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The squeezing spectra for the output fields of several intracavity nonlinear optical systems are obtained. It is shown that at critical points, e.g., the turning points for optical bistability, the threshold for parametric oscillation, and the self-pulsing instability in second-harmonic generation, perfect squeezing in the output field is, in principle, possible.
The linear theory of electromagnetic instabilities driven by an energetic ion beam streaming parallel to a magnetic field in a homogeneous Vlasov plasma is considered. Numerical solutions of the full dispersion equation are presented. At propagation parallel to the magnetic field, there are four distinct instabilities. A sufficiently energetic beam gives rise to two unstable modes with right-hand polarization, one resonant with the beam, the other nonresonant. A beam with sufficiently large T (perpendicular to B)/T (parallel to B) gives rise to the left-hand ion cyclotron anisotropy instability at relatively small beam velocities, and a sufficiently hot beam drives unstable a left-hand beam resonant mode. The parametric dependences of the growth rates for the three high beam velocity instabilities are presented here. In addition, some properties at oblique propagation are examined. It is demonstrated that, as the beam drift velocity is increased, relative maxima in growth rates can arise at harmonics of the ion cyclotron resonance for both right and left elliptically polarized modes.
The results of Gary et al. (1984) on the properties of the right-hand resonant and nonresonant electromagnetic ion beam instabilities for relatively cool beam temperatures are extended. In particular, the parametric dependence of the real frequency at maximum growth of these modes is examined. It is demonstrated that the right-hand resonant ion beam instability can have maximum growth at frequencies near the ion-cyclotron frequency if the beam main component relative drift speed is about twice the Alfven speed and at least one of two conditions holds: that the ion beta or the beam main component relative temperature are sufficiently small, or the perpendicular-to-parallel beam temperature ratio is sufficiently large. These results support the identification of the right-hand resonant instability as the source of the large amplitude magnetic fluctuations observed upstream of slow shocks in the earth's magnetotail.
When a jet is perturbed by a periodic excitation of suitable frequency, a large-scale coherent structure develops and grows in amplitude as it propagates downstream. The structure eventually rolls up into vortices at some downstream location. The wavy flow associated with the roll-up of a coherent structure is approximated by a parallel mean flow and a small, spatially periodic, axisymmetric wave whose phase velocity and mode shape are given by classical (primary) stability theory. The periodic wave acts as a parametric excitation in the differential equations governing the secondary instability of a subharmonic disturbance. The (resonant) conditions for which the periodic flow can strongly destabilize a subharmonic disturbance are derived. When the resonant conditions are met, the periodic wave plays a catalytic role to enhance the growth rate of the subharmonic. The stability characteristics of the subharmonic disturbance, as a function of jet Mach number, jet heating, mode number and the amplitude of the periodic wave, are studied via a secondary instability analysis using two independent but complementary methods: (1) method of multiple scales, and (2) normal mode analysis. It is found that the growth rates of the subharmonic waves with azimuthal numbers beta = 0 and beta = 1 are enhanced strongly, but comparably, when the amplitude of the periodic wave is increased. Furthermore, compressibility at subsonic Mach numbers has a moderate stabilizing influence on the subharmonic instability modes. Heating suppresses moderately the subharmonic growth rate of an axisymmetric mode, and it reduces more significantly the corresponding growth rate for the first spinning mode. Calculations also indicate that while the presence of a finite-amplitude periodic wave enhances the growth rates of subharmonic instability modes, it minimally distorts the mode shapes of the subharmonic waves.
Combustion instability in liquid rocket engines is simulated computationally by using a simple two-parameter model for the combustion response function. The objectives of the study are to assess the capabilities of CFD algorithms for instability studies and to investigate the response to parametric effects such as bombs and distributed combustion. Results indicate that numerical solutions of high accuracy can be obtained if a sufficient number of grid points are used per wavelength of the disturbance. The short-term response to bombs or pulses triggers a large number of modes in the combustor whose faithful resolution requires highly dense grids, although there is evidence that correct long-term solutions can be obtained even if all the short-term frequencies are not resolved. Long-term responses to pulses are shown to decay to the most unstable mode in small amplitude cases, and to exhibit limit cycles in large amplitude cases. Comparison of distributed with concentrated heat release indicates the former is more stable for given values of the combustion response parameters, and that the distributed heat release gives rise to higher frequency disturbances. Wave steepening is observed in the solutions, but its effect is less pronounced in multidimensional waves than in one-dimensional waves.
We examine whistler mode instabilities arising from electron beams in interplanetary space at 1 AU. Both parallel and obliquely propagating solutions are considered. We demonstrate that the generation of two simultaneous whistler mode waves is possible, and even reasonably likely, for beam parameters frequently encountered upstream of the Earth's bow shock and at interplanetary shocks. We also explore the generation of left-hand polarized waves at whistler mode frequencies under these same conditions. We offer both parametric variations derived from numerical solutions of the various instabilities as well as an analytical treatment of the problem which succeeds in unifying the various numerical results.
