Results for “Gradient Limiters” — Page 7

DOE OSTI2021

Pulse Length Monitor for Breakdown Diagnostics in THz and Mm-Wave Accelerators

The development of novel high-gradient accelerating structures operating at THz frequencies is critical for future free-electron lasers and TeV scale linear colliders. To reach high energies with reasonable length requires high accelerating gradients of ~100 MV/m. The main limitation to reaching these high-energy gradients is the vacuum RF breakdown phenomenon, which disrupts normal accelerator operations. For stable operations and to understand the breakdown microscopic dynamics, a new device capable of detecting the breakdown occurrences is required. In this paper, we provide the design of a pulse length monitor based on an analog to digital converter for fast signal digitization without the need to use high-speed digitizers to be used in a commercial mm-wave heterodyne spectrometer.

43 PARTICLE ACCELERATORS↗

DOE OSTI2023

Three-Dimensional Reconstruction of Nb 3 Sn Films by Focused Ion Beam Cross Sectional Microscopy

Niobium has been the material of choice for SRF cavities for several decades due to its formability and superconducting properties. The accelerating gradient of niobium cavities is, however, rapidly approaching a theoretical limit. To achieve higher accelerating gradients a new material is needed that can sustain high fields. Nb 3 Sn is a promising competitor with a higher superconducting transition temperature and a higher critical field than pure niobium. However, Nb 3 Sn is very brittle and cannot be formed readily into a cavity. The main method for creating Nb 3 Sn cavities is to form a Nb 3 Sn film into a niobium surface using a tin vapor-diffusion method. This technique creates a microcrystalline Nb 3 Sn thin film on the inner surface of the cavity. Tin depleted regions are known to form in the film during this process. Previous studies have analyzed these regions using transmission electron microscopy on cross-sectional lamellae prepared by focused ion beam/scanning electron microscope (FIB/SEM). This method does not provide any three-dimensional (3-D) information about the distribution of tin-deficient regions. In this study we employ a focused ion beam tomographic technique to analyze the 3-D structure of the film. Electron dispersive X-ray spectroscopy is used to image the tin concentration of the film in 3-D. Tin-deficient regions are discovered close to the surface of the Nb 3 Sn film.

Viklund, E.↗

DOE OSTI2022

Ab-initio Cu alloy design for high-gradient accelerating structures

Operation of normal conducting accelerator structures at high accelerating gradients is beneficial for many accelerator applications in basic science, industry, medicine, and National Security. RF breakdown is the major factor that limits the achievable accelerating gradients. Previous experiments on copper (Cu) have demonstrated that RF breakdown probability can be significantly decreased by hardening the material and alloying Cu with solutes such as silver (Ag). In this paper, we propose a figure-of-merit (FOM) that characterizes the ability of Cu alloys to withstand high-gradients. The FOM represents a trade-off between hardening through solid solution strengthening and the additional thermal stress induced by incremental RF pulse heating resulting from changes in electronic properties induced by alloying. We performed high-throughput ab initio calculations and computed the FOM for a large number of binary Cu alloys. Several promising candidate alloys for high-gradient accelerating structures were identified, such as CuAg, CuCd, CuHg, CuAu, CuIn, and CuMg. CuAg alloys have previously exhibited low RF breakdown rates in experiments. The results provide guidance for selecting alloys for the future high-gradient normal conducting accelerating structures operating at very high gradients.

36 MATERIALS SCIENCE↗

DOE OSTI2019

A Model of Solar Equilibrium: The Hydrodynamic Limit

Helioseismology has revealed the internal density and rotation profiles of the Sun. Yet, knowledge of its magnetic fields and meridional circulation is confined much closer to the surface, and latitudinal entropy gradients are below detectable limits. While numerical simulations can offer insight into the interior dynamics and help identify which ingredients are necessary to reproduce particular observations, some features of the Sun can be understood analytically from an equilibrium perspective. Examples of such features include: the 1D density profile arising from steady-state energy transport from the core to the surface, and the tilting of isorotation contours in the convection zone (CZ) due to baroclinic forcing. To help answer the question of which features can be explained by equilibrium, we propose analyzing stationary axisymmetric ideal magnetohydrodynamic flows in the solar regime. By prescribing an appropriate entropy at the surface, we recover a rotation profile that reasonably matches observations in the bulk of the CZ. Additionally, by including the effects of poloidal flow, we reproduce a feature that is reminiscent of the near surface shear layer. Furthermore, no tachocline-like feature is seen in hydrodynamic equilibrium, suggesting the importance of either dynamics or magnetic fields in its description.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2022

