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At least 1,063 records · Page 59

Degenerate Hamiltonian operator in higher-order canonical gravity — The problem and a remedy

Different routes towards canonical formulation of a classical theory result in different canonically equivalent Hamiltonians, while their quantum counterparts are related through appropriate unitary transformation. However, for higher-order theory of gravity although two Hamiltonians emerging from the same action differing by total derivative terms are related through canonical transformation, the difference transpires while attempting canonical quantization, which is predominant in non-minimally coupled higher-order theory of gravity. We follow Dirac’s constraint analysis to formulate phase-space structures, in the presence (case-I) and absence (case-II) of total derivative terms. While the coupling parameter plays no significant role as such for case-I, quantization depends on its form explicitly in case-II, and as a result unitary transformation relating the two is not unique. We also find certain mathematical inconsistencies in case-I, for modified Gauss–Bonnet-Dilatonic coupled action, in particular. Thus, we conclude that total derivative terms indeed play a major role in the quantum domain and should be taken care of a-priori, for consistency.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Near midplane scintillator-based fast ion loss detector on DIII-D

A new scintillator-based fast-ion loss detector (FILD) installed near the outer midplane of the plasma has been commissioned on DIII-D. This detector successfully measures coherent fast ion losses produced by fast-ion driven instabilities ({<=}500 kHz). Combined with the first FILD at {approx}45 Degree-Sign below the outer midplane [R. K. Fisher, et al., Rev. Sci. Instrum. 81, 10D307 (2010)], the two-detector system measures poloidal variation of losses. The phase space sensitivity of the new detector (gyroradius r{sub L}{approx}[1.5-8] cm and pitch angle {alpha}{approx}[35 Degree-Sign -85 Degree-Sign ]) is calibrated using neutral beam first orbit loss measurements. Since fast ion losses are localized poloidally, having two FILDs at different poloidal locations allows for the study of losses over a wider range of plasma shapes and types of loss orbits.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Attractors of relaxation discrete-time systems with chaotic dynamics on a fast time scale

In this work, a new type of relaxation systems is considered. Their prominent feature is that they comprise two distinct epochs, one is slow regular motion and another is fast chaotic motion. Unlike traditionally studied slow-fast systems that have smooth manifolds of slow motions in the phase space and fast trajectories between them, in this new type one observes, apart the same geometric objects, areas of transient chaos. Alternating periods of slow regular motions and fast chaotic ones as well as transitions between them result in a specific chaotic attractor with chaos on a fast time scale. We formulate basic properties of such attractors in the framework of discrete-time systems and consider several examples. Finally, we provide an important application of such systems, the neuronal electrical activity in the form of chaotic spike-burst oscillations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Boltzmann hierarchy for interacting neutrinos I: formalism

Starting from the collisional Boltzmann equation, we derive for the first time and from first principles the Boltzmann hierarchy for neutrinos including interactions with a scalar particle. Such interactions appear, for example, in majoron-like models of neutrino mass generation. We study two limits of the scalar mass: (i) An extremely massive scalar whose only role is to mediate an effective 4-fermion neutrino-neutrino interaction, and (ii) a massless scalar that can be produced in abundance and thus demands its own Boltzmann hierarchy. In contrast to, e.g., the first-order Boltzmann hierarchy for Thomson-scattering photons, our interacting neutrino/scalar Boltzmann hierarchies contain additional momentum-dependent collision terms arising from a non-negligible energy transfer in the neutrino-neutrino and neutrino-scalar interactions. This necessitates that we track each momentum mode of the phase space distributions individually, even if the particles were massless. Comparing our hierarchy with the commonly used (c{sub eff}{sup 2},c{sub vis}{sup 2})-parameterisation, we find no formal correspondence between the two approaches, which raises the question of whether the latter parameterisation even has an interpretation in terms of particle scattering. Lastly, although we have invoked majoron-like models as a motivation for our study, our treatment is in fact generally applicable to all scenarios in which the neutrino and/or other ultrarelativistic fermions interact with scalar particles.

