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NASA NTRS1975

Effects of friction and heat conduction on sound propagation in ducts

A theoretical formulation of the propagation of sound in a viscous and heat conducting medium is presented. The problem is reduced to the determination of two scalar potentials related to pressure and entropy fluctuations respectively, and a vector potential related to vorticity fluctuations. The particular case of a two-dimensional duct of constant width is thoroughly investigated in the low, high, and very high frequency ranges. It is shown that three distinct families of modes may propagate along the duct axis, namely, pressure, entropy, and vorticity dominated modes. Perturbation methods are used to study the variations of attenuation rates, phase velocities, and mode shapes, as a function of frequency and duct width.

Huerre, P.↗

NASA NTRS1987

A three-dimensional dual potential procedure with applications to wind tunnel inlets and interacting boundary layers

A dual potential decomposition of the velocity field into a scalar and a vector potential function is extended to three dimensions and used in the finite-difference simulation of steady three-dimensional inviscid rotational flows and viscous flow. The finite-difference procedure was used to simulate the flow through the 80 by 120 ft wind tunnel at NASA Ames Research Center. Rotational flow produced by the stagnation pressure drop across vanes and screens which are located at the entrance of the inlet is modeled using actuator disk theory. Results are presented for two different inlet vane and screen configurations. The numerical predictions are in good agreement with experimental data. The dual potential procedure was also applied to calculate the viscous flow along two and three dimensional troughs. Viscous effects are simulated by injecting vorticity which is computed from a boundary layer algorithm. For attached flow over a three dimensional trough, the present calculations are in good agreement with other numerical predictions. For separated flow, it is shown from a two dimensional analysis that the boundary layer approximation provides an accurate measure of the vorticity in regions close to the wall; whereas further away from the wall, caution has to be exercised in using the boundary-layer equations to supply vorticity to the dual potential formulation.

Rao, K. V.↗

NASA NTRS1987

A three-dimensional dual potential procedure for inlets and indraft wind tunnels

Rao, K. V.↗

NASA NTRS1992

Role of inductive electric fields in substorm development

A study discussing and investigating the role of inductive electric fields in substorm development is presented. It is common to use the scalar potential phi to calculate the electrostatic field E(sup ES)-(inverted Delta)(phi). However, vector potential A has not been extensively used to analyze results by the relation for the inductive electric field E(sup IND)-delta A/delta t. Because of the weak dependence in distance (1/r) these potentials show the effect of distant sources, unlike MHD (Magnetohydrodynamic) theory which is strictly local. The two can be separated by the choice of the Coulomb (transverse) gauge. It is proper to consider that the plasma polarizes to counteract the activation of the inductive electric field; this is a matter of cause and effect. However, such polarization produces a curl free electrostatic field and thus cannot alter the electromotive force due to induction. This idea has some interesting consequences for plasma physics, including violations of MHD theory, creation of the substorm current diversion, and a fresh look at dayside merging via plasma transfer events.

Heikkila, Walter J.↗

NASA NTRS1990

Far field velocity potential induced by a rapidly decaying vorticity distribution

The velocity field induced by a vorticity distribution decaying rapidly in the distance from the origin is investigated. It is shown that the sum of vector potentials for the velocity field can be expressed as a linear combination of Mn values, where Mn denotes the number of linearly independent vector functions of nth order. It is then shown that only the linear combinations 2n + 1 of these Mn vector functions contribute to the far field velocity which is irrotational, and that the corresponding scalar potential is then represented by a linear combination of 2n + 1 spherical harmonics of nth order whose coefficients are linear combinations of nth moments of vorticity.

Klein, Rupert↗

NASA NTRS1995

Phase space analysis in anisotropic optical systems

From the minimal action principle follows the Hamilton equations of evolution for geometric optical rays in anisotropic media. As in classical mechanics of velocity-dependent potentials, the velocity and the canonical momentum are not parallel, but differ by an anisotropy vector potential, similar to that of linear electromagnetism. Descartes' well known diagram for refraction is generalized and a factorization theorem holds for interfaces between two anisotropic media.

Rivera, Ana Leonor↗

DOE OSTI2025

First Principles Cable Braid Electromagnetic Penetration Model - Potential Impedance Clarification

In this report the lack of assumed connectivity between braid carriers imposes the need to use the original magnetic vector potential formulas for transfer and self impedances rather than the final simplified results in the magnetic coupling and propagation formulas. Each of the magnetic sections in the previous journal article and Sandia report are addressed with references to the appropriate formulas.

