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At least 1,153 records · Page 64
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DOE OSTI2013

Spectral properties of a confined nonlinear quantum oscillator in one and three dimensions

We analyze the spectral behaviour of a nonlinear quantum oscillator model under confinement. The underlying potential is given by a harmonic oscillator interaction plus a nonlinear term that can be weakened or strengthened through a parameter. Numerical eigenvalues of the model in one and three dimensions are presented. The asymptotic behaviour of the eigenvalues for confinement relaxation and for vanishing nonlinear term in the potential is investigated. Our findings are compared with existing results.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

Nonlinear interaction of kinetic Alfven wave and whistler: Turbulent spectra and anisotropic scaling

In this work, we are presenting the excitation of oblique propagating whistler wave as a consequence of nonlinear interaction between whistler wave and kinetic Alfven wave (KAW) in intermediate beta plasmas. Numerical simulation has been done to study the transient evolution of magnetic field structures of KAW when the nonlinearity arises due to ponderomotive effects by taking the adiabatic response of the background density. Weak oblique propagating whistler signals in these nonlinear plasma density filaments (produced by KAW localization) get amplified. The spectral indices of the power spectrum at different times are calculated with given initial conditions of the simulations. Anisotropic scaling laws for KAW and whistlers are presented. The relevance of the present investigation to solar wind turbulence and its acceleration is also pointed out.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2013

Weakly nonlinear incompressible Rayleigh-Taylor instability growth at cylindrically convergent interfaces

A weakly nonlinear (WN) model has been developed for the incompressible Rayleigh-Taylor instability (RTI) in cylindrical geometry. The transition from linear to nonlinear growth is analytically investigated via a third-order solutions for the cylindrical RTI initiated by a single-mode velocity perturbation. The third-order solutions can depict the early stage of the interface asymmetry due to the bubble-spike formation, as well as the saturation of the linear (exponential) growth of the fundamental mode. The WN results in planar RTI [Wang et al., Phys. Plasmas 19, 112706 (2012)] are recovered in the limit of high-mode number perturbations. The difference between the WN growth of the RTI in cylindrical geometry and in planar geometry is discussed. It is found that the interface of the inward (outward) development spike/bubble is extruded (stretched) by the additional inertial force in cylindrical geometry compared with that in planar geometry. For interfaces with small density ratios, the inward growth bubble can grow fast than the outward growth spike in cylindrical RTI. Moreover, a reduced formula is proposed to describe the WN growth of the RTI in cylindrical geometry with an acceptable precision, especially for small-amplitude perturbations. Using the reduced formula, the nonlinear saturation amplitude of the fundamental mode and the phases of the Fourier harmonics are studied. Thus, it should be included in applications where converging geometry effects play an important role, such as the supernova explosions and inertial confinement fusion implosions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2013

Nonlinear instability in simulations of Large Plasma Device turbulence

Several simulations of turbulence in the Large Plasma Device (LAPD) [Gekelman et al., Rev. Sci. Instrum. 62, 2875 (1991)] are energetically analyzed and compared with each other and with the experiment. The simulations use the same model, but different axial boundary conditions. They employ either periodic, zero-value, zero-derivative, or sheath axial boundaries. The linear stability physics is different between the scenarios because the various boundary conditions allow the drift wave instability to access different axial structures, and the sheath boundary simulation contains a conducting wall mode instability which is just as unstable as the drift waves. Nevertheless, the turbulence in all the simulations is relatively similar because it is primarily driven by a robust nonlinear instability that is the same for all cases. The nonlinear instability preferentially drives k{sub ∥}=0 potential energy fluctuations, which then three-wave couple to k{sub ∥}≠0 potential energy fluctuations in order to access the adiabatic response to transfer their energy to kinetic energy fluctuations. The turbulence self-organizes to drive this nonlinear instability, which destroys the linear eigenmode structures, making the linear instabilities ineffective.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2013

Comparisons of linear and nonlinear plasma response models for non-axisymmetric perturbations

