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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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At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Solution of the linear wave-particle kinetic equation for global modes of arbitrary frequency in a tokamak

The linear response of a plasma to perturbations of arbitrary frequency and wavelength is derived for any axisymmetric magnetized toroidal plasma. An explicit transformation to action-angle coordinates is achieved using orthogonal magnetic coordinates and the Littlejohn Lagrangian, establishing the validity of this result to arbitrary order in normalized Larmor radius. The global resonance condition for compressional modes is clarified in more detail than in previous works, confirming that the poloidal orbit-average of the cyclotron frequency gives the desired result at lowest order in Larmor radius. The global plasma response to the perturbation at each resonance is captured by a poloidal and gyroaverage of the perturbing potential. A “global gyroaveraging” of the potential is a natural by-product of this analysis which takes into account the changing of the magnetic field over an orbit. The resonance condition depends on two arbitrary integers which completely separately capture the effects poloidal non-uniformity and finite Larmor radius in generating sidebands. We learn that poloidal sidebands generated for compressional modes are dominated by the change in gyrofrequency over the orbit, which is very different to shear modes where the gyrofrequency only contributes via a finite Larmor radius effect. This increases the number of bounce harmonics required to compute the linear drive, giving a more complicated resonance map. An example calculation is given comparing resonance of shear and compressional modes in a published DIII-D case.

Compressional↗
DOE OSTI2026

Cooperative Agreement To Analyze variabiLity, change and predictabilitY in the earth SysTem (CATALYST)

CATALYST proposes to perform foundational coordinated research in a team-oriented collaborative effort aimed at advancing a robust understanding of modes of Earth system variability and change using models, observations and process studies. The proposed research will address the DOE/BER mission by exploring the limits to predictability, identifying fundamental underlying mechanisms, quantifying interactions among modes of variability, and discovering tipping points in the Earth system to understand the current and future impacts of these phenomena on regional and global climate. Four fundamental gaps are identified in our knowledge of the Earth system: 1) What are the limits to predictability on various timescales? 2) What are the interactions among modes of Earth system variability? 3) How may modes of Earth system variability change in response to changes in external forcing, and what are the tipping points involved with those changes? 4) How are high impact events connected to modes of Earth system variability and how may they change in the future? Related to those gaps in our knowledge, we formulate four research objectives to address those gaps using a combination of Earth system models (ESMs) and machine learning (ML) methods. Research Objective 1 (RO1) addresses the first gap above and proposes to understand modes of variability and their limits of predictability on subseasonal to decadal timescales using ESMs and ML. Research Objective 2 (RO2) addresses the second gap and proposes to use a hierarchy of models to understand relevant processes and feedbacks related to how modes of variability interact with each other. Research Objective 3 (RO3) is designed to study the third gap and proposes to examine the role of external forcings in changes of modes of Earth system variability and their interactions, and the likelihood and predictability of tipping points and irreversible changes. Research Objective 4 (RO4) will address the fourth gap and proposes to use high resolution ESMs, regionally refined models (RRMs), and ML methods to investigate the relationships between high impact events (e.g. flash droughts and precipitation extremes, atmospheric rivers (ARs), tropical cyclones (TCs), storm surge/sea level rise), the synoptic systems that produce them, and their changes related to modes of Earth system variability. The research will involve the use of the Community Earth System Model (CESM), Energy Exascale Earth System Model (E3SM), CMIP multi-model data sets, a hierarchy of simpler models, and numerous observational data sets. In the course of the proposed research, CATALYST will contribute to metrics and diagnostics that will be integrated in Coordinated Model Evaluation Capabilities (CMEC), particularly with regards to the Quasi-biennial Oscillation (QBO) and its interactions with the Madden-Julian Oscillation (MJO), high atmospheric pressure blocking, and new precipitation metrics.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

On the origin of ground-state vacuum-field catalysis: Equilibrium consideration

Recent experiments suggest that vibrational strong coupling (VSC) may significantly modify ground-state chemical reactions and their rates even without external pumping. The intrinsic mechanism of this “vacuum-field catalysis” remains largely unclear. Generally, modifications of thermal reactions in the ground electronic states can be caused by equilibrium or non-equilibrium effects. The former are associated with modifications of the reactant equilibrium distribution as expressed by the transition state theory of chemical reaction rates, while the latter stem from the dynamics of reaching and leaving transition state configurations. In this work, we examine how VSC can affect chemical reactions rates in a cavity environment according to transition state theory. Our approach is to examine the effect of coupling to cavity mode(s) on the potential of mean force (PMF) associated with the reaction coordinate. Within the context of classical nuclei and classical photons and also assuming no charge overlap between molecules, we find that while the PMF can be affected by the cavity environment, this effect is negligible for the usual micron-length cavities used to examine VSC situations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

First DIII-D-West hybrid scenario similarity experiments for iter-relevant long-pulse operation

