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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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DOE OSTI2022

Numerical study of $\delta$-function current sheets arising from resonant magnetic perturbations

We report general three-dimensional toroidal ideal magnetohydrodynamic equilibria with a continuum of nested flux surfaces are susceptible to forming singular current sheets when resonant perturbations are applied. The presence of singular current sheets indicates that, in the presence of non-zero resistivity, magnetic reconnection will ensue, leading to the formation of magnetic islands and potentially regions of stochastic field lines when islands overlap. Numerically resolving singular current sheets in the ideal magnetohydrodynamics (MHD) limit has been a significant challenge. This work presents numerical solutions of the Hahm–Kulsrud–Taylor (HKT) problem, which is a prototype for resonant singular current sheet formation. The HKT problem is solved by two codes: a Grad–Shafranov (GS) solver and the Stepped Pressure Equilibrium Code (SPEC) code. The GS solver has built-in nested flux surfaces with prescribed magnetic fluxes. The SPEC code implements multi-region relaxed magnetohydrodynamics (MRxMHD), whereby the solution relaxes to a Taylor state in each region while maintaining force balance across the interfaces between regions. As the number of regions increases, the MRxMHD solution appears to approach the ideal MHD solution assuming a continuum of nested flux surfaces. We demonstrate agreement between the numerical solutions obtained from the two codes through a convergence study.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2014

A white noise approach to the Feynman integrand for electrons in random media

Using the Feynman path integral representation of quantum mechanics it is possible to derive a model of an electron in a random system containing dense and weakly coupled scatterers [see F. Edwards and Y. B. Gulyaev, “The density of states of a highly impure semiconductor,” Proc. Phys. Soc. 83, 495–496 (1964)]. The main goal of this paper is to give a mathematically rigorous realization of the corresponding Feynman integrand in dimension one based on the theory of white noise analysis. We refine and apply a Wick formula for the product of a square-integrable function with Donsker's delta functions and use a method of complex scaling. As an essential part of the proof we also establish the existence of the exponential of the self-intersection local times of a one-dimensional Brownian bridge. As a result we obtain a neat formula for the propagator with identical start and end point. Thus, we obtain a well-defined mathematical object which is used to calculate the density of states [see, e.g., F. Edwards and Y. B. Gulyaev, “The density of states of a highly impure semiconductor,” Proc. Phys. Soc. 83, 495–496 (1964)].

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Final Results from the Jefferson Lab Qweak Experiment and Constraints on Physics Beyond the Standard Model

The $Q_{weak}$ $\vec{e}p$ elastic scattering experiment used to extract an asymmetry at $Q^2$ = 0.0248 $GeV^2$ will be described. The final result was -226.5 ± 9.3 ppb- the most precise ep asymmetry ever measured. Some of the backgrounds and corrections applied in the experiment will be explained and quantified, and some of the experimental challenges will be described. Several methods used to extract consistent values of the proton's weak charge $Q^p_w$ from our asymmetry measurement will be outlined. We also show the multi-TeV mass reach for beyond-the-Standard-Model physics obtained from our determination of the proton's weak charge, and discuss our sensitivity to specific examples of new physics like compositeness. From the proton's weak charge, a result for the fundamental standard model parameter $sin^2θ_W$ is obtained at the energy scale of our experiment. We compare that to the few other determinations of $sin^2θ_W$ available in the literature, as well as the predicted behaviour based on SM input.

Smith, Gregory↗
DOE OSTI2019

Geometric scattering of a scalar particle moving on a curved surface in the presence of point defects

A nonrelativistic scalar particle that is constrained to move on an asymptotically flat curved surface undergoes a geometric scattering that is sensitive to the mean and Gaussian curvatures of the surface. A careful study of possible realizations of this phenomenon in typical condensed matter systems requires dealing with the presence of defects. We examine the effect of delta-function point defects residing on a curved surface S. In particular, we solve the scattering problem for a multi-delta-function potential in plane, which requires a proper regularization of divergent terms entering its scattering amplitude, and include the effects of nontrivial geometry of S by treating it as a perturbation of the plane. This allows us to obtain analytic expressions for the geometric scattering amplitude for a surface consisting of one or more Gaussian bumps. In general the presence of the delta-function defects enhances the geometric scattering effects.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Massive celestial fermions