42 ENGINEERING↗

NASA NTRS1988

A scalar/vector potential formulation of an airfoil in nonuniform stream

A recent innovation in aerodynamic calculation techniques is the formulation based upon scalar and vector potentials (Stokes-Helmholtz decomposition) for the velocity field. This technique is presented: an implementation involving classical panel method is studied. The application of interest is to two-dimensional airfoils moving into a nonuniform approach flow. Comparisons with theoretical and numerical results are included. Furthermore the variations of lift and moment coefficients of quasi-steady simulated flight of an airfoil through microburst wind shear data are studied.

Wang, J. C. A.↗

NASA NTRS2007

Simple and Efficient Numerical Evaluation of Near-Hypersingular Integrals

Simple and efficient numerical procedures for evaluating the gradient of Newton-type potentials are presented. Convergences of both normal and tangential components of the gradient are examined. The convergence of the vector potential is also examined, and it is shown that the scheme for handling near-hypersingular integrals also is effective for the nearly singular potential terms.

Fink, Patricia W.↗

NASA NTRS1993

Navier-Stokes calculations for vortex rings in an unbounded domain

A computational code for the vorticity-potential method is developed for a three-dimensional bounded vorticity field. The evaluation of the boundary data for the vector potential in the code is improved so that the numerical solution simulates that in an unbounded domain to a high order. The time evolution of two vortex rings and that of an elliptic ring are investigated with this code. The cut-and-connect phenomena of vortex rings are successfully captured. The results are compared with those of asymptotic theory and the experiment. They also highlight the need for additional theoretical and numerical investigations.

Ishii, Katsuya↗

NASA NTRS1989

Meteorological atlas of the Northern Hemisphere lower stratosphere for January and February 1989 during the Airborne Arctic Stratospheric Expedition

Northern Hemisphere meteorological data for the months of January and February 1989 in the lower stratosphere are shown. National Meteorological Center (NMC) data, and Total Ozone Mapping Spectrometer (TOMS) data are used to display polar stereographic projections of 100-mb temperatures, 50-mb temperatures, 50-mb geopotential heights, total ozone, and Ertel's potential vorticity (Epv) on both 400 K and 460 K isentropic surfaces. In addition, latitude/height cross sections at 10 E of balanced wind isotachs, wind vectors, potential temperature, and temperature are also shown. Horizontal traces of NASA ER-2 and DC-8 flight tracks are also included. Vertical profiles of NMC temperatures following flight paths of both aircraft are shown. In addition, vertical profiles of wind speed are contoured following the ER-2 for estimating the lateral penetration into the polar vortex, while vertical profiles of Ertel's potential vorticity are included for estimating the vertical penetration of the DC-8 into the stratosphere.

Newman, Paul A.↗

NASA NTRS2012

Statistical Theory of the Ideal MHD Geodynamo

A statistical theory of geodynamo action is developed, using a mathematical model of the geodynamo as a rotating outer core containing an ideal (i.e., no dissipation), incompressible, turbulent, convecting magnetofluid. On the concentric inner and outer spherical bounding surfaces the normal components of the velocity, magnetic field, vorticity and electric current are zero, as is the temperature fluctuation. This allows the use of a set of Galerkin expansion functions that are common to both velocity and magnetic field, as well as vorticity, current and the temperature fluctuation. The resulting dynamical system, based on the Boussinesq form of the magnetohydrodynamic (MHD) equations, represents MHD turbulence in a spherical domain. These basic equations (minus the temperature equation) and boundary conditions have been used previously in numerical simulations of forced, decaying MHD turbulence inside a sphere [1,2]. Here, the ideal case is studied through statistical analysis and leads to a prediction that an ideal coherent structure will be found in the form of a large-scale quasistationary magnetic field that results from broken ergodicity, an effect that has been previously studied both analytically and numerically for homogeneous MHD turbulence [3,4]. The axial dipole component becomes prominent when there is a relatively large magnetic helicity (proportional to the global correlation of magnetic vector potential and magnetic field) and a stationary, nonzero cross helicity (proportional to the global correlation of velocity and magnetic field). The expected angle of the dipole moment vector with respect to the rotation axis is found to decrease to a minimum as the average cross helicity increases for a fixed value of magnetic helicity and then to increase again when average cross helicity approaches its maximum possible value. Only a relatively small value of cross helicity is needed to produce a dipole moment vector that is aligned at approx.10deg with the rotation axis.

