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DOE OSTI2024

Simulations of vertical displacement oscillatory modes and global Alfvén Eigenmodes in JET geometry

Vertical Displacement Oscillatory Modes (VDOM), with frequency in the Alfvén range, are natural modes of oscillation of magnetically confined laboratory plasmas with elongated cross-section. These axisymmetric modes arise from the interaction between the plasma current, which is in equilibrium with currents flowing in external coils, and perturbed currents induced on a nearby conducting wall. The restoring force exerted by these perturbed currents on the vertical motion of the plasma column leads to its oscillatory behavior. An analytic model for VDOM was proposed based on an idealized 'straight tokamak' equilibrium with uniform equilibrium current density. This article introduces the first numerical simulations of VDOM in a realistic JET tokamak configuration, using the extended-MHD code NIMROD and drawing comparisons with Global Alfvén Eigenmodes (GAE). The results show qualitative agreement with analytic predictions regarding mode frequency and radial structure, supporting the identification of VDOM as a fundamental oscillation mode in tokamak plasmas. VDOM and GAE are modeled in a representative JET discharge, where axisymmetric perturbations with toroidal mode number n = 0 driven unstable by fast ions were observed. The two modes are examined separately using a forced oscillator within the NIMROD code, which enables a comparison of their characteristics and helps identify the experimentally observed mode possibly as a GAE.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Observation of pedestal mode spreading into SOL and broadening of divertor particle flux width on EAST tokamak

Pedestal turbulence spreading into a crape-off layer (SOL) can be used to explain the experimentally observed strong pedestal-SOL coupling and is expected to be important for the broadening of divertor deposition profiles in future devices (Xu et al 2019 Nucl. Fusion 59 126039). In the EAST tokamak, it is found that an electromagnetic (EM) mode in the pedestal region can spread into the SOL and broaden the divertor particle flux width. Multi-channel fluctuation reflectometry is used to measure the density fluctuations at the plasma edge. The EM mode rotates in the electron diamagnetic drift direction in the lab frame with a frequency range of [40–90] kHz, toroidal mode number n= 12–13 and poloidal wavenumber k θ = 0.41 cm −1 . The mode amplitude peaks around the maximum of the pedestal density gradient. As the mode amplitude increases, the reflectometry channel in the SOL can clearly capture the mode. This result suggests that the EM mode is excited in the pedestal gradient region and spreads into the SOL. It is further found that the particle flux deposition profile in the divertor is broadened as the EM mode appears.

Energy↗

DOE OSTI2024

Inverter Intensive Hybrid Power Plant Modeling with Small-Signal Stability Augmentation through Flexible Operation Mode Transition

Hybrid power plants (HPPs) prompt the penetration of inverter-based renewable energy sources (RES) in transmission systems; however, given their low-inertia nature, HPPs are dominated by power electronic inverters, so there are inevitable challenges in system stability when increasing numbers of HPPs are integrated into the modern power grids. To boost the penetration level of HPPs without jeopardizing system stability, it is desirable to equip them with operational characteristics (i.e., grid-forming capabilities) that are comparable to those of conventional power plants dominated by synchronous generators (SGs). In this paper, a holistic model of inverter intensive HPP is derived and a bi-level hierarchical control is developed to allow HPPs to flexibly switch among the designed operation modes (i.e., P-Q, P-V, and isochronous modes). Compared to SGs, which have limited controllability, the operation mode of each HPP could vary as requested. Such flexible mode transitions could be integrated into the secondary plant-level control and be leveraged as an additional control degree to further augment system stability. Further, the system small-signal stability margin is quantified with varying HPP operation modes. More importantly, modal analysis is thereby conducted to quantify the impacts of mode transition on the system oscillatory modes. The effectiveness of the proposed HPP bi-level hierarchical control is verified using extensive case studies based on the simplified real-world island power grid, and the results validate that the system small-signal stability margin can be enhanced with the additional degree of control flexibility enabled by HPP operation mode transition. The real-time hardware-in-the-loop (HIL) results are also provided to verify the proposed method.

grid-forming control↗

NASA NTRS2022

A Cohesive Element Formulation for Simulation of General Mode I, II and III Delamination

Cohesive element formulations proposed thus far have assumed that Mode II and Mode III fracture processes, and hence traction-separation laws, are identical. However, experimental observations suggest that such an assumption may not hold in general. The approach described herein consists of a cohesive element formulation in which the assumption of identical Mode II and Mode III fracture processes is not required. This assumption is alleviated by estimating the normal to the delamination front based on the gradient of the displacement jumps determined within each element. The estimated normal is used to rotate the cohesive element coordinate system. Determining the displacement jumps in the rotated coordinate system enables the distinction between Mode II sliding, and Mode III tearing. This information is subsequently used to extend a recently proposed cohesive formulation, resulting in an approach that can simulate mixed-mode I/II/III fracture via prescribing piecewise-linear traction-separation laws combined with a 3D mixed-mode fracture criteria.