Optimization of a traveling wave superconducting radiofrequency cavity for upgrading the International Linear Collider

The standing wave TESLA niobium-based superconducting radio frequency structure is limited to an accelerating gradient of about 50 MV/m by the critical rf magnetic field. To break through this barrier, we explore the option of niobium-based traveling wave (TW) structures. Optimization of TW structures was done considering experimentally known limiting electric and magnetic fields. It is shown that a TW structure can have an accelerating gradient above 70 MeV/m that is about 1.5 times higher than contemporary standing wave structures with the same critical magnetic field. The other benefit of TW structures shown is R/Q about 2 times higher than the TESLA structure that reduces the dynamic heat load by a factor of 2. A method is proposed how to make TW structures multipactor-free. Some design proposals are offered to facilitate fabrication. Further increase of the real-estate gradient (equivalent to 80 MV/m active gradient) is also possible by increasing the length of the accelerating structure because of higher group velocity and cell-to-cell coupling. Realization of this work opens paths to International Linear Collider energy upgrades beyond 1 to 3 TeV in competition with CLIC. The paper will discuss corresponding opportunities and challenges.

43 PARTICLE ACCELERATORS↗

NASA NTRS2003

Optimization Based Efficiencies in First Order Reliability Analysis

This paper develops a method for updating the gradient vector of the limit state function in reliability analysis using Broyden's rank one updating technique. In problems that use commercial code as a black box, the gradient calculations are usually done using a finite difference approach, which becomes very expensive for large system models. The proposed method replaces the finite difference gradient calculations in a standard first order reliability method (FORM) with Broyden's Quasi-Newton technique. The resulting algorithm of Broyden updates within a FORM framework (BFORM) is used to run several example problems, and the results compared to standard FORM results. It is found that BFORM typically requires fewer functional evaluations that FORM to converge to the same answer.

Peck, Jeffrey A.↗

NASA NTRS1979

Generalized lower-hybrid-drift instability

The theory of lower-hybrid-drift instability is extended to include a finite value of the component of wave vector parallel to the ambient magnetic field so that the analysis bridges the usual lower-hybrid-drift instability of flute modes and the modified-two-stream instability. The present theory also includes electromagnetic and ambient magnetic field-gradient effects. It is found that in the cold-electron limit the density and magnetic gradients can qualitatively modify the conclusion obtained in the early theory of the modified-two-stream instability. For example, even if the relative drift far exceeds the Alfven speed of the plasma, the instability may still persist. This result is in contrast to that established in the literature. When the electron temperature is finite, the problem is complicated. Numerical solutions are obtained for a number of cases.

Hsia, J. B.↗

DOE OSTI2021

When and why PINNs fail to train: A neural tangent kernel perspective

Physics-informed neural networks (PINNs) have lately received great attention thanks to their flexibility in tackling a wide range of forward and inverse problems involving partial differential equations. However, despite their noticeable empirical success, little is known about how such constrained neural networks behave during their training via gradient descent. More importantly, even less is known about why such models sometimes fail to train at all. Here in this work, we aim to investigate these questions through the lens of the Neural Tangent Kernel (NTK); a kernel that captures the behavior of fully-connected neural networks in the infinite width limit during training via gradient descent. Specifically, we derive the NTK of PINNs and prove that, under appropriate conditions, it converges to a deterministic kernel that stays constant during training in the infinite-width limit. This allows us to analyze the training dynamics of PINNs through the lens of their limiting NTK and find a remarkable discrepancy in the convergence rate of the different loss components contributing to the total training error. To address this fundamental pathology, we propose a novel gradient descent algorithm that utilizes the eigenvalues of the NTK to adaptively calibrate the convergence rate of the total training error. Finally, we perform a series of numerical experiments to verify the correctness of our theory and the practical effectiveness of the proposed algorithms.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2016

Physics of Limiting Phenomena in Superconducting Microwave Resonators: Vortex Dissipation, Ultimate Quench and Quality Factor Degradation Mechanisms