In an effort to further the study of amplitudes in the celestial CFT (CCFT), we construct conformal primary wavefunctions for massive fermions. Upon explicitly calculating the wavefunctions for Dirac fermions, we deduce the corresponding transformation of momentum space amplitudes to celestial amplitudes. The shadow wavefunctions are shown to have opposite spin and conformal dimension 2 - Δ. The Dirac conformal primary wave- functions are delta function normalizable with respect to the Dirac inner product provided they lie on the principal series with conformal dimension Δ = 1 + iλ for λ ∈ $\mathbb{R}$. It is shown that there are two choices of a complete basis: single spin J=$\frac{1}{2}$ or J=-$\frac{1}{2}$ and λ ∈ $\mathbb{R}$ or multiple spin J=±$\frac{1}{2}$ and λ $\mathbb{R}$ +∪0 . The massless limit of the Dirac conformal primary wavefunctions is shown to agree with previous literature. The momentum generators on the celestial sphere are derived and, along with the Lorentz generators, form a representation of the Poincaré algebra. Finally, we show that the massive spin-1 conformal primary wavefunctions can be constructed from the Dirac conformal primary wavefunctions using the standard Clebsch-Gordan coefficients. We use this procedure to write the massive spin-$\frac{3}{2}$, Rarita-Schwinger, conformal primary wavefunctions. This provides a prescription for constructing all massive fermionic and bosonic conformal primary wavefunctions starting from spin-$\frac{1}{2}$.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2013

The coordinate coherent states approach revisited

We revisit the coordinate coherent states approach through two different quantization procedures in the quantum field theory on the noncommutative Minkowski plane. The first procedure, which is based on the normal commutation relation between an annihilation and creation operators, deduces that a point mass can be described by a Gaussian function instead of the usual Dirac delta function. However, we argue this specific quantization by adopting the canonical one (based on the canonical commutation relation between a field and its conjugate momentum) and show that a point mass should still be described by the Dirac delta function, which implies that the concept of point particles is still valid when we deal with the noncommutativity by following the coordinate coherent states approach. In order to investigate the dependence on quantization procedures, we apply the two quantization procedures to the Unruh effect and Hawking radiation and find that they give rise to significantly different results. Under the first quantization procedure, the Unruh temperature and Unruh spectrum are not deformed by noncommutativity, but the Hawking temperature is deformed by noncommutativity while the radiation specturm is untack. However, under the second quantization procedure, the Unruh temperature and Hawking temperature are untack but the both spectra are modified by an effective greybody (deformed) factor. - Highlights: Black-Right-Pointing-Pointer Suggest a canonical quantization in the coordinate coherent states approach. Black-Right-Pointing-Pointer Prove the validity of the concept of point particles. Black-Right-Pointing-Pointer Apply the canonical quantization to the Unruh effect and Hawking radiation. Black-Right-Pointing-Pointer Find no deformations in the Unruh temperature and Hawking temperature. Black-Right-Pointing-Pointer Provide the modified spectra of the Unruh effect and Hawking radiation.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2011

Symmetric and asymmetric solitons trapped in H-shaped potentials

We report results of numerical and analytical studies of the spontaneous symmetry breaking in solitons, both two- and one-dimensional (2D and 1D), which are trapped in H-shaped potential profiles built of two parallel potential troughs linked by a narrow rung in the transverse direction. This system can be implemented in self-attractive Bose-Einstein condensates (BECs), as well as in a nonlinear bulk optical waveguide. We demonstrate that the introduction of the transverse link changes the character of the symmetry-breaking bifurcation (SBB) in the system from subcritical to supercritical. (In terms of the corresponding phase transition, it is a change between the first and second kinds.) A noteworthy feature of the SBB in this setting is a nonmonotonous dependence of the soliton's norm at the bifurcation point on the strength of the transverse link. In the full 2D system, the results are obtained in a numerical form. An exact analytical solution is found for the bifurcation in the 1D version of the model, with the transverse rung modeled by the local linear coupling between the parallel troughs with the {delta}-functional longitudinal profile. By replacing the {delta} function by its finite-width Gaussian counterpart, similar results are obtained by means of the variational approximation (VA). The VA is also applied to the 1D system with a mixed linear and nonlinear transverse localized coupling. Comparison of the results produced by the different varieties of the system clearly reveals basic features of its the symmetry-breaking transition.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2017

Unified halo-independent formalism from convex hulls for direct dark matter searches