79 ASTRONOMY AND ASTROPHYSICS↗

ASSESSING ASTROPHYSICAL UNCERTAINTIES IN DIRECT DETECTION WITH GALAXY SIMULATIONS

We study the local dark matter velocity distribution in simulated Milky Way-mass galaxies, generated at high resolution with both dark matter and baryons. We find that the dark matter in the solar neighborhood is influenced appreciably by the inclusion of baryons, increasing the speed of dark matter particles compared to dark matter-only simulations. The gravitational potential due to the presence of a baryonic disk increases the amount of high velocity dark matter, resulting in velocity distributions that are more similar to the Maxwellian Standard Halo Model than predicted from dark matter-only simulations. Furthermore, the velocity structures present in baryonic simulations possess a greater diversity than expected from dark matter-only simulations. We show that the impact on the direct detection experiments LUX, DAMA/Libra, and CoGeNT using our simulated velocity distributions, and explore how resolution and halo mass within the Milky Way’s estimated mass range impact the results. A Maxwellian fit to the velocity distribution tends to overpredict the amount of dark matter in the high velocity tail, even with baryons, and thus leads to overly optimistic direct detection bounds on models that are dependent on this region of phase space for an experimental signal. Our work further demonstrates that it is critical to transform simulated velocity distributions to the lab frame of reference, due to the fact that velocity structure in the solar neighborhood appears when baryons are included. There is more velocity structure present when baryons are included than in dark matter-only simulations. Even when baryons are included, the importance of the velocity structure is not as apparent in the Galactic frame of reference as in the Earth frame.

79 ASTRONOMY AND ASTROPHYSICS↗

Hybrid (Vlasov-Fluid) simulation of ion-acoustic solitons chain formation including trapped electrons

Disintegration of a Gaussian profile into ion-acoustic solitons in the presence of trapped electrons [H. Hakimi Pajouh and H. Abbasi, Phys. Plasmas 15, 082105 (2008)] is revisited. Through a hybrid (Vlasov-Fluid) model, the restrictions associated with the simple modified Korteweg de-Vries (mKdV) model are studied. For instance, the lack of vital information in the phase space associated with the evolution of electron velocity distribution, the perturbative nature of mKdV model which limits it to the weak nonlinear cases, and the special spatio-temporal scaling based on which the mKdV is derived. Remarkable differences between the results of the two models lead us to conclude that the mKdV model can only monitor the general aspects of the dynamics, and the precise picture including the correct spatio-temporal scales and the properties of solitons should be studied within the framework of hybrid model.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

GLOBAL DRAG-INDUCED INSTABILITIES IN PROTOPLANETARY DISKS

We use the Fokker-Planck equation and model the dispersive dynamics of solid particles in annular protoplanetary disks whose gas component is more massive than the particle phase. We model particle-gas interactions as hard sphere collisions, determine the functional form of diffusion coefficients, and show the existence of two global unstable modes in the particle phase. These modes have spiral patterns with the azimuthal wavenumber m = 1 and rotate slowly. We show that in ring-shaped disks, the phase-space density of solid particles increases linearly in time toward an accumulation point near the location of pressure maximum, while instabilities grow exponentially. Therefore, planetesimals and planetary cores can be efficiently produced near the peaks of unstable density waves. In this mechanism, particles migrating toward the accumulation point will not participate in the formation of planets, and should eventually form a debris ring like the main asteroid belt or classical Kuiper Belt objects. We present the implications of global instabilities to the formation of ice giants and terrestrial planets in the solar system.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Gaussian-windowed frame based method of moments formulation of surface-integral-equation for extended apertures

Scattering or coupling of electromagnetic beam-field at a surface discontinuity separating two homogeneous or inhomogeneous media with different propagation characteristics is formulated using surface integral equation, which are solved by the Method of Moments with the aid of the Gabor-based Gaussian window frame set of basis and testing functions. The application of the Gaussian window frame provides (i) a mathematically exact and robust tool for spatial-spectral phase-space formulation and analysis of the problem; (ii) a system of linear equations in a transmission-line like form relating mode-like wave objects of one medium with mode-like wave objects of the second medium; (iii) furthermore, an appropriate setting of the frame parameters yields mode-like wave objects that blend plane wave properties (as if solving in the spectral domain) with Green's function properties (as if solving in the spatial domain); and (iv) a representation of the scattered field with Gaussian-beam propagators that may be used in many large (in terms of wavelengths) systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

SPENDING TOO MUCH TIME AT THE GALACTIC BAR: CHAOTIC FANNING OF THE OPHIUCHUS STREAM

The Ophiuchus stellar stream is peculiar: (1) its length is short given the age of its constituent stars, and (2) several probable member stars have dispersions in sky position and velocity that far exceed those seen within the stream. The stream’s proximity to the Galactic center suggests that its dynamical history is significantly influenced by the Galactic bar. We explore this hypothesis with models of stream formation along orbits consistent with Ophiuchus’ properties in a Milky Way potential model that includes a rotating bar. In all choices for the rotation parameters of the bar, orbits fit to the stream are strongly chaotic. Mock streams generated along these orbits qualitatively match the observed properties of the stream: because of chaos, stars stripped early generally form low-density, high-dispersion “fans” leaving only the most recently disrupted material detectable as a strong over-density. Our models predict that there should be a significant amount of low-surface-brightness tidal debris around the stream with a complex phase-space morphology. The existence of or lack of these features could provide interesting constraints on the Milky Way bar and would rule out formation scenarios for the stream. This is the first time that chaos has been used to explain the properties of a stellar stream and is the first demonstration of the dynamical importance of chaos in the Galactic halo. The existence of long, thin streams around the Milky Way, presumably formed along non- or weakly chaotic orbits, may represent only a subset of the total population of disrupted satellites.

