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DOE OSTI2016

CALCULATING ROTATING HYDRODYNAMIC AND MAGNETOHYDRODYNAMIC WAVES TO UNDERSTAND MAGNETIC EFFECTS ON DYNAMICAL TIDES

To understand magnetic effects on dynamical tides, we study the rotating magnetohydrodynamic (MHD) flow driven by harmonic forcing. The linear responses are analytically derived in a periodic box under the local WKB approximation. Both the kinetic and Ohmic dissipations at the resonant frequencies are calculated, and the various parameters are investigated. Although magnetic pressure may be negligible compared to thermal pressure, the magnetic field can be important for the first-order perturbation, e.g., dynamical tides. It is found that the magnetic field splits the resonant frequency, namely the rotating hydrodynamic flow has only one resonant frequency, but the rotating MHD flow has two, one positive and the other negative. In the weak field regime the dissipations are asymmetric around the two resonant frequencies and this asymmetry is more striking with a weaker magnetic field. It is also found that both the kinetic and Ohmic dissipations at the resonant frequencies are inversely proportional to the Ekman number and the square of the wavenumber. The dissipation at the resonant frequency on small scales is almost equal to the dissipation at the non-resonant frequencies, namely the resonance takes its effect on the dissipation at intermediate length scales. Moreover, the waves with phase propagation that is perpendicular to the magnetic field are much more damped. It is also interesting to find that the frequency-averaged dissipation is constant. This result suggests that in compact objects, magnetic effects on tidal dissipation should be considered.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2017

Tunneling-assisted transport of carriers through heterojunctions.

The formulation of carrier transport through heterojunctions by tunneling and thermionic emission is derived from first principles. The treatment of tunneling is discussed at three levels of approximation: numerical solution of the one-band envelope equation for an arbitrarily specified potential profile; the WKB approximation for an arbitrary potential; and, an analytic formulation assuming constant internal field. The effects of spatially varying carrier chemical potentials over tunneling distances are included. Illustrative computational results are presented. The described approach is used in exploratory physics models of irradiated heterojunction bipolar transistors within Sandia's QASPR program.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

WKB Estimate of Bilayer Graphene’s Magic Twist Angles

We report that graphene bilayers exhibit zero-energy flatbands at a discrete series of magic twist angles. In the absence of intrasublattice interlayer hopping, zero-energy states satisfy a Dirac equation with a non-Abelian SU(2) gauge potential that cannot be diagonalized globally. We develop a semiclassical WKB approximation scheme for this Dirac equation by introducing a dimensionless Planck’s constant proportional to the twist angle, solving the linearized Dirac equation around AB and BA turning points, and connecting Airy function solutions via bulk WKB wave functions. We find zero-energy solutions at a discrete set of values of the dimensionless Planck’s constant, which we obtain analytically. Our analytic flatband twist angles correspond closely to those determined numerically in previous work.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Bootstrapping closed string field theory

The determination of the string vertices of closed string field theory is shown to be a conformal field theory problem solvable by combining insights from Liouville theory, hyperbolic geometry, and conformal bootstrap. We first demonstrate how Strebel differentials arise from hyperbolic string vertices by performing a WKB approximation to the associated Fuchsian equation, which we subsequently use it to derive a Polyakov-like conjecture for Strebel differentials. This result implies that the string vertices are generated by the interactions of n zero momentum tachyons, or equivalently, a certain limit of suitably regularized on-shell Liouville action. We argue that the latter can be related to the interaction of three zero momentum tachyons on a generalized cubic vertex through classical conformal blocks. We test this claim for the quartic vertex and discuss its generalization to higher-string interactions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2020

A WKB based preconditioner for the 1D Helmholtz wave equation

Frequency-domain full-wave solutions to the cold-plasma problem have become ubiquitous in the study of radio frequency power in fusion plasmas. However, recent efforts at extreme levels of geometric fidelity have revealed fundamental limits in the problem size that can be solved by typical sparse direct solver based methods. These limits are of particular importance in the 3D study of RF launchers, where the number of degrees of freedom required can exceed 100 million. In such cases, it would be advantageous to solve the system via iterative means, but due to the large null space of the curl-curl operator, the convergence properties of algorithms like GMRES are poor. Here we present a physics-based preconditioner in the form of a WKB solution and demonstrate the iterative solution to the frequency-domain Helmholtz problem in 1D for several cases ranging from satisfying the WKB approximation to strongly violating it.