Using the Fenchel-Eggleston theorem for convex hulls (an extension of the Caratheodory theorem), we prove that any likelihood can be maximized by either a dark matter 1- speed distribution F ( v ) in Earth's frame or 2- Galactic velocity distribution f gal ( ) , consisting of a sum of delta functions. The former case applies only to time-averaged rate measurements and the maximum number of delta functions is ( -1) , where is the total number of data entries. The second case applies to any harmonic expansion coefficient of the time-dependent rate and the maximum number of terms is . Using time-averaged rates, the aforementioned form of F ( v ) results in a piecewise constant unmodulated halo function 0 BF ( v min ) (which is an integral of the speed distribution) with at most ( -1) downward steps. The authors had previously proven this result for likelihoods comprised of at least one extended likelihood, and found the best-fit halo function to be unique. This uniqueness, yet, cannot be guaranteed in the more general analysis applied to arbitrary likelihoods. Thus we introduce a method for determining whether there exists a unique best-fit halo function, and provide a procedure for constructing either a pointwise confidence band, if the best-fit halo function is unique, or a degeneracy band, if it is not. Using measurements of modulation amplitudes, the aforementioned form of f gal ( ) , which is a sum of Galactic streams, yields a periodic time-dependent halo function BF ( v min , t ) which at any fixed time is a piecewise constant function of v min with at most downward steps. In this case, we explain how to construct pointwise confidence and degeneracy bands from the time-averaged halo function. Lastly, we show that requiring an isotropic Galactic velocity distribution leads to a Galactic speed distribution F ( u ) that is once again a sum of delta functions, and produces a time-dependent BF ( v min , t ) function (and a time-averaged 0 BF ( v min )) that is piecewise linear, differing significantly from best-fit halo functions obtained without the assumption of isotropy.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

Stabilization of solitons under competing nonlinearities by external potentials

We report results of the analysis for families of one-dimensional (1D) trapped solitons, created by competing self-focusing (SF) quintic and self-defocusing (SDF) cubic nonlinear terms. Two trapping potentials are considered, the harmonic-oscillator (HO) and delta-functional ones. The models apply to optical solitons in colloidal waveguides and other photonic media, and to matter-wave solitons in Bose-Einstein condensates loaded into a quasi-1D trap. For the HO potential, the results are obtained in an approximate form, using the variational and Thomas-Fermi approximations, and in a full numerical form, including the ground state and the first antisymmetric excited one. For the delta-functional attractive potential, the results are produced in a fully analytical form, and verified by means of numerical methods. Both exponentially localized solitons and weakly localized trapped modes are found for the delta-functional potential. The most essential conclusions concern the applicability of competing Vakhitov-Kolokolov (VK) and anti-VK criteria to the identification of the stability of solitons created under the action of the competing SF and SDF terms.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

A non-modal analytical method to predict turbulent properties applied to the Hasegawa-Wakatani model

Linear eigenmode analysis often fails to describe turbulence in model systems that have non-normal linear operators and thus nonorthogonal eigenmodes, which can cause fluctuations to transiently grow faster than expected from eigenmode analysis. When combined with energetically conservative nonlinear mode mixing, transient growth can lead to sustained turbulence even in the absence of eigenmode instability. Since linear operators ultimately provide the turbulent fluctuations with energy, it is useful to define a growth rate that takes into account non-modal effects, allowing for prediction of energy injection, transport levels, and possibly even turbulent onset in the subcritical regime. We define such a non-modal growth rate using a relatively simple model of the statistical effect that the nonlinearities have on cross-phases and amplitude ratios of the system state variables. In particular, we model the nonlinearities as delta-function-like, periodic forces that randomize the state variables once every eddy turnover time. Furthermore, we estimate the eddy turnover time to be the inverse of the least stable eigenmode frequency or growth rate, which allows for prediction without nonlinear numerical simulation. We test this procedure on the 2D and 3D Hasegawa-Wakatani model [A. Hasegawa and M. Wakatani, Phys. Rev. Lett. 50, 682 (1983)] and find that the non-modal growth rate is a good predictor of energy injection rates, especially in the strongly non-normal, fully developed turbulence regime.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Application of a Chemical Index to Aerosol Mass Spectrometry: Delta Plots and Functional Group Distributions

A better understanding of the chemical properties of organic aerosol (OA) particles will improve our ability to characterize their sources and predict their lifetime. The high-resolution time-of-flight aerosol mass spectrometer (HR-ToF-AMS) is widely used to measure OA in real time using thermal vaporization followed by electron ionization (EI). EI creates fragment ions that can be assigned to functional groups using delta analysis, a method of classifying mass spectra according to the presence of different chemically related ion series. In this study, we demonstrate the application of delta analysis to characterize molecular structures using a new visualization method. We also use delta analysis to quantify the functional group distribution with an average absolute error of ∼5–6% for individual standard molecules, comparable to the error observed for OA mixtures from biomass and coal combustion fit with Fourier transform infrared spectroscopy. Finally, we apply delta functional group analysis to AMS positive matrix factorization (PMF) factors across seven different field campaigns and find a similar composition across the more oxidized factors with about 55% acid and 26% alcohol groups. The analysis method described here can be applied to any HR-ToF-AMS data set to provide quantitative relative functional group distributions for OA mixtures.