Superconducting niobium accelerating cavities are devices operating in radio-frequency and able to accelerate charged particles up to energy of tera-electron-volts. Such accelerating structures are though limited in terms of quality factor and accelerating gradient, that translates--in some cases--in higher capital costs of construction and operation of superconducting rf accelerators. Looking forward for a new generation of more affordable accelerators, the physical description of limiting mechanisms in superconducting microwave resonators is discussed. In particular, the physics behind the dissipation introduced by vortices in the superconductor, the ultimate quench limitations and the quality factor degradation mechanism after a quench are described in detail. One of the limiting factor of the quality factor is the dissipation introduced by trapped magnetic flux vortices. The radio-frequency complex response of trapped vortices in superconductors is derived by solving the motion equation for a magnetic flux line, assuming a bi-dimensional and mean free path-dependent Lorentzian-shaped pinning potential. The resulting surface resistance shows the bell-shaped trend as a function of the mean free path, in agreement with the experimental data observed. Such bell-shaped trend of the surface resistance is described in terms of the interplay of the two limiting regimes identified as pinning and flux flow regimes, for low and large mean free path values respectively. The model predicts that the dissipation regime--pinning- or flux-flow-dominated--can be tuned either by acting on the frequency or on the electron mean free path value. The effect of different configurations of pinning sites and strength on the vortex surface resistance are also discussed. Accelerating cavities are also limited by the quench of the superconductive state, which limits the maximum accelerating gradient achievable. The accelerating field limiting factor is usually associate d to the superheating field, which is intimately correlated to the penetration of magnetic flux vortices in the material. Experimental data for N-doped cavities suggest that uniform Ginzburg-Landau parameter cavities are statistically limited by the lower critical field, in terms of accelerating gradient. By introducing a Ginzburg-Landau parameter profile at the cavity rf surface--dirty layer--the accelerating gradient of superconducting resonators can be enhanced. The description of the physics behind the accelerating gradient enhancement as a consequence of the dirty layer is carried out by solving numerically the Ginzburg-Landau equations for the layered system. The enhancement is showed to be promoted by the higher energy barrier to vortex penetration, and by the enhanced lower critical field. Another serious threat to the quality factor during the cavity operation is the extra dissipation introduced by the quench. Such quality factor degradation mechanism due to the quench, is generated by the trapping of external magnetic flux at quench spot. The purely extrinsic origin of such extra dissipation is proven by the impossibility of decrease the quality factor by quenching in a magnetic field-free environment. Also, a clear relation of the dissipation introduced by quenching to the orientation of the applied magnetic field is observed. The full recover of the quality factor by re-quenching in compensated field is possible when the trapped flux at the quench spot is modest. On the contrary, when the trapped magnetic flux is too large, the quality factor degradation may become irreversible by this technique, likely due to the outward flux migration beyond the normal zone opening during the quench.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2016

Physics of Limiting Phenomena in Superconducting Microwave Resonators: Vortex Dissipation, Ultimate Quench and Quality Factor Degradation Mechanisms

Superconducting niobium accelerating cavities are devices operating in radio-frequency and able to accelerate charged particles up to energy of tera-electron-volts. Such accelerating structures are though limited in terms of quality factor and accelerating gradient, that translates--in some cases--in higher capital costs of construction and operation of superconducting rf accelerators. Looking forward for a new generation of more affordable accelerators, the physical description of limiting mechanisms in superconducting microwave resonators is discussed. In particular, the physics behind the dissipation introduced by vortices in the superconductor, the ultimate quench limitations and the quality factor degradation mechanism after a quench are described in detail. One of the limiting factor of the quality factor is the dissipation introduced by trapped magnetic flux vortices. The radio-frequency complex response of trapped vortices in superconductors is derived by solving the motion equation for a magnetic flux line, assuming a bi-dimensional and mean free path-dependent Lorentzian-shaped pinning potential. The resulting surface resistance shows the bell-shaped trend as a function of the mean free path, in agreement with the experimental data observed. Such bell-shaped trend of the surface resistance is described in terms of the interplay of the two limiting regimes identified as pinning and flux flow regimes, for low and large mean free path values respectively. The model predicts that the dissipation regime--pinning- or flux-flow-dominated--can be tuned either by acting on the frequency or on the electron mean free path value. The effect of different configurations of pinning sites and strength on the vortex surface resistance are also discussed. Accelerating cavities are also limited by the quench of the superconductive state, which limits the maximum accelerating gradient achievable. The accelerating field limiting factor is usually associate d to the superheating field, which is intimately correlated to the penetration of magnetic flux vortices in the material. Experimental data for N-doped cavities suggest that uniform Ginzburg-Landau parameter cavities are statistically limited by the lower critical field, in terms of accelerating gradient. By introducing a Ginzburg-Landau parameter profile at the cavity rf surface--dirty layer--the accelerating gradient of superconducting resonators can be enhanced. The description of the physics behind the accelerating gradient enhancement as a consequence of the dirty layer is carried out by solving numerically the Ginzburg-Landau equations for the layered system. The enhancement is showed to be promoted by the higher energy barrier to vortex penetration, and by the enhanced lower critical field. Another serious threat to the quality factor during the cavity operation is the extra dissipation introduced by the quench. Such quality factor degradation mechanism due to the quench, is generated by the trapping of external magnetic flux at quench spot. The purely extrinsic origin of such extra dissipation is proven by the impossibility of decrease the quality factor by quenching in a magnetic field-free environment. Also, a clear relation of the dissipation introduced by quenching to the orientation of the applied magnetic field is observed. The full recover of the quality factor by re-quenching in compensated field is possible when the trapped flux at the quench spot is modest. On the contrary, when the trapped magnetic flux is too large, the quality factor degradation may become irreversible by this technique, likely due to the outward flux migration beyond the normal zone opening during the quench.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2021