Shebalin, J. V.↗

NASA NTRS2012

Variance of the Quantum Dwell Time for a Nonrelativistic Particle

Munoz, Seidel, and Muga [Phys. Rev. A 79, 012108 (2009)], following an earlier proposal by Pollak and Miller [Phys. Rev. Lett. 53, 115 (1984)] in the context of a theory of a collinear chemical reaction, showed that suitable moments of a two-flux correlation function could be manipulated to yield expressions for the mean quantum dwell time and mean square quantum dwell time for a structureless particle scattering from a time-independent potential energy field between two parallel lines in a two-dimensional spacetime. The present work proposes a generalization to a charged, nonrelativistic particle scattering from a transient, spatially confined electromagnetic vector potential in four-dimensional spacetime. The geometry of the spacetime domain is that of the slab between a pair of parallel planes, in particular those defined by constant values of the third (z) spatial coordinate. The mean Nth power, N = 1, 2, 3, . . ., of the quantum dwell time in the slab is given by an expression involving an N-flux-correlation function. All these means are shown to be nonnegative. The N = 1 formula reduces to an S-matrix result published previously [G. E. Hahne, J. Phys. A 36, 7149 (2003)]; an explicit formula for N = 2, and of the variance of the dwell time in terms of the S-matrix, is worked out. A formula representing an incommensurability principle between variances of the output-minus-input flux of a pair of dynamical variables (such as the particle s time flux and others) is derived.

Hahne, Gerhard↗

DOE OSTI2023

Simulations Supporting the Development of Northstar's Indirect Beam Parameters Monitoring System

NorthStar Medical Radioisotopes, LLC is planning to produce the important medical radioisotope molybdenum-99 (Mo-99), the parent of technetium-99m (Tc-99m), through photonuclear reactions in molybdenum-100 (Mo-100). In this approach, a target comprising multiple thin disks of enriched molybdenum metal is bombarded with a 40-MeV electron beam. Electrons impinged on the molybdenum target produce bremsstrahlung X-rays that cause the nuclear reaction. Because enriched Mo-100 is expensive, there is a desire to utilize as much beam power as possible to achieve maximum production yield and minimize the size of the target. This requirement leads to very high beam power density (and heat deposition in the target), which creates challenging requirements for the cooling of the target. The critical part of the target is the target window. It separates the high-pressure helium cooled target from the vacuum beamline and the subject of structural and thermal stress. The temperature of the target window is proportional to the energy density deposited by the beam, so it is critical to maintain the desired beam profile on the target window. The feasibility of indirectly monitoring the maximum energy density of the beam on the beam window through beam losses at the main collimator (Collimator) before the production target was verified. A model of the NorthStar beam transport line was constructed for this purpose using MAD-X and Tao/Bmad codes. Beam optics were computed for the standard operational scenario, followed by an investigation involving approximately 400 cases with parameter variations in the last tuning quadrupoles. This was done to assess the correlation between losses in the collimator and the peak energy density on the target. We developed a model to explore the potential application of Optical transition radiation (OTR) for controlling beam parameters in the NorthStar beam delivery system. This model was based on a generic formula derived from the fundamental solution of the inhomogeneous wave equation of the vector potential, and allowed us to consider various surfaces, even those with irregular or random features, using numerical integration. We applied the model to OTR generated by relativistic electrons impacting an Inconel® 718 beam window. We examined cases with different levels of the window’s surface roughness, ranging from 0.5 to 3.0 microns of root square mean (RMS) deviation. The results of the OTR simulations provided distributions of OTR photons that can be used to study the limitations of optical systems for controlling beam parameters.

43 PARTICLE ACCELERATORS↗

NASA NTRS1999

Geometric Representations of Condition Queries on Three-Dimensional Vector Fields

Condition queries on distributed data ask where particular conditions are satisfied. It is possible to represent condition queries as geometric objects by plotting field data in various spaces derived from the data, and by selecting loci within these derived spaces which signify the desired conditions. Rather simple geometric partitions of derived spaces can represent complex condition queries because much complexity can be encapsulated in the derived space mapping itself A geometric view of condition queries provides a useful conceptual unification, allowing one to intuitively understand many existing vector field feature detection algorithms -- and to design new ones -- as variations on a common theme. A geometric representation of condition queries also provides a simple and coherent basis for computer implementation, reducing a wide variety of existing and potential vector field feature detection techniques to a few simple geometric operations.