79 ASTRONOMY AND ASTROPHYSICS↗

The effect of electron beam pitch angle and density gradient on solar type III radio bursts

1.5D particle-in-cell simulations of a hot, low density electron beam injected into magnetized, maxwellian plasma were used to further explore the alternative non-gyrotropic beam driven electromagnetic (EM) emission mechanism, first studied in Tsiklauri, Phys. Plasmas 18, 052903 (2011). Variation of beam injection angle and background density gradient showed that the emission process is caused by the perpendicular component of the beam injection current, whereas the parallel component only produces Langmuir waves, which play no role in the generation of EM waves in our mechanism. Particular emphasis was put on the case, where the beam is injected perpendicularly to the background magnetic field, as this turned off any electrostatic wave generation along the field and left a purely electromagnetic signal in the perpendicular components. The simulations establish the following key findings: (i) Initially, waves at a few {omega}{sub ce}/{gamma} are excited, mode converted and emitted at Almost-Equal-To {omega}{sub pe} (ii) The emission intensity along the beam axis is proportional to the respective component of the kinetic energy of the beam; (iii) The frequency of the escaping EM emission is independent of the injection angle; (iv) A stronger background density gradient causes earlier emission; (v) The beam electron distribution function in phase space shows harmonic oscillation in the perpendicular components at the relativistic gyrofrequency; (vi) The requirement for cyclotron maser emission, ({partial_derivative}f/{partial_derivative}v{sub Up-Tack })>0, is fulfilled; (vii) The degree of linear polarization of the emission is strongly dependent on the beam injection angle; (viii) The generated electromagnetic emission is left-hand elliptically polarized as the pitch angle tends to 90 Degree-Sign ; and (ix) The generated electromagnetic energy is of the order of 0.1% of the initial beam kinetic energy.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Improving the accuracy and efficiency of time-resolved electronic spectra calculations: Cellular dephasing representation with a prefactor

Time-resolved electronic spectra can be obtained as the Fourier transform of a special type of time correlation function known as fidelity amplitude, which, in turn, can be evaluated approximately and efficiently with the dephasing representation. Here we improve both the accuracy of this approximation—with an amplitude correction derived from the phase-space propagator—and its efficiency—with an improved cellular scheme employing inverse Weierstrass transform and optimal scaling of the cell size. We demonstrate the advantages of the new methodology by computing dispersed time-resolved stimulated emission spectra in the harmonic potential, pyrazine, and the NCO molecule. In contrast, we show that in strongly chaotic systems such as the quartic oscillator the original dephasing representation is more appropriate than either the cellular or prefactor-corrected methods.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Maximal energy extraction under discrete diffusive exchange

Waves propagating through a bounded plasma can rearrange the densities of states in the six-dimensional velocity-configuration phase space. Depending on the rearrangement, the wave energy can either increase or decrease, with the difference taken up by the total plasma energy. In the case where the rearrangement is diffusive, only certain plasma states can be reached. It turns out that the set of reachable states through such diffusive rearrangements has been described in very different contexts. Building upon those descriptions, and making use of the fact that the plasma energy is a linear functional of the state densities, the maximal extractable energy under diffusive rearrangement can then be addressed through linear programming.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Coherent distributions for the rigid rotator

Coherent solutions of the classical Liouville equation for the rigid rotator are presented as positive phase-space distributions localized on the Lagrangian submanifolds of Hamilton-Jacobi theory. These solutions become Wigner-type quasiprobability distributions by a formal discretization of the left-invariant vector fields from their Fourier transform in angular momentum. The results are consistent with the usual quantization of the anisotropic rotator, but the expected value of the Hamiltonian contains a finite “zero point” energy term. It is shown that during the time when a quasiprobability distribution evolves according to the Liouville equation, the related quantum wave function should satisfy the time-dependent Schrödinger equation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Effect of ion-to-electron mass ratio on the evolution of ion beam driven instability in particle-in-cell simulations

In particle-in-cell (PIC) simulation studies of ion-ion two-stream instability, a reduced ion-to-electron mass ratio is often employed to save computation time. It is tacitly assumed that electrons do not play a significant role in the evolution of the instability as the ion-ion interactions are regarded to occur on time scales much slower than the response time of electrons. However, as the effect of such a reduced mass ratio has never been closely examined, we have studied the evolution of the ion beam driven instability using a one-dimensional electrostatic PIC code by rescaling the simulation parameters according to the ion-electron mass ratio. We made a reference simulation run with a mass ratio of 100 first and compared the results to the simulation results using the real mass ratio with parameters rescaled from those of the reduced mass ratio. External electric fields were applied in these simulations, which accelerated the electrons and excited an ion acoustic type instability, forming electron phase space holes. Merging of the electron holes affected the ion dynamics significantly when the reduced mass ratio was used, while the interplay between the electron and ion dynamics became different depending on the rescaling methods in the case of the real mass ratio. Another simulation test with much enhanced external electric field results in similar mass ratio dependence. The present simulation results clearly show that the reduced mass ratio should be used cautiously in PIC simulations as the electron dynamics can modify the ion instabilities significantly by affecting the ion motions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Monte Carlo implementation of a guiding-center Fokker-Planck kinetic equation