Green, David↗

DOE OSTI2023

Stationary Bragg reflection of laser light in inhomogeneous absorbing plasmas inside inertial confinement fusion Hohlraums

Laser-produced plasma in inertial confinement fusion (ICF) Hohlraums are marked with density non-uniformity whose length scale can go down to micrometers. This scale is of the order of the laser wavelength. The WKB approximation, which is classically used in radiation-hydrodynamic codes to compute the laser trajectory, cannot correctly take into account such small-scale inhomogeneity of the plasma. Going beyond this approximation, we predict a novel mechanism for the laser reflection. Here we show that an electromagnetic plane wave with wave number k resonates with the k B =2 k Fourier component of a multimode perturbation of the background density and generates a reflected wave. It is the first time that this reflection is considered for stationary inhomogeneous ICF plasmas, and the energy absorption is taken into account. This mechanism, which is a form of Bragg reflection, can occur away from the critical surface and generate a drift of the location of the laser absorption. Furthermore, this absorption will be periodically modulated with a k B wave number. The stationary Bragg reflection can explain ongoing discrepancies between experimental and numerical data about laser trajectory and absorption in ICF Hohlraums.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2020

ISCOs in AdS/CFT

Abstract We study stable circular orbits in spherically symmetric AdS black holes in various dimensions and their limiting innermost stable circular orbits. We provide analytic expressions for their size, angular velocity and angular momentum in a large black hole mass regime. The dual interpretation is in terms of meta-stable states not thermalising in typical thermal scales and whose existence is due to non-perturbative effects on the spatial curvature. Our calculations reproduce the binding energy known in the literature, but also include a binding energy in the radial fluctuations corresponding to near circular trajectories. We also describe how particles are placed on these orbits from integrated operators on the boundary: they tunnel inside in a way that can be computed from both complex geodesics in the black hole background and from the WKB approximation of the wave equation. We explain how these two computations are related.

Astronomy & Astrophysics↗

DOE OSTI2024

One-dimensional reflection in the quantum mechanical bootstrap

We describe the application of the quantum mechanical bootstrap to the solution of one-dimensional scattering problems. By fixing a boundary and modulating the Robin parameter of the boundary conditions we are able to extract the reflection coefficient for various potentials and compare to physical expectations. This includes an application of semidefinite programming to solving a half line Schrodinger problem with arbitrary Robin boundary conditions. Finally, the WKB approximation is used to numerically determine the scattering behavior of the exponential potential of Liouville theory. Published by the American Physical Society 2024

Astronomy & Astrophysics↗

DOE OSTI2021

Adiabatic behavior of an elliptical vortex in a time-dependent external strain flow

The adiabatic behavior of two-dimensional (2D) fluid vortices subject to slowly varying, time-dependent external strain flows is studied theoretically, and experimentally using magnetized non-neutral electron plasmas. Here the E × B drift dynamics of the electrons perpendicular to the magnetic field are analogous to the motion of fluid vorticity under the 2D Euler equations describing ideal fluids. A low-dimensional elliptical vortex patch model is used along with a WKB approximation to derive a formula for the breaking of an adiabatic invariant due to the changing external flow. The invariant is interpreted as the amplitude of a perturbative oscillation about a stable fixed point corresponding to a steady elliptical vortex. Smooth, hyperbolic tangent and piecewise linear ramp functions are considered for the external strain time dependence. Standard exponential breaking is observed in the former case, whereas the latter exhibits a power-law breaking curve with periodic modulation. It is found that a driving term in the equations of motion contributes the majority of the breaking whereas the frequency variation plays a weaker, but significant role. The experimental data agree closely with the theoretical model. The most significant deviation is due to inviscid damping behavior associated with the smooth edges of the experimental vortices, which tends to reduce the amplitude of the oscillation. Finally, the results are compared and contrasted with other related experimental, numerical, and theoretical work.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2014

Final Technical Report for NSF/DOE partnership grant 1004284/ER54905/SC0004660: 2011- 2013