aerosol↗
DOE OSTI2020

Collisional effects on resonant particles in quasilinear theory

A careful examination of the effects of collisions on resonant wave–particle interactions leads to an alternate interpretation and deeper understanding of the quasilinear operator originally formulated by Kennel & Engelmann ( Phys. Fluids , vol. 9, 1966, pp. 2377–2388) for collisionless, magnetized plasmas, and widely used to model radio frequency heating and current drive. The resonant and nearly resonant particles are particularly sensitive to collisions that scatter them out of and into resonance, as for Landau damping as shown by Johnston ( Phys. Fluids , vol. 14, 1971, pp. 2719–2726) and Auerbach ( Phys. Fluids , vol. 20, 1977, pp. 1836–1844). As a result, the resonant particle–wave interactions occur in the centre of a narrow collisional boundary when the collision frequency $\unicode[STIX]{x1D708}$ is very small compared to the wave frequency $\unicode[STIX]{x1D714}$ . The diffusive nature of the pitch angle scattering combined with the wave–particle resonance condition enhances the collision frequency by $(\unicode[STIX]{x1D714}/\unicode[STIX]{x1D708})^{2/3}\gg 1$ , resulting in an effective resonant particle collisional interaction time of $\unicode[STIX]{x1D70F}_{\text{int}}\sim (\unicode[STIX]{x1D708}/\unicode[STIX]{x1D714})^{2/3}/\unicode[STIX]{x1D708}\ll 1/\unicode[STIX]{x1D708}$ . A collisional boundary layer analysis generalizes the standard quasilinear operator to a form that is fully consistent with Kennel–Englemann, but allows replacing the delta function appearing in the diffusivity with a simple integral (having the appropriate delta function limit) retaining the new physics associated with the narrow boundary layer, while preserving the entropy production principle. The limitations of the collisional boundary layer treatment are also estimated, and indicate that substantial departures from Maxwellian are not permitted.

Physics↗
DOE OSTI2021

Collisional effects on resonant particles in quasilinear theory

A careful examination of the effects of collisions on resonant wave-particle interactions leads to an alternate interpretation and deeper understanding of the quasilinear operator originally formulated by Kennel and Engelmann (Phys. Fluids vol. 9, 1966, pp. 2377- 2388) for collisionless, magnetized plasmas, and widely used to model radio frequency heating and current drive. The resonant and nearly resonant particles are particularly sensitive to collisions that pitch angle scatter them out of and into resonance. As a result, the resonant particle-wave interactions occur in the center of a narrow collisional boundary when the collision frequency nu is very small compared to the wave frequency omega. The diffusive nature of the pitch angle scattering combined with the wave-particle resonance condition enhances the collision frequency by (omega/nu)2/3 >>1, resulting in an effective resonant particle collision time of tau_int ~ (nu /omega)2/3 nu <<1/ nu . A rigorous collisional boundary layer analysis generalizes the standard quasilinear operator to a form that is fully consistent with Kennel-Englemann, but allows replacing the delta function appearing in the diffusivity with a simple integral (having the appropriate delta function limit) retaining the new physics associated with the narrow boundary layer, while preserving the entropy production principle. The limitations of the collisional boundary layer treatment are also estimated, and indicate that substantial departures from Maxwellian are not permitted.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2017

An Immersed Boundary method with divergence-free velocity interpolation and force spreading

The Immersed Boundary (IB) method is a mathematical framework for constructing robust numerical methods to study fluid–structure interaction in problems involving an elastic structure immersed in a viscous fluid. The IB formulation uses an Eulerian representation of the fluid and a Lagrangian representation of the structure. The Lagrangian and Eulerian frames are coupled by integral transforms with delta function kernels. The discretized IB equations use approximations to these transforms with regularized delta function kernels to interpolate the fluid velocity to the structure, and to spread structural forces to the fluid. It is well-known that the conventional IB method can suffer from poor volume conservation since the interpolated Lagrangian velocity field is not generally divergence-free, and so this can cause spurious volume changes. In practice, the lack of volume conservation is especially pronounced for cases where there are large pressure differences across thin structural boundaries. The aim of this paper is to greatly reduce the volume error of the IB method by introducing velocity-interpolation and force-spreading schemes with the properties that the interpolated velocity field in which the structure moves is at least $\mathscr{C}$ 1 and satisfies a continuous divergence-free condition, and that the force-spreading operator is the adjoint of the velocity-interpolation operator. We confirm through numerical experiments in two and three spatial dimensions that this new IB method is able to achieve substantial improvement in volume conservation compared to other existing IB methods, at the expense of a modest increase in the computational cost. Further, the new method provides smoother Lagrangian forces (tractions) than traditional IB methods. Finally, the method presented here is restricted to periodic computational domains. Its generalization to non-periodic domains is important future work.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Photoacoustic effect generated by moving optical sources: Motion in one dimension