A Monte Carlo method for the collisional guiding-center Fokker-Planck kinetic equation is derived in the five-dimensional guiding-center phase space, where the effects of magnetic drifts due to the background magnetic field nonuniformity are included. It is shown that, in the limit of a homogeneous magnetic field, our guiding-center Monte Carlo collision operator reduces to the guiding-center Monte Carlo Coulomb operator previously derived by Xu and Rosenbluth [Phys. Fluids B 3, 627 (1991)]. Applications of the present work will focus on the collisional transport of energetic ions in complex nonuniform magnetized plasmas in the large mean-free-path (collisionless) limit, where magnetic drifts must be retained.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

MERIDIONAL FLOW IN THE SOLAR CONVECTION ZONE. II. HELIOSEISMIC INVERSIONS OF GONG DATA

Meridional flow is thought to play a very important role in the dynamics of the solar convection zone; however, because of its relatively small amplitude, precisely measuring it poses a significant challenge. Here we present a complete time–distance helioseismic analysis of about 2 years of ground-based Global Oscillation Network Group (GONG) Doppler data to retrieve the meridional circulation profile for modest latitudes in an attempt to corroborate results from other studies. We use an empirical correction to the travel times due to an unknown center-to-limb systematic effect. The helioseismic inversion procedure is first tested and reasonably validated on artificial data from a large-scale numerical simulation followed by a test to broadly recover the solar differential rotation found from global seismology. From GONG data, we measure poleward photospheric flows at all latitudes with properties that are comparable with earlier studies and a shallow equatorward flow about 65 Mm beneath the surface, in agreement with recent findings from Helioseismic and Magnetic Imager (HMI) data. No strong evidence of multiple circulation cells in depth or latitude is found, yet the whole phase space has not yet been explored. Tests of mass flux conservation are then carried out on the inferred GONG and HMI flows and compared to a fiducial numerical baseline from models, and we find that the continuity equation is poorly satisfied. While the two disparate data sets do give similar results for about the outer 15% of the interior radius, the total inverted circulation pattern appears to be unphysical in terms of mass conservation when interpreted over modest time scales. We can likely attribute this to both the influence of realization noise and subtle effects in the data and measurement procedure.

79 ASTRONOMY AND ASTROPHYSICS↗

Generation of Coherent X-Ray Radiation through Modulation Compression

In this paper, we propose a scheme to generate tunable coherent X-ray radiation for future light source applications. This scheme uses an energy chirped electron beam, a laser modulator, a laser chirper and two bunch compressors to generate a prebunched kilo-Ampere current electron beam from a few tens Ampere electron beam out of a linac. The initial modulation energy wavelength can be compressed by a factor of 1 + h{sub b}R{sub 56}{sup a} in phase space, where h{sub b} is the energy bunch length chirp introduced by the laser chirper, R{sub 56}{sup a} is the momentum compaction factor of the first bunch compressor. As an illustration, we present an example to generate more than 400 MW, 170 attoseconds pulse, 1 nm coherent X-ray radiation using a 60 A electron beam out of the linac and 200 nm laser seed. Both the final wavelength and the radiation pulse length in the proposed scheme are tunable by adjusting the compression factor and the laser parameters.

43 PARTICLE ACCELERATORS↗

Comparison of toroidicity-induced Alfvén eigenmodes and energetic particle modes by gyrokinetic particle simulations

This work reports on linear global gyrokinetic particle simulations of the excitation of toroidicity-induced Alfvén eigenmodes (TAE) and energetic particle modes (EPM), and the comparison between these two modes. The TAE excitation by antenna clarifies the magnetohydrodynamic (MHD) mode structure and the discrete eigenmode exists in the gap between the upper and lower accumulation points. The TAE excitation by fast ions modifies the MHD mode structure because of radial symmetry breaking and the eigenmode frequency moves towards the lower accumulation point. The phase space structure of fast ions shows that both passing and trapped particles contribute to the TAE excitation and that trapped particles dominate the wave-particle resonance in our simulations. The growth rate of TAE is sensitive to the fast ion energy, density, and density gradient, which are also important factors contributing to the transition of the TAE to the EPM. The gyrokinetic particle simulations also confirm the excitation of EPM when the drive is stronger. The frequency of the EPM is determined by the characteristic frequencies of fast ion motion in toroidal geometry.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