Research has been performed on two topics: (1) Nonlinear time-dependent phenomena in the regime of electron magnetohydrodynamics (EMHD). (2) Plasma structures forming ”bubbles”. The latter are regions of localized density depletions or enhancements separated from the ambient plasma by sheaths or double layers. Three-dimensional magnetic null points can also be considered as ”magnetic bubbles”. Nonlinear EMHD fields are generated by pulsed magnetic loops. The magnetic field varies in time faster than an ion cyclotron period, hence interacts only with electrons. Space charge electric fields are created when magnetic forces try to separate electrons from ions. Electric and magnetic forces nearly balance to keep the plasma quasi neutral. This leads to rotational electron motions, i.e. Hall currents and associated magnetic perturbations. When the time scale falls between the ion and electron cyclotron period the magnetic perturbation is convected in the whistler mode. When the time-varying magnetic field exceeds the background magnetic field the whistler mode becomes highly nonlinear since its properties depend on the total magnetic field. When the time-varying magnetic field creates magnetic null points or null lines EMHD breaks down. Electrons can be accelerated in null lines which dissipated magnetic energy like in magnetic reconnection. Energized electrons with anisotropic distributions create secondary whistler instabilities. These effects have been observed in field topologies resembling spheromaks and field-reversed configurations (FRCs). The whistler mode propagation near magnetic nulls is not trivial when the field gradients and wavelength are comparable. Ray tracing is inappropriate when the WKB approximation breaks down. Experiments have been started to map wave propagation on curved field lines with null points. Initial results show that whistlers in highly nonuniform fields have highly oblique phase velocities but the energy flow remains dominantly along the field. Density bubbles are created by anode discharges, typically forming spherical ”fireballs” bounded by a double layer. In a magnetized plasma the shape becomes cylindrical, in nonuniform magnetic fields many asymmetric fireball shapes are possible. Due to electron energization the fireball plasma has higher density and temperature than the ambient plasma. The double layer can also be produced by a high transparency positively biased grid. Instabilities arise from the electron transit through the plasma bubble and the double layer. When a permanent magnet is biased positively the electrons perform ExB drifts in the equatorial plane between the poles. Electron drift modes are excited with a high spectral contents. Similarly, a negatively biased magnet produces a disk-shaped plasma bubble. The cold magnet emits secondary electrons due to the impact of energetic ions. Such magnetron discharges exhibit a variety of instabilities which affect the cross-field transport and sputtering applications. This report will summarize the main effects observed and provide references to more detailed publications.

, nonlinear time-dependent phenomena↗

DOE OSTI2020

Theoretical study of various nonlinear phenomena in plasma systems and scaling of magneto-inertial-fusion targets

Plasma physics is an exciting field of study with a wide variety of nonlinear processes that come into play. Examples of such processes include the interaction of small-scale turbulence with large-scale plasma structures and the nonlinear saturation of plasma instabilities, for example those of magneto-hydrodynamical nature. During this Truman LDRD project, I studied a collection of nonlinear problems that are of interest to the field of plasma physics. This LDRD report summarizes four main research accomplishments. First, a new statistical model for describing inhomogeneous drift-wave turbulence inter- acting with zonal flows was developed. This new model includes the effects of nonlinear wave-wave collisions, which are expected to change the spectrum of the underlying DW turbulence and therefore the generation of zonal flows. Second, a new mathematical formalism was proposed to systematically apply the non- linear WKB approximation to general field theories, including those often used in fluid dynamics. This formalism represents an interesting tool for studying physical systems that show an explicit scale separation. Third, a weakly nonlinear model was developed to describe the magneto-Rayleigh-Taylor instability. This instability is of paramount importance to understand as it can reduce the performance of magnetic-inertial-fusion (MIF) platforms. The developed models captures the effects of harmonic generation and saturation of the linear growth of the instability. Finally, a framework was proposed for scaling magneto-inertial fusion (MIF) targets to larger pulsed-power drivers. From this framework, a set of scaling rules were derived that conserve the physical regimes of MIF systems when scaling up in peak current. By doing so, deleterious nonlinear processes that affect MIF performance may be kept at bay.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2015

Understanding channel and contact effects on transport in 1-dimensional nanotransistors.

Nanowire transistors are generally formed by metal contacts to a uniformly doped nanowire. The transistor can be modeled as a series combination of resistances from both the channel and the contacts. In this study, a simple model is proposed consisting of a resistive channel in series with two Schottky metal-semiconductor contacts modeled using the WKB approximation. This model captures several phenomena commonly observed in nanowire transistor measurements, including the mobility as a function of gate potential, mobility reduction with respect to bulk mobility, and non-linearities in output characteristics. For example, the maximum measured mobility as a function of gate voltage in a nanowire transistor can be predicted based on the semiconductor bulk mobility in addition to barrier height and other properties of the contact. The model is then extended to nanowires with axial p-n junctions having an inde- pendent gate over each wire segment by splitting the channel resistance into a series component for each doping segment. Finally, the contact-channel model is applied to low-frequency noise analysis in nanowire devices, where the noise can be generated in both the channel and the contacts. Because contacts play a major, yet often neglected, role in nanowire transistor operation, they must be accounted for in order to extract meaningful parameters from I-V and noise measurements.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

DOE OSTI2016

Logarithmic divergences in the k-inflationary power spectra computed through the uniform approximation