With the installation of non-axisymmetric coil systems on major tokamaks for the purpose of studying the prospects of ELM-free operation, understanding the plasma response to the applied fields is a crucial issue. Application of different response models, using standard tools, to DIII-D discharges with applied non-axisymmetric fields from internal coils, is shown to yield qualitatively different results. The plasma response can be treated as an initial value problem, following the system dynamically from an initial unperturbed state, or from a nearby perturbed equilibrium approach, and using both linear and nonlinear models [A. D. Turnbull, Nucl. Fusion 52, 054016 (2012)]. Criteria are discussed under which each of the approaches can yield a valid response. In the DIII-D cases studied, these criteria show a breakdown in the linear theory despite the small 10{sup −3} relative magnitude of the applied magnetic field perturbations in this case. For nonlinear dynamical evolution simulations to reach a saturated nonlinear steady state, appropriate damping mechanisms need to be provided for each normal mode comprising the response. Other issues arise in the technical construction of perturbed flux surfaces from a displacement and from the presence of near nullspace normal modes. For the nearby equilibrium approach, in the absence of a full 3D equilibrium reconstruction with a controlled comparison, constraints relating the 2D system profiles to the final profiles in the 3D system also need to be imposed to assure accessibility. The magnetic helicity profile has been proposed as an appropriate input to a 3D equilibrium calculation and tests of this show the anticipated qualitative behavior.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2013

Parameter spaces for linear and nonlinear whistler-mode waves

We examine the growth of magnetospheric whistler-mode waves which comprises a linear growth phase followed by a nonlinear growth phase. We construct time-profiles for the wave amplitude that smoothly match at the transition between linear and nonlinear wave growth. This matching procedure can only take place over a limited “matching region” in (N{sub h}/N{sub 0},A{sub T})-space, where A{sub T} is the electron thermal anisotropy, N{sub h} is the hot (energetic) electron number density, and N{sub 0} is the cold (background) electron number density. We construct this matching region and determine how the matching wave amplitude varies throughout the region. Further, we specify a boundary in (N{sub h}/N{sub 0},A{sub T})-space that separates a region where only linear chorus wave growth can occur from the region in which fully nonlinear chorus growth is possible. We expect that this boundary should prove of practical use in performing computationally expensive full-scale particle simulations, and in interpreting experimental wave data.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2013

Nonlinear dynamics of toroidal Alfvén eigenmodes driven by energetic particles

A kinetic simulation code based on a reduced model is developed to study dynamic evolutions of a single toroidicity-induced shear Alfvén eigenmode driven by energetic particles. For zero background damping, it is found that the wave amplitude in nonlinear phase can either saturate for weak energetic particle drives or slowly increase for strong drives. This slow nonlinear growth in strong drive cases is found to be associated with broadening and overlapping of resonances between the wave and trapped particles. For the near-marginal-stability case with a large background damping, the mode nonlinear evolution exhibits strong upward and downward frequency chirping in multiple branches. A hole/clump formation is observed clearly in the corresponding evolution of energetic particle distribution.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2013

Nonlinear resonance absorption of laser in an inhomogeneous plasma

A formalism of nonlinear resonance absorption of p-polarized laser in a plasma with density gradient is developed. The nonlinearity is taken to arise through the relativistic mass effect. As the laser incident at an angle to the density gradient approaches the turning point, dielectric swelling leads to field enhancement, causing strong electron mass enhancement and reduction in local plasma frequency. When the critical layer is within a laser wavelength away from the turning point, the laser field is greatly enhanced at the critical layer and absorption of the laser is strongly affected by the nonlinear effect.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2013

Nonlinear dust acoustic waves in inhomogeneous four-component dusty plasma with opposite charge polarity dust grains