Solar wind electrons are observed often to consist of two components: a core and a halo. The anisotropics and relative average speeds of these components correspond to a heat flux that has the potential to excite several different electromagetic instabilities; wave-particle scattering by the resulting enhanced fluctuations can limit this heat flux. This manuscript describes theoretical studies using the linear Vlasco dispersion equation for drifting bi-Maxwellian component distributions in a homogeneous plasma to examine the threshold of the whistler heat flux instability. Expressions for this threshold are obtained from two different parametric baselines: a local model that yields scalings as functions of local dimensionless plasma paramaters, and a global model based on average electron properties observed during the in-eliptic phase of the Ulysses mission. The latter model yields an expression for the heat flux at threshold of the whistler instability as a function of helisopheric radius that scales in the same way as the average heat flux observed form Ulysses and that provides an approximate upper bound for that same quantity. This theoretical scaling is combined with the observational results to yield a semi-empirical closure relation for the average electron heat flux in the solar wind between 1 and 5 AU.
Recent satellite observations at high altitudes (greater than 5000 km) in the auroral zone have shown the existence of hybrid or bimodal ion beam distributions that are evidence of both parallel and perpendicular ion acceleration. Acceleration parallel to the magnetic field is most likely due to quasi-static electric fields (double layers) which can create outflowing ion beams; since ions of different mass will have different drift speeds due to this acceleration, a plasma configuration unstable to the ion-ion two-stream acoustic mode develops. When the net drift velocity (U) between the two ion species is greater than the sound speed (C(sub 0)), the ion-ion instability has maximum growth at oblique wave propagation. To study the nonlinear effects of the ion-ion instability in terms of plasma heating, a numerical simulation parametric study has been performed. It was found that the parallel acceleration that forms the ion beams occurs on a time scale faster than ion- ion wave growth at low drifts; thus ion-ion wave growth is expected to occur primarily for higher drift speeds (U greater than C(sub 0)) which results in strong oblique heating of the ions (both hydrogen and oxygen) forming elevated ion conics (sometimes called 'bowl' distributions). Also, strong parallel electron heating in the direction of the ion beams can occur, and electrons near the top of the acceleration region may attain a net upward drift along with the elevated ion conics. Variation of the oxygen density greatly affects the ion heating due to the ion-ion instability; as the oxygen density decreases, oxygen heating increases, in agreement with observations (Collin et al., 1987). Ion-ion electrostatic wave properties and the plasma heating that results over a wide range of auroral zone parameters are included.
The air and ground resonance instabilities of hingeless rotor helicopters are examined on a relatively broad parametric basis including the effects of blade tuning, virtual hinge locations, and blade hysteresis damping, as well as size and scale effects in the gross weight range from 5,000 to 48,000 pounds. A special case of a 72,000 pound helicopter air resonance instability is also included. The study shows that nominal to moderate and readily achieved levels of blade inertial hysteresis damping in conjunction with a variety of tuning and/or feedback conditions are highly effective in dealing with these instabilities. Tip weights and reductions in pre-coning angles are also shown to be effective means for improving the air resonance instability.
When strongly pumped at twice their resonant frequency, nonlinear resonators develop a high-amplitude intracavity field, a phenomenon known as parametric self-oscillations. The boundary over which this instability occurs can be extremely sharp and thereby presents an opportunity for realizing a detector. Here, we operate such a device based on a superconducting microwave resonator whose nonlinearity is engineered from kinetic inductance. The device indicates the absorption of low-power microwave wavepackets by transitioning to a self-oscillating state. Using calibrated pulses, we measure the detection efficiency to zeptojoule energy wavepackets. We then apply it to measurements of electron spin resonance, using an ensemble of 209 Bi donors in silicon that are inductively coupled to the resonator. We achieve a latched readout of the spin signal with an amplitude that is five hundred times greater than the underlying spin echoes.
Recent satellite observations at high altitudes (above 5000 km) in the auroral zone have shown the existence of hybrid or bimodal ion beam distributions that are evidence of both parallel and perpendicular ion acceleration. To study the nonlinear effects of the ion-ion instability in terms of plasma heating, a numerical simulation parametric study has been performed. It was found that the parallel acceleration that forms the ion beams occurs on a time scale faster than ion-ion wave growth at low drifts; thus ion-ion wave growth is expected to occur primarily for higher drift speeds, which results in strong oblique heating of the ions (both hydrogen and oxygen) forming elevated ion conics.
Viscous flow over discrete or distributed surface roughness has great implications for hypersonic flight due to aerothermodynamic considerations related to laminar-turbulent transition. Current prediction capability is greatly hampered by the limited knowledge base for such flows. To help fill that gap, numerical computations are used to investigate the intricate flow physics involved. An unstructured mesh, compressible Navier-Stokes code based on the space-time conservation element, solution element (CESE) method is used to perform time-accurate Navier-Stokes calculations for two roughness shapes investigated in wind tunnel experiments at NASA Langley Research Center. It was found through 2D parametric study that at subcritical Reynolds numbers, spontaneous absolute instability accompanying by sustained vortex shedding downstream of the roughness is likely to take place at subsonic free-stream conditions. On the other hand, convective instability may be the dominant mechanism for supersonic boundary layers. Three-dimensional calculations for both a rectangular and a cylindrical roughness element at post-shock Mach numbers of 4.1 and 6.5 also confirm that no self-sustained vortex generation from the top face of the roughness is observed, despite the presence of flow unsteadiness for the smaller post-shock Mach number case.