Henze, Chris↗

DOE OSTI2021

Robust and ultrafast state preparation by ramping artificial gauge potentials

Abstract The implementation of static artificial magnetic fields in ultracold atomic systems has become a powerful tool, e.g. for simulating quantum-Hall physics with charge-neutral atoms. Taking an interacting bosonic flux ladder as a minimal model, we investigate protocols for adiabatic state preparation via magnetic flux ramps. Considering the fact that it is actually the artificial vector potential (in the form of Peierls phases) that can be experimentally engineered in optical lattices, rather than the magnetic field, we find that the time required for adiabatic state preparation dramatically depends on which pattern of Peierls phases is used. This can be understood intuitively by noting that different patterns of time-dependent Peierls phases that all give rise to the same magnetic field ramp, generally lead to different artificial electric fields during the ramp. As an intriguing result, we find that an optimal choice allows for preparing the ground state almost instantaneously in the non-interacting system, which can be related to the concept of counterdiabatic driving. Remarkably, we find extremely short preparation times also in the strongly-interacting regime. Our findings open new possibilities for robust state preparation in atomic quantum simulators.

Wang, Botao (ORCID:0000000282202452)↗

DOE OSTI2022

Topological monopole's gauge field‐induced anomalous Hall effect in artificial honeycomb lattice

Abstract Vortex magnetic structure in artificial honeycomb lattice provides a unique platform to explore emergent properties due to the additional Berry phase curvature imparted by chiral magnetization to circulating electrons via direct interaction. We argue that while the perpendicularly aligned magnetic component leads to the quantized flux of monopole at the center of the Berry sphere, the in‐plane vortex circulation of magnetization gives rise to unexpected nontrivial topological Berry phase due to the gauge field transformation. The unprecedented effect signifies the importance of vector potential in multiply connected geometrical systems. Experimental confirmations to proposed hypotheses are obtained from Hall resistance measurements on permalloy honeycomb lattice. Investigation of the topological gauge transformation due to the in‐plane chirality reveals anomalous quasi‐oscillatory behavior in Hall resistance as a function of perpendicular field. The oscillatory nature of is owed to the fluctuation in equilibrium current as a function of Fermi wave‐vector , envisaged under the proposed new formulation in this article. Our synergistic approach suggests that artificially tunable nanostructured material provides new vista to the exploration of topological phenomena of strong fundamental importance. Key Points Demonstration of gauge field flux due to vortex magnetism. Anomalous Hall effect in magnetic honeycomb lattice. Topological monopole‐induced magnetic flux.

Guo, Jiasen↗

DOE OSTI2024

Charge Conservation beyond Uniformity: Spatially Inhomogeneous Electromagnetic Response in Periodic Solids

Nonlinear electromagnetic response functions have reemerged as a crucial tool for studying quantum materials, due to recently appreciated connections between optical response functions, quantum geometry, and band topology. Most attention has been paid to responses to spatially uniform electric fields, relevant to low-energy optical experiments in conventional solid state materials. However, magnetic and magnetoelectric phenomena are naturally connected by responses to spatially varying electric fields due to Maxwell’s equations. Furthermore, in the emerging field of moiré materials, characteristic lattice scales are much longer, allowing spatial variation of optical electric fields to potentially have a measurable effect in experiments. In order to address these issues, we develop a formalism for computing linear and nonlinear responses to spatially inhomogeneous electromagnetic fields. Starting with the continuity equation, we derive an expression for the second-quantized current operator that is manifestly conserved and model independent. Crucially, our formalism makes no assumptions on the form of the microscopic Hamiltonian and so is applicable to model Hamiltonians derived from tight-binding or calculations. We then develop a diagrammatic Kubo formalism for computing the wave vector dependence of linear and nonlinear conductivities, using Ward identities to fix the value of the diamagnetic current order by order in the vector potential. We apply our formula to compute the magnitude of the Kerr effect at oblique incidence for a model of a moiré-Chern insulator and demonstrate the experimental relevance of spatially inhomogeneous fields in these systems. We further show how our formalism allows us to compute the (orbital) magnetic multipole moments and magnetic susceptibilities in insulators. Turning to nonlinear response, we use our formalism to compute the second-order transverse response to spatially varying transverse electric fields in our moiré-Chern insulator model, with an eye toward the next generation of experiments in these systems. Published by the American Physical Society 2024

Physics↗