Delamination↗

DOE OSTI2024

Evidence of a distinct collective mode in Kagome superconductors

The collective modes of the superconducting order parameter fluctuation can provide key insights into the nature of the superconductor. Recently, a family of superconductors has emerged in non-magnetic kagome materials AV 3 Sb 5 (A = K, Rb, Cs), exhibiting fertile emergent phenomenology. However, the collective behaviors of Cooper pairs have not been studied. Here, we report a distinct collective mode in CsV 3-x Ta x Sb 5 using scanning tunneling microscope/spectroscopy. The spectral line-shape is well-described by one isotropic and one anisotropic superconducting gap, and a bosonic mode due to electron-mode coupling. With increasing x, the two gaps move closer in energy, merge into two isotropic gaps of equal amplitude, and then increase synchronously. The mode energy decreases monotonically to well below 2Δ and survives even after the charge density wave order is suppressed. We propose the interpretation of this collective mode as Leggett mode between different superconducting components or the Bardasis-Schrieffer mode due to a subleading superconducting component.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2024

An extended variational method for the resistive wall mode in toroidal plasma confinement devices

The external-kink stability of a toroidal plasma surrounded by a rigid resistive wall is investigated. The well-known analysis of Haney and Freidberg is rigorously extended to allow for a wall that is sufficiently thick that the thin-shell approximation does not necessarily hold. A generalized Haney–Freidberg formula for the growth-rate of the resistive wall mode is obtained. Thick-wall effects do not change the marginal stability point of the mode but introduce an interesting asymmetry between growing and decaying modes. Growing modes have growth-rates that exceed those predicted by the original Haney–Freidberg formula. On the other hand, decaying modes have decay-rates that are less than those predicted by the original formula. The well-known Hu–Betti formula for the rotational stabilization of the resistive wall mode is also generalized to take thick-wall effects into account. Increasing wall thickness facilitates the rotational stabilization of the mode, because it decreases the critical toroidal electromagnetic torque that the wall must exert on the plasma. On the other hand, the real frequency of the mode at the marginal stability point increases with increasing wall thickness.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

On resistive interchange, double tearing, and resonant and non-resonant infernal modes in spherical tokamak negative central shear discharges

We examine the linear and nonlinear stability of a sequence of reversed shear NSTX equilibria with the same toroidal current density and pressure profile but with different toroidal field strengths. All equilibria have two q = 2 surfaces and have q > 1 everywhere. For this sequence, which all have β P ∼ 0.5, as the minimum value of q decreases below about 1.4, the localized resistive interchange criterion is strongly violated, and the unstable mode with toroidal mode number n=1 changes its dominant poloidal mode number m from a (m,n)=(2,1) double tearing mode to a non-resonant (1,1) infernal mode. This (1,1) mode nonlinearly flattens both the current density and the pressure near the magnetic axis. The higher-n unstable modes are all resistive infernal modes localized around the surface where q has a minimum and the magnetic shear vanishes. They generally saturate nonlinearly at low amplitude but can cause magnetic surface breakup near the axis.

Spitzer resistivity↗

DOE OSTI2024

Extraordinary frequency stabilization by resonant nonlinear mode coupling

Here, we show that a self-sustained oscillator with a frequency-selective element operating with two nonlinearly coupled modes can achieve a level of frequency stability well beyond that available using single-mode operation. The system of interest consists of a self-sustained oscillator based on a nonlinear primary mode that is coupled via an internal resonance to a passive secondary mode. Analysis of a generic model for this resonance with both additive and multiplicative noises reveals that the stability improvements accrue from two sources: (i) nonlinear frequency veering in the primary mode, a classical analogue to quantum-level repulsion, that eliminates amplitude-to-frequency noise conversion; and (ii) phase cleaning of the oscillator through an intrinsic phase constraint arising from synchronization of the modes. This latter effect can significantly reduce the effects of intrinsic frequency fluctuations of the primary mode, which are not accessible by any known strategy using single-mode operation. The theoretical predictions are supported by experimental measurements of a microelectromechanical systems-based oscillator that demonstrate a reduction in oscillator line width of several orders of magnitude. This approach offers a means of optimizing frequency stability in self-sustained oscillators, which has direct implications for applications in timekeeping and sensing.

