parametric interaction is studied. Theoretical results are compared with experimental data on phase conjugate wave gain measurements in ferrite. It is shown that the pumping exhaustion mechanism of nonlinearity provides a reproduction of incident wave field distribution in the output of the active zone by parametric phase conjugation in the overthreshold regime of giant amplification in ferrite. The signal and fluctuation mode competition is shown to be essential for overthreshold limitation of phase conjugate wave amplitude.

On the threshold of parametric instability of spin waves in a film with a rough surface

The threshold of parametric excitation of spin waves in a ferrite film with a rough surface is calculated. The influence of the surface on the threshold is twofold: (i) the normal component of the wave vector of a spin wave is quantized and (ii) surface roughnesses scatter a spin wave elastically. The elastic scattering conserves energy of spin waves and mixes phases of spin waves with different wave vectors. The threshold of parametric excitation hth depends on the relationship between the film thickness d and the mean free path l. The threshold in a thick film (d≫l) is close to that in an unbounded sample of ferromagnet hth0: (hth/hth0)2 = 1 + (πl/d)2. In a thin film (d≪l) the threshold is close to that in a randomly inhomogeneous ferromagnet (hth/hth0)2 ∼ γs/γ, where γ is the spin-wave damping and γs is the frequency of elastic scattering of spin waves on surface roughnesses.

Threshold of Lower Hybrid Parametric Instability in a Modulated Electron-Beam–Plasma System

An experimental study of parametric instability driven by a beam modulation near the lower hybrid frequency is presented. If the modulation voltage exceeds a threshold value, the pump wave appears to decay into an ion acoustic wave and a lower hybrid wave. The threshold electron drift speed is found to be of the order of the ion acoustic speed as predicted by a theory of parametric instability in an inhomogeneous plasma.