We investigate a calculation method for solving the Mukhanov-Sasaki equation in slow-roll k-inflation based on the uniform approximation (UA) in conjunction with an expansion scheme for slow-roll parameters with respect to the number of e-folds about the so-called turning point. Earlier works on this method have so far gained some promising results derived from the approximating expressions for the power spectra among others, up to second order with respect to the Hubble and sound flow parameters, when compared to other semi-analytical approaches (e.g., Green's function and WKB methods). However, a closer inspection is suggestive that there is a problem when higher-order parts of the power spectra are considered; residual logarithmic divergences may come out that can render the prediction physically inconsistent. Looking at this possibility, we map out up to what order with respect to the mentioned parameters several physical quantities can be calculated before hitting a logarithmically divergent result. It turns out that the power spectra are limited up to second order, the tensor-to-scalar ratio up to third order, and the spectral indices and running converge to all orders. This indicates that the expansion scheme is incompatible with the working equations derived from UA for the power spectra but compatible with that of the spectral indices. For those quantities that involve logarithmically divergent terms in the higher-order parts, existing results in the literature for the convergent lower-order parts calculated in the equivalent fashion should be viewed with some caution; they do not rest on solid mathematical ground.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2010

Collocation method for fractional quantum mechanics

We show that it is possible to obtain numerical solutions to quantum mechanical problems involving a fractional Laplacian, using a collocation approach based on little sinc functions, which discretizes the Schroedinger equation on a uniform grid. The different boundary conditions are naturally implemented using sets of functions with the appropriate behavior. Good convergence properties are observed. A comparison with results based on a Wentzel-Kramers-Brillouin analysis is performed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2015

SAUSAGE WAVES IN TRANSVERSELY NONUNIFORM MONOLITHIC CORONAL TUBES

We investigate fast sausage waves in a monolithic coronal magnetic tube, modeled as a local density inhomogeneity with a continuous radial profile. This work is a natural extension of our previous results, obtained for a slab loop model for the case of cylindrical geometry. Using Kneser’s oscillating theorem, we provided the criteria for the existence of trapped and leaky wave regimes as a function of the profile features. For a number of density profiles there are only trapped modes for the entire range of longitudinal wave numbers. The phase speed of these modes tends toward the external Alfvén speed in the long wavelength limit. The generalized results were supported by the analytic solution of the wave equation for the specific density profiles. The approximate Wentzel–Kramers–Brillouin solutions allowed us to obtain the desired dispersion relations and to study their properties as a function of the profile parameters. The multicomponent quasi-periodic pulsations in flaring loops, observed on 2001 May 2 and 2002 July 3, are interpreted in terms of the transversely fundamental trapped fast sausage mode with several longitudinal harmonics in a smooth coronal waveguide.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2011

The internal waves and Rayleigh-Taylor instability in compressible quantum plasmas

In this paper, we investigate the quantum effect on internal waves and Rayleigh-Taylor (RT) instability in compressible quantum plasmas. First of all, let us consider the case of the limit of short wavelength perturbations. In the case, the dispersion relation including quantum and compressibility effects and the RT instability growth rate can be derived using Wentzel-Kramers-Brillouin method. The results show that the internal waves can propagate along the transverse direction due to the quantum effect, which was first pointed out by Bychkov et al.[Phys. Lett. A 372, 3042 (2008)], and the coupling between it and compressibility effect, which is found out in this paper. Then, without making the approximation assumption of short wavelength limit, we examine the linearized perturbation equation following Qiu et al.'s solving process [Phys. Plasmas 10, 2956 (2003)]. It is found that the quantum effect always stabilizes the RT instability in either incompressible or compressible quantum plasmas. Moreover, in the latter case, the coupling between it and compressibility effect makes this stabilization further enhance.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2015

Self-focusing of Hermite-Gaussian laser beam with relativistic nonlinearity

This paper presents an investigation of self-focusing of Hermite-Gaussian laser beams in plasma considering relativistic nonlinearity. The differential equations for beam width parameters are obtained using the usual Wentzel–Kramers–Brillouin and paraxial approximations. The nonlinearity in the dielectric constant is assumed to be aroused mainly due to the relativistic mass correction of electron. To highlight the nature of focusing, graphical results of the behavior of beam-width parameters with the dimensionless distance of propagation is presented. The numerical computation is completed by using Taylor series method. The present work is helpful to understand issues related to the beam propagation in laser plasma interaction experiments.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2014

Alfvén ion-cyclotron instability in an axisymmetric trap with oblique injection of fast atoms

Conditions for the onset of Alfvén ion-cyclotron instability and the spatial structure of unstable modes in an axisymmetric mirror trap with oblique injection of fast atoms are studied. It is shown that the main contribution to instability comes from the inverse population of ions in the velocity space domain into which atoms are injected. Using the distribution function of fast ions obtained by approximately solving the Fokker-Planck equation, the instability threshold in terms of β{sub ⊥} is determined in the Wentzel-Kramers-Brillouin approximation as a function of the geometric parameters and the parameters of injection and target plasma. It is demonstrated that the stability threshold increases substantially when the radius of the hot plasma decreases to a size comparable with the Larmor radius of fast ions. It is shown that the perturbed fields near the axis and at the plasma periphery can rotate in opposite directions, which is important for the interpretation of experimental data.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