Although the photoacoustic effect is typically generated by pulsed or amplitude modulated optical beams, it is clear from examination of the wave equation for pressure that motion of an optical source in space will result in the production of sound as well. Here, the properties of the photoacoustic effect generated by moving sources in one dimension are investigated. The cases of a moving Gaussian beam, an oscillating delta function source, and an accelerating Gaussian optical sources are reported. The salient feature of one-dimensional sources in the linear acoustic limit is that the amplitude of the beam increases in time without bound.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

Three independent one-dimensional margins for single-fraction frameless stereotactic radiosurgery brain cases using CBCT

Purpose: Setting a proper margin is crucial for not only delivering the required radiation dose to a target volume, but also reducing the unnecessary radiation to the adjacent organs at risk. This study investigated the independent one-dimensional symmetric and asymmetric margins between the clinical target volume (CTV) and the planning target volume (PTV) for linac-based single-fraction frameless stereotactic radiosurgery (SRS).Methods: The authors assumed a Dirac delta function for the systematic error of a specific machine and a Gaussian function for the residual setup errors. Margin formulas were then derived in details to arrive at a suitable CTV-to-PTV margin for single-fraction frameless SRS. Such a margin ensured that the CTV would receive the prescribed dose in 95% of the patients. To validate our margin formalism, the authors retrospectively analyzed nine patients who were previously treated with noncoplanar conformal beams. Cone-beam computed tomography (CBCT) was used in the patient setup. The isocenter shifts between the CBCT and linac were measured for a Varian Trilogy linear accelerator for three months. For each plan, the authors shifted the isocenter of the plan in each direction by ±3 mm simultaneously to simulate the worst setup scenario. Subsequently, the asymptotic behavior of the CTV V{sub 80%} for each patient was studied as the setup error approached the CTV-PTV margin.Results: The authors found that the proper margin for single-fraction frameless SRS cases with brain cancer was about 3 mm for the machine investigated in this study. The isocenter shifts between the CBCT and the linac remained almost constant over a period of three months for this specific machine. This confirmed our assumption that the machine systematic error distribution could be approximated as a delta function. This definition is especially relevant to a single-fraction treatment. The prescribed dose coverage for all the patients investigated was 96.1%± 5.5% with an extreme 3-mm setup error in all three directions simultaneously. It was found that the effect of the setup error on dose coverage was tumor location dependent. It mostly affected the tumors located in the posterior part of the brain, resulting in a minimum coverage of approximately 72%. This was entirely due to the unique geometry of the posterior head.Conclusions: Margin expansion formulas were derived for single-fraction frameless SRS such that the CTV would receive the prescribed dose in 95% of the patients treated for brain cancer. The margins defined in this study are machine-specific and account for nonzero mean systematic error. The margin for single-fraction SRS for a group of machines was also derived in this paper.

61 RADIATION PROTECTION AND DOSIMETRY↗
DOE OSTI2017

Multifield stochastic particle production: beyond a maximum entropy ansatz

In this work, we explore non-adiabatic particle production for N f coupled scalar fields in a time-dependent background with stochastically varying effective masses, cross-couplings and intervals between interactions. Under the assumption of weak scattering per interaction, we provide a framework for calculating the typical particle production rates after a large number of interactions. After setting up the framework, for analytic tractability, we consider interactions (effective masses and cross couplings) characterized by series of Dirac-delta functions in time with amplitudes and locations drawn from different distributions. Without assuming that the fields are statistically equivalent, we present closed form results (up to quadratures) for the asymptotic particle production rates for the N f =1 and N f =2 cases. We also present results for the general N f >2 case, but with more restrictive assumptions. We find agreement between our analytic results and direct numerical calculations of the total occupation number of the produced particles, with departures that can be explained in terms of violation of our assumptions. We elucidate the precise connection between the maximum entropy ansatz (MEA) used in Amin & Baumann (2015) and the underlying statistical distribution of the self and cross couplings. We provide and justify a simple to use (MEA-inspired) expression for the particle production rate, which agrees with our more detailed treatment when the parameters characterizing the effective mass and cross-couplings between fields are all comparable to each other. However, deviations are seen when some parameters differ significantly from others. We show that such deviations become negligible for a broad range of parameters when N f >> 1.

79 ASTRONOMY AND ASTROPHYSICS↗