Low Redox Decreases Potential Phosphorus Limitation on Soil Biogeochemical Cycling Along a Tropical Rainfall Gradient

Not provided.

Environmental Sciences & Ecology↗

DOE OSTI2023

L-BFGS Class Implementation in C++

This report presents a header-only C++ class implementation of the Limited-memory BroydenFletcher-Goldfarb-Shanno (L-BFGS) algorithm. The L-BFGS method is a general purpose quasi-Netwon optimization method that builds an approximation of the descent direction from consecutive iterate and gradient vectors. The limited-memory aspect stems from the replacement of the N × N approximation matrix of the original BFGS method with M vectors of length N. An example usage of the class is included along with the reference source code.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1986

Developmental testing of a programmable multizone furnace

A multizone furnace was evaluated for its potential utilization for process experimentation on board the Space Shuttle. A temperature gradient can be created through the use of a series of connected temperature zones and can be translated by the coordinated sequencing of zone temperatures. The Bridgman-Stockbarger thermal configuration for directional solidification was implemented so that neither the sample nor furnace was translated. The thermal behavior of the furnace was measured and characterized. Limitations due to both thermal and electronic (computer) factors are identified. The results indicate that the multizone design is limited to low temperature gradients because of the indirect furnace-to-sample thermal coupling needed to blend the discrete thermal zones. The multizone furnace design inherently consumes more power than a similar (two temperature) conventional Bridgman type directional solidification furnace because every zone must be capable of the high cooling rates needed to produce the maximum desired temperature drop. Typical achievable static temperature gradients for the furnace tested were between 6 and 75 C/in. The maximum gradient velocity was approximately 10 in./hr. Several aspects of the tested system could be improved, but the dependence of the multizone design on high heat loss will limit Space Shuttle applications in the form tested unless additional power is available. The multizone furnace offers great flexibility but requires a high level of operator understanding for full advantage to be obtained.

Ting, E. Y.↗

DOE OSTI2015

RF breakdown of 805 MHz cavities in strong magnetic fields

Ionization cooling of intense muon beams requires the operation of high-gradient, normal-conducting RF structures in the presence of strong magnetic fields. We have measured the breakdown rate in several RF cavities operating at several frequencies. Cavities operating within solenoidal magnetic fields B > 0.25 T show an increased RF breakdown rate at lower gradients compared with similar operation when B = 0 T. Ultimately, this breakdown behavior limits the maximum safe operating gradient of the cavity. Beyond ionization cooling, this issue affects the design of photoinjectors and klystrons, among other applications. We have built an 805 MHz pillbox-type RF cavity to serve as an experimental testbed for this phenomenon. This cavity is designed to study the problem of RF breakdown in strong magnetic fields using various cavity materials and surface treatments, and with precise control over sources of systematic error. We present results from tests in which the cavity was run with all copper surfaces in a variety of magnetic fields.

43 PARTICLE ACCELERATORS↗

DOE OSTI2017

Nonlinear verification of a linear critical gradient model for energetic particle transport by Alfven eigenmodes

Here, a “stiff transport” critical gradient model of energetic particle (EP) transport by EPdriven Alfven eigenmodes (AEs) is verified against local nonlinear gyrokinetic simulations of a well-studied beam-heated DIII-D discharge 146102. A greatly simplifying linear “recipe” for the limiting EP-density gradient (critical gradient) is considered here. In this recipe, the critical gradient occurs when the AE linear growth rate, driven mainly by the EP gradient, exceeds the ion temperature gradient (ITG) or trapped electron mode (TEM) growth rate, driven by the thermal plasma gradient, at the same toroidal mode number (n) as the AE peak growth, well below the ITG/TEM peak n. This linear recipe for the critical gradient is validated against the critical gradient determined from far more expensive local nonlinear simulations in the gyrokinetic code GYRO, as identified by the point of transport runaway when all driving gradients are held fixed. The reduced linear model is extended to include the stabilization from equilibrium E×B velocity shear. The nonlinear verification unambiguously endorses one of two alternative recipes proposed in Ref. 1: the EP-driven AE growth rate should be determined with rather than without added thermal plasma drive.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2016