36 MATERIALS SCIENCE↗

DOE OSTI2025

ModE Regulates Alternative Nitrogenase Expression in the Methanogen Methanosarcina acetivorans

ABSTRACT All methanogens that can fix nitrogen use molybdenum (Mo) nitrogenase. Some methanogens, including Methanosarcina acetivorans , also contain alternative vanadium‐ and iron‐nitrogenases, encoded by the vnf and anf operons, respectively. These nitrogenases are produced when there is insufficient Mo to support Mo‐nitrogenase activity. The factors that control the expression of the alternative nitrogenases in response to Mo availability are unknown in methanogens. Here we show that ModE is the regulator that represses transcription of the vnf and anf operons in M. acetivorans when cells are grown with Mo. CRISPRi repression of modE results in a significant increase in the transcription of the vnf and anf operons as well as the detection of Fe‐nitrogenase during nitrogen fixation in the presence of Mo. Gel shift assays with recombinant ModE demonstrated that ModE binds a specific sequence motif upstream of the vnf and anf operons, as well as other genes and operons related to nitrogen fixation and Mo transport. However, purified ModE does not contain Mo, and the addition of Mo does not alter the affinity of ModE for DNA, indicating M. acetivorans ModE may not directly bind Mo. This study shows that ModE is the primary Mo‐responsive regulator of alternative nitrogenase expression in M. acetivorans , but other factor(s) are likely involved in directly sensing Mo.

Chanderban, Melissa [Department of Biological Scie↗

NASA NTRS1973

The design and development of an automatic control system for the in-duct cancellation of spinning modes of sound

The reduction is discussed of the discrete tones generated by jet engines which is essential for jet aircraft to meet present and proposed noise standards. The discrete tones generated by the blades and vanes propagate in the inlet and exhaust duct in the form of spiraling acoustic waves, or spinning modes. The reduction of these spinning modes by the cancellation effect of the combination of two acoustic fields was investigated. The spinning mode synthesizer provided the means for effective study of this noise reduction scheme. Two sets of electrical-acoustical transducers located in an equally-spaced circular array simultaneously generate a specified spinning mode and the cancelling mode. Analysis of the wave equation for the synthesizer established the optimum cancelling array acoustic parameters for maximum sound pressure level reduction. The parameter dependence of the frequency ranges of propagation of single, specified circumferential modes generated by a single array, and of effective cancellation of the modes generated by two arrays, was determined. Substantial sound pressure level reduction was obtained for modes within these limits.

Harrington, W. W.↗

NASA NTRS1975

Single laser beam of spatial coherence from an array of GaAs lasers - Free-running mode

Spatially coherent radiation from a monolithic array of three GaAs lasers in a free-running mode is reported. The lasers, with their mirror faces antireflection coated, are operated in an external optical cavity built of spherical lenses and plane mirrors. The spatially coherent-beam formation makes use of the Fourier-transformation property of the internal lenses. Transverse mode control is accomplished by a spatial filter. The optical cavity is similar to that used for the phase-controlled mode of spatially coherent-beam formation; only the spatial filters are different. In the far field (when restored by an external lens), the intensities of the lasers in the array are concentrated in a single laser beam of spatial coherence, without any grating lobes. The far-field distribution of the laser array in the free-running mode differs significantly from the interference pattern of the phase-controlled mode. The modulation characteristics of the optical waveforms of the two modes are also quite different because modulation is related to the interaction of the spatial filter with the longitudinal modes of the laser array within the optical cavity. The modulation of the optical waveform of the free-running mode is nonperiodic, confirming that the fluctuations of the optical fields of the lasers are random.

Philipp-Rutz, E. M.↗

NASA NTRS1980

The collective excitation of g-modes in the sun

Oscillations of the solar interior (linear g-modes) may be strongly driven by the collective influence of all the modes upon the nuclear reactions in the core. This heretofore neglected effect could couple the modes, reduce the effective amplitudes near the center, and spatially concentrate most of the oscillation energy into just a portion of the radiative interior. If operating at sufficient strength, this can reverse the conventional conclusion, drawn from single mode calculations, that almost all solar g-modes are damped. Furthermore, it would put the theory into rough harmony with three otherwise troubling observations: (1) the 'low' neutrino flux measured by Davis (1978), (2) the high correspondence found by Wolff (1976) between recurrence periods in solar activity and the rotational beat periods of g-modes, and (3) the fluctuations in the sun's diameter which imply g-mode activity at high angular harmonics (Hill and Caudell 1979). A nonlinear expression is derived for the local rate of work done on an array of oscillation modes by the nuclear reactions. Three additional tests of the model are suggested.