The reductive perturbation technique is employed to investigate the propagation properties of nonlinear dust acoustic (DA) waves in a four-component inhomogeneous dusty plasma (4CIDP). The 4CIDP consists of both positive- and negative-charge dust grains, characterized by different mass, temperature, and density, in addition to a background of Maxwellian electrons and ions. The inhomogeneity caused by nonuniform equilibrium values of particle densities, fluid velocities, and electrostatic potential leads to a significant modification to the nature of nonlinear DA solitary waves. It is found that this model reveals two DA wave velocities, one slow, λ{sub s}, and the other is fast, λ{sub f}. The nonlinear wave evolution is governed by a modified Kortweg-de Vries equation, whose coefficients are space dependent. Both the two soliton types; compressive and rarefactive are allowed corresponding to λ{sub s}. However, only compressive soliton is created corresponding to λ{sub f}. The numerical investigations illustrate the dependence of the soliton amplitude, width, and velocity on the plasma inhomogeneities in each case. The relevance of these theoretical results with 4CIDPs observed in a multi-component plasma configurations in the polar mesosphere is discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

Linear stability and nonlinear dynamics of the fishbone mode in spherical tokamaks

Extensive linear and nonlinear simulations have been carried out to investigate the energetic particle-driven fishbone instability in spherical tokamak plasmas with weakly reversed q profile and the q{sub min} slightly above unity. The global kinetic-MHD hybrid code M3D-K is used. Numerical results show that a fishbone instability is excited by energetic beam ions preferentially at higher q{sub min} values, consistent with the observed appearance of the fishbone before the “long-lived mode” in MAST and NSTX experiments. In contrast, at lower q{sub min} values, the fishbone tends to be stable. In this case, the beam ion effects are strongly stabilizing for the non-resonant kink mode. Nonlinear simulations show that the fishbone saturates with strong downward frequency chirping as well as radial flattening of the beam ion distribution. An (m, n) = (2, 1) magnetic island is found to be driven nonlinearly by the fishbone instability, which could provide a trigger for the (2, 1) neoclassical tearing mode sometimes observed after the fishbone instability in NSTX.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2013

Nonlinear propagation of Rossby-Khantadze electromagnetic planetary waves in the ionospheric E-layer

Nonlinear vortex propagation of electromagnetic coupled Rossby and Khantadze planetary waves in the weakly ionized ionospheric E-layer is investigated with numerical simulations. Large scale, finite amplitude vortex structures are launched as initial conditions at low, mid, and high latitudes. For each k-vector the linear dispersion relation has two eigenmodes corresponding to the slow magnetized Rossby wave and the fast magnetic Khantadze wave. Both waves propagate westward with local speeds of the order of 10–20 m/s for the slow wave and of the order of 500–1000 km/s for the fast wave. We show that for finite amplitudes there are dipole solitary structures emitted from the initial conditions. These structures are neutrally stable, nonlinear states that avoid radiating waves by propagating faster than the corresponding linear wave speeds. The condition for these coherent structures to occur is that their amplitudes are such that the nonlinear convection around the core of the disturbance is faster than the linear wave speed for the corresponding dominant Fourier components of the initial disturbance. The presence of the solitary vortex states is indicative of an initial strong disturbance such as that from a solar storm or a tectonic plate movement. We show that for generic, large amplitude initial disturbances both slow and fast vortex structures propagate out of the initial structure.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2013

The role of deposited layers in the nonlinear constitutive behavior of Si nanowires

The experimentally measured elastic moduli and yield strengths of nanowires and nanofilaments vary widely in the literature and are often beyond the theoretical limits of the particular material. In this work, Si nanowires with very low defect densities were loaded in uniaxial tension to establish the origins of their apparently nonlinear constitutive behavior. The diameters of the nanowires ranged from 230 to 460 nm and the growth directions were primarily [112] with the exception of a [111] oriented nanowire. The resulting fracture strengths of the nanowires ranged from 3.88 to 10.1 GPa. The nonlinear constitutive behavior was accompanied by fracture surfaces with features that were not commonly observed in Si. A nonlinear continuum elasticity model and electron microscopy established that reports of unusual deformation behavior and fracture surface morphologies are a direct byproduct of the electron and ion beam deposited adhesives (Pt-based in this work) used to affix specimens in place for testing.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