NifH -Harboring Bacterial Community Composition across an Alaskan Permafrost Thaw Gradient

Since nitrogen (N) is often limiting in permafrost soils, we investigated the N 2 -fixing genetic potential and the inferred taxa harboring those genes by sequencing nifH gene fragments in samples taken along a permafrost thaw gradient in an Alaskan boreal soil. Samples from minimally, moderately and extensively thawed sites were taken to a depth of 79 cm to encompass zones above and below the depth of the water table. NifH reads were translated with frameshift correction and 112,476 sequences were clustered at 5% amino acid dissimilarity resulting in 1,631 OTUs. Sample depth in relation to water table depth was correlated to differences in the NifH sequence classes with those most closely related to group I nifH -harboring Alpha- and Beta-Proteobacteria in higher abundance above water table depth while those related to group III nifH -harboring Delta Proteobacteria more abundant below. The most dominant below water table depth NifH sequences, comprising 1/3 of the total, were distantly related to Verrucomicrobia-Opitutaceae . Overall, these results suggest that permafrost thaw alters the class-level composition of N 2 -fixing communities in the thawed soil layers and that this distinction corresponds to the depth of the water table. These nifH data were also compared to nifH sequences obtained from a study at an Alaskan taiga site, and to those of other geographically distant, non-permafrost sites. The two Alaska sites were differentiated largely by changes in relative abundances of the same OTUs, whereas the non-Alaska sites were differentiated by the lack of many Alaskan OTUs, and the presence of unique halophilic, sulfate- and iron-reducing taxa in the Alaska sites.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2016

On the role of the ΩΓ limit in the formation of population III massive stars

We explore the role of the modified Eddington limit due to rapid rotation (the so-called ΩΓ limit) in the formation of Population III stars. We performed one-dimensional stellar evolution simulations of zero-metallicity protostars accreting mass at a very high rate ( M-dot ∼10{sup −3} M{sub ⊙} yr{sup −1}) and dealt with stellar rotation as a separate post-process. The protostar would reach the Keplerian rotation very soon after the onset of mass accretion, but mass accretion would continue as stellar angular momentum is transferred outward to the accretion disk by viscous stress. The envelope of the protostar expands rapidly when the stellar mass reaches ∼5–7 M{sub ⊙} and the Eddington factor increases sharply. This makes the protostar rotate critically at a rate that is significantly below the Keplerian value (i.e., the ΩΓ limit). The resultant positive gradient of the angular velocity in the boundary layer between the protostar and the Keplerian disk prohibits angular momentum transport from the star to the disk, and consequently further rapid mass accretion. This would prevent the protostar from growing significantly beyond 20–40 M{sub ⊙}. Another important consequence of the ΩΓ limit is that the protostar can remain fairly compact (R ≲ 50 R{sub ⊙}) and avoid a fluffy structure (R ≳ 500 R{sub ⊙}) that is usually found with a very high rate of mass accretion. This effect would make the protostar less prone to binary interactions during the protostar phase. Although our analysis is based on Population III protostar models, this role of the ΩΓ limit would be universal in the formation process of massive stars, regardless of metallicity.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2017

A Fluid Pulse on the Hikurangi Subduction Margin: Evidence From a Heat Flux Transect Across the Upper Limit of Gas Hydrate Stability: Fluid Pulse on the Hikurangi Margin

A transect of seafloor heat probe measurements on the Hikurangi Margin shows a significant increase of thermal gradients upslope of the updip limit of gas hydrate stability at the seafloor. We interpret these anomalously high thermal gradients as evidence for a fluid pulse leading to advective heat flux, while endothermic cooling from gas hydrate dissociation depresses temperatures in the hydrate stability field. Previous studies predict a seamount on the subducting Pacific Plate to cause significant overpressure beneath our study area, which may be the source of the fluid pulse. Double-bottom simulating reflections are present in our study area and likely caused by uplift based on gas hydrate phase boundary considerations, although we cannot exclude a thermogenic origin. We suggest that uplift may be associated with the leading edge of the subducting seamount. Our results provide further evidence for the transient nature of fluid expulsion in subduction zones.

58 GEOSCIENCES↗