Wolff, C. L.↗

NASA NTRS1984

Computational aspects of the nonlinear normal mode initialization of the GLAS 4th order GCM

Using the normal modes of the GLAS 4th Order Model, a Machenhauer nonlinear normal mode initialization (NLNMI) was carried out for the external vertical mode using the GLAS 4th Order shallow water equations model for an equivalent depth corresponding to that associated with the external vertical mode. A simple procedure was devised which was directed at identifying computational modes by following the rate of increase of BAL sub M, the partial (with respect to the zonal wavenumber m) sum of squares of the time change of the normal mode coefficients (for fixed vertical mode index) varying over the latitude index L of symmetric or antisymmetric gravity waves. A working algorithm is presented which speeds up the convergence of the iterative Machenhauer NLNMI. A 24 h integration using the NLNMI state was carried out using both Matsuno and leap-frog time-integration schemes; these runs were then compared to a 24 h integration starting from a non-initialized state. The maximal impact of the nonlinear normal mode initialization was found to occur 6-10 hours after the initial time.

Navon, I. M.↗

NASA NTRS1985

The Vertical Structure of Global Rotational Normal Modes

In a recent study, Lindzen et al. (1984) examined the amplitude and phase evolution of Hough mode projections at 500 mb. The Hough modes represent the simplest normal mode approximation available, and correspond to the neutral eigenfunctions of a shallow water fluid with no mean zonal flow. It was found that when the observed amplitude of a rotational Hough mode was large, it tended to propagate at the phase speed of a normal mode in the presence of mean 500 mb winds, giving a strong indication that normal modes are of relevance to the atmosphere. The vertical structure of the approximately defined rotational normal modes were explored by projecting observed data onto Hough functions at levels other than 500 mb. The stationary and eastward propagating components were filtered out at each level. The evolution of the amplitude in time throughout the troposphere is given for several modes during summer and winter.

Straus, D. M.↗

NASA NTRS1985

Influence of the resin on interlaminar mixed-mode fracture

Both literature review data and new data on toughness behavior of seven matrix and adhesive systems in four types of tests were studied in order to assess the influence of the resin on interlaminar fracture. Mixed mode (i.e., various combinations of opening mode 1, G sub 1, and shearing mode 2; G sub 2) fracture toughness data showed that the mixed mode relationship for failure appears to be linear in terms of G sub 1 and G sub 2. The study further indicates that fracture of brittle resins is controlled by the G sub 1 component, and that fracture of many tough resins is controlled by total strain-energy release rate, G sub T. Regarding the relation of polymer structure and the mixed mode fracture: high mode 1 toughness requires resin dilatation; dilatation is low in unmodified epoxies at room temperature/dry conditions; dilatation is higher in plasticized epoxies, heated epoxies, and in modified epoxies; modification improves mode 2 toughness only slightly compared with mode 1 improvements. Analytical aspects of the cracked lap shear test specimen were explored.

Johnson, W. S.↗

NASA NTRS1986

Condensation modes in magnetized plasmas

Condensation modes in magnetized cylindrical plasmas, with concentration on how magnetic field affects the stability were studied. It is found that the effects of magnetic field (shear, twist, and strength) on the condensation modes are different depending on the wave vector. For modes whose wave vector is not perpendicular to magnetic field lines the plasma motion is mainly along the field lines; the effects of magnetic field on the modes are negligible except on the heat flow parallel to the field line. For a mode which is localized near a surface where the wave vector is perpendicular to the field line, the plasma moves perpendicular to the line carrying the field line into the condensed region; magnetic field affects the mode by building up magnetic pressure in the condensed region. The stability of condensation modes strongly depends on how density and temperature vary with field twist. The stable nature of global quiescent prominence magnetic configurations implies that prominences form for low field twist for which ideal MHD modes are stable; plasma temperature should increase with field twist for stable prominence formation.

An, Chang-Hyuk↗

NASA NTRS1987

The normal modes of the thermosphere

The linearized momentum, energy, and continuity equations for the thermosphere can be reduced to a form that gives the vertical structure for each horizontal wave mode. The vertical structure equation can be described in terms of the normal modes, or eigenmodes, of the thermosphere. The latter are obtained by using a 27-layer model that includes a realistic temperature profile and the effects of the Lorentz force, viscosity, and heat conduction. The normal modes have one real eigenfrequency for every two complex conjugate eigenfrequency values. The real modes have a dominant rotational wind component and are nonpropagating. The complex modes have comparable divergent and rotational wind components. The complex eigenvalues give vertically propagating modes, primarily associated with the transient response to forcing, and are significantly affected by the dissipation in the upper E region and F region. Results show that the rotational wind component dominates in the steady state when the forcing is due to the two-cell convection pattern at high latitudes and that the normal modes explain the large shears and large winds speeds that are typically observed in the high-latitude E region. The vertical energy flux for the normal modes is also calculated. The results show that the flux is upward above 130 km but downward in the lower E region for the total solution. The downward energy flux is a contribution from the real eigenmode structure.

Larsen, M. F.↗

NASA NTRS1987

Influence of the resin on interlaminar mixed-mode fracture

Johnson, W. S.↗