Third-order nonlinear optical response of colloidal gold nanoparticles prepared by sputtering deposition

The nonlinear optical responses of gold nanoparticles dispersed in castor oil produced by sputtering deposition were investigated, using the thermally managed Z-scan technique. Particles with spherical shape and 2.6 nm of average diameter were obtained and characterized by transmission electron microscopy and small angle X-ray scattering. This colloid was highly stable, without the presence of chemical impurities, neither stabilizers. It was observed that this system presents a large refractive third-order nonlinear response and a negligible nonlinear absorption. Moreover, the evaluation of the all-optical switching figures of merit demonstrated that the colloidal nanoparticles prepared by sputtering deposition have a good potential for the development of ultrafast photonic devices.

36 MATERIALS SCIENCE↗
DOE OSTI2013

Self-focusing of a high-intensity laser in a collisional plasma under weak relativistic-ponderomotive nonlinearity

Self-focusing a laser beam in collisional plasma is investigated under the weak relativistic-ponderomotive nonlinearity. In this case, the plasma equilibrium density is modified and it causes generation of the nonlinearity due to the Ohmic heating of electrons, collisions, and the weak relativistic-ponderomotive force during the interaction of the laser beam with the plasma. Our theoretical and simulation results show that a significant nonlinearity in laser self-focusing can occur under the weak relativistic-ponderomotive regime for some appropriate simulation parameters.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2013

Nonlinear electron oscillations in a warm plasma

A class of nonstationary solutions for the nonlinear electron oscillations of a warm plasma are presented using a Lagrangian fluid description. The solution illustrates the nonlinear steepening of an initial Gaussian electron density disturbance and also shows collapse behavior in time. The obtained solution may indicate a class of nonlinear transient structures in an unmagnetized warm plasma.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2013

Nonlinear electron acoustic waves in presence of shear magnetic field

Nonlinear electron acoustic waves are studied in a quasineutral plasma in the presence of a variable magnetic field. The fluid model is used to describe the dynamics of two temperature electron species in a stationary positively charged ion background. Linear analysis of the governing equations manifests dispersion relation of electron magneto sonic wave. Whereas, nonlinear wave dynamics is being investigated by introducing Lagrangian variable method in long wavelength limit. It is shown from finite amplitude analysis that the nonlinear wave characteristics are well depicted by KdV equation. The wave dispersion arising in quasineutral plasma is induced by transverse magnetic field component. The results are discussed in the context of plasma of Earth's magnetosphere.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2013

Complex dynamics of a nonlinear voter model with contrarian agents

We investigate mean-field dynamics of a nonlinear opinion formation model with congregator and contrarian agents. Each agent assumes one of the two possible states. Congregators imitate the state of other agents with a rate that increases with the number of other agents in the opposite state, as in the linear voter model and nonlinear majority voting models. Contrarians flip the state with a rate that increases with the number of other agents in the same state. The nonlinearity controls the strength of the majority voting and is used as a main bifurcation parameter. We show that the model undergoes a rich bifurcation scenario comprising the egalitarian equilibrium, two symmetric lopsided equilibria, limit cycle, and coexistence of different types of stable equilibria with intertwining attractive basins.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

Nonlinearity measure and internal model control based linearization in anti-windup design

This paper considers the problem of internal model control based linearization in anti-windup design. The nonlinearity measure concept is used for quantifying the control system degree of nonlinearity. The linearizing effect of a modified internal model control structure is presented by comparing the nonlinearity measures of the open-loop and closed-loop systems. It is shown that the linearization properties are improved by increasing the control system local feedback gain. However, it is emphasized that at the same time the stability of the system deteriorates. The conflicting goals of stability and linearization are resolved by solving the design problem in different frequency ranges.

97 MATHEMATICS AND COMPUTING↗