The Anderson model of wave localization in random media is involved to study the effect of solar wind density turbulence on plasma processes associated with the solar type III radio burst. ISEE-3 satellite data indicate that a possible model for the type III process is the parametric decay of Langmuir waves excited by solar flare electron streams into daughter electromagnetic and ion acoustic waves. The threshold for this instability, however, is much higher than observed Langmuir wave levels because of rapid wave convection of the transverse electromagnetic daughter wave in the case where the solar wind is assumed homogeneous. Langmuir and transverse waves near critical density satisfy the Ioffe-Reigel criteria for wave localization in the solar wind with observed density fluctuations -1 percent. Numerical simulations of wave propagation in random media confirm the localization length predictions of Escande and Souillard for stationary density fluctations. For mobile density fluctuations localized wave packets spread at the propagation velocity of the density fluctuations rather than the group velocity of the waves. Computer simulations using a linearized hybrid code show that an electron beam will excite localized Langmuir waves in a plasma with density turbulence. An action principle approach is used to develop a theory of non-linear wave processes when waves are localized. A theory of resonant particles diffusion by localized waves is developed to explain the saturation of the beam-plasma instability. It is argued that localization of electromagnetic waves will allow the instability threshold to be exceeded for the parametric decay discussed above.
Small perturbation analysis on mass conservation stability in solid propellant combustor, discussing parametric model
Assuming a uniform magnetic field and using the local approximation, the Vlassov theory for an electrostatic instability driven by a parabolic density gradient is considered. It is found that the instability grows only in the case of a sufficiently large, positive second derivative of the density. Linear growth rate parametric dependences are given, in addition to weakly nonlinear calculations on wave-particle transport due to this instability.
Despite advancements in high-performance computing and modern numerical algorithms, computational cost remains prohibitive for multi-query kinetic plasma simulations. Here, in this work, we develop data-driven reduced-order models (ROMs) for collisionless electrostatic plasma dynamics, based on the kinetic Vlasov-Poisson equation. Our ROM approach projects the equation onto a linear subspace defined by the proper orthogonal decomposition (POD) modes. We introduce an efficient tensorial method to update the nonlinear term using a precomputed third-order tensor. We capture multiscale behavior with a minimal number of POD modes by decomposing the solution manifold into multiple time windows and creating temporally local ROMs. We consider two strategies for decomposition: one based on the physical time and the other based on the electric field energy. Applied to the 1D1V Vlasov–Poisson simulations, that is, prescribed E-field, Landau damping, and two-stream instability, we demonstrate that our ROMs accurately capture the total energy of the system both for parametric and time extrapolation cases. The temporally local ROMs are more efficient and accurate than the single ROM. In addition, in the two-stream instability case, we show that the energy-windowing reduced-order model (EW-ROM) is more efficient and accurate than the time-windowing reduced-order model (TW-ROM). With the tensorial approach, EW-ROM solves the equation approximately 90 times faster than Eulerian simulations while maintaining a maximum relative error of 7.5% for the training data and 11% for the testing data.
Spectrally incoherent laser pulses with sufficiently large fractional bandwidth are in demand for the mitigation of laser–plasma instabilities occurring in high-energy laser–target interactions. Here, we modeled, implemented, and optimized a dual-stage high-energy optical parametric amplifier for broadband, spectrally incoherent pulses in the near-infrared. The amplifier delivers close to 400 mJ of signal energy through noncollinear parametric interaction of 100-nJ-scale broadband, spectrally incoherent seed pulses near 1053 nm with a narrowband high-energy pump operating at 526.5 nm. Mitigation strategies for high-frequency spatial modulations in the amplified signal caused by index inhomogeneities in the Nd:YLF rods of the pump laser are explored and discussed in detail.
Recent analyses on the instability of the orbital debris population in the low Earth orbit (LEO) region and the collision between Iridium 33 and Cosmos 2251 have reignited the interest in using active debris removal (ADR) to remediate the environment. There are; however, monumental technical, resource, operational, legal, and political challenges in making economically viable ADR a reality. Before a consensus on the need for ADR can be reached, a careful analysis of its effectiveness must be conducted. The goal is to demonstrate the need and feasibility of using ADR to better preserve the future environment and to guide its implementation to maximize the benefit-to-cost ratio. This paper describes a new sensitivity study on using ADR to stabilize the future LEO debris environment. The NASA long-term orbital debris evolutionary model, LEGEND, is used to quantify the effects of several key parameters, including target selection criteria/constraints and the starting epoch of ADR implementation. Additional analyses on potential ADR targets among the currently existing satellites and the benefits of collision avoidance maneuvers are also included.