For the first time, similarity experiments between DIII-D and WEST were performed in the ITER "hybrid-like" regime during dedicated campaigns in April and May 2025. The matched parameters include elongation, triangularity, ion ∇B drift direction toward the X-point, qprofile, and core normalized physics quantities in terms of normalized pressure, normalized gyroradius, electron collisionality, ratio of ion to electron temperature, T i /T e . Core transport physics is explored with different aspect ratio (R/a) values (typically 3 at DIII-D and 5 on WEST). DIII-D explored high-beta conditions (electromagnetic effect) with low torque injection (~0 ± 0.5 N•m) using high heating power (up to 6 MW NBI and 2 MW ECRH powers), while scanning the heating mix (ion vs electron), beta, T i /T e , core radiation via controlled tungsten injection using the Laser Blow-Off system. WEST extended operation toward long-duration pulses using its actively cooled tungsten divertor, achieving dominated electron heating regimes with reduced tungsten contamination. Boron impurity injection were scanned on WEST to control edge conditions and core performance. It is found that core confinement improves-manifested by higher electron temperature, total energy content, neutron rate, and ion temperatureunder conditions of low separatrix density, consistent with previous observations [Bourdelle et al., Nucl. Fusion 63 (2023) 056021]. Conditions for Hmode access and for ion heating in electron-dominated regimes in both WEST and DIII-D will be discussed and compared. The ratio of the thermal energy confinement time (τ E ) to the volume-averaged electron-ion collisional heat exchange time (τ e-i ) is a key parameter to enhance ion heating and potentially facilitate H-mode access in electron-heated regimes. These first-of-a-kind coordinated DIII-D and WEST experiments provide a unique multi-machine dataset to validate predictive models and to optimize ITER hybrid-scenario performance under diverse core and edge conditions.

DIII-D↗
DOE OSTI2021

Capturing 3D atomic defects and phonon localization at the 2D heterostructure interface

The three-dimensional (3D) local atomic structures and crystal defects at the interfaces of heterostructures control their electronic, magnetic, optical, catalytic, and topological quantum properties but have thus far eluded any direct experimental determination. Here, we use atomic electron tomography to determine the 3D local atomic positions at the interface of a MoS 2 -WSe 2 heterojunction with picometer precision and correlate 3D atomic defects with localized vibrational properties at the epitaxial interface. We observe point defects, bond distortion, and atomic-scale ripples and measure the full 3D strain tensor at the heterointerface. By using the experimental 3D atomic coordinates as direct input to first-principles calculations, we reveal new phonon modes localized at the interface, which are corroborated by spatially resolved electron energy-loss spectroscopy. We expect that this work will pave the way for correlating structure-property relationships of a wide range of heterostructure interfaces at the single-atom level.

42 ENGINEERING↗
DOE OSTI2021

The magnetic structure of long-wavelength magnetohydrodynamic modes in current-carrying stellarator plasmas

Magnetic field fluctuations are observed in current-carrying stellarator plasmas when the rotational transform is close to a rational value at the edge of the plasma. At low plasma pressure, these fluctuations are associated with perturbed currents parallel to the equilibrium magnetic field lines. A model for these magnetohydrodynamic modes in a low-β, three-dimensional stellarator equilibria has been developed. A set of helical current filaments are constrained to mimic the structure of magnetic field lines on rational surfaces derived from three-dimensional (3D) equilibrium reconstructions. Transformation to straight field line coordinates then allows fitting of the poloidal magnetic sensor data to a single harmonic function, which fixes the modeled toroidal mode structure via the field line flow geometry. The developed procedure accurately captures phase and amplitude variation for m/n = 3/2, 3/1, and 4/1 modes in the 3D equilibria of the compact toroidal hybrid experiment.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Parametric reduced-order modeling for component-oriented treatment and localized nonlinear feature inclusion

Abstract We propose coupling a physics-based reduction framework with a suited response decomposition technique to derive a component-oriented reduction (COR) approach, which is suitable for assembly systems featuring localized nonlinearities. Dependencies on influencing parameters are injected into the reduced-order model (ROM), thus ensuring robustness and validity over a domain of parametric inputs, while capturing nonlinear effects. The implemented approach employs individual component modes to capture localized features while additionally relying on reduced modes of a global nature to approximate the system’s dynamics accurately. The global modes are derived from a linear monolithic system, defined as a result of a coordinate separation scheme, which permits the proposed COR-ROM to naturally couple the response between linear and nonlinear subdomains. The derived low-order representation utilizes a proper orthogonal decomposition projection and is additionally reinforced with the inclusion of a hyper-reduction technique to capture the underlying high-fidelity model response while providing accelerated computations. The resulting approach is exemplified in the synthetic case studies of a four-story shear frame with multiple nonlinear regions driven by hysteresis and a large-scale kingpin connection featuring plasticity.

Vlachas, Konstantinos (ORCID:000000029124219X)↗
DOE OSTI2023

Vibrational signature of hydrated protons confined in MXene interlayers

Here, the hydration structure of protons has been studied for decades in bulk water and protonated clusters due to its importance but has remained elusive in planar confined environments. Two-dimensional (2D) transition metal carbides known as MXenes show extreme capacitance in protic electrolytes, which has attracted attention in the energy storage field. We report here that discrete vibrational modes related to protons intercalated in the 2D slits between Ti 3 C 2 T x MXene layers can be detected using operando infrared spectroscopy. The origin of these modes, not observed for protons in bulk water, is attributed to protons with reduced coordination number in confinement based on Density Functional Theory calculations. This study therefore demonstrates a useful tool for the characterization of chemical species under 2D confinement.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Effect of outer-cylinder rotation on the radially heated Taylor–Couette flow

A Taylor–Couette setup with radial heating is considered where a Boussinesq fluid is sheared in the annular region between two concentric, independently rotating cylinders maintained at different temperatures. Linear stability analysis is performed to determine the Taylor number for the onset of instability. Two radius ratios corresponding to wide and thin gaps with several rotation rate ratios are considered. The rotation of the outer cylinder is found to have a general stabilizing effect on the stability threshold as compared to pure inner-cylinder rotation, with a few exceptions. The radial heating sets up an axial flow which breaks the reflection symmetry of isothermal Taylor–Couette flow in the axial coordinate. This symmetry breaking separates linear stability thresholds, and we find the fastest growing modes with both positive and negative azimuthal numbers for different parameters. Another important finding of the current study is the discovery of unstable modes in the Rayleigh-stable regime. Furthermore, closed disconnected neutral curves (CDNCs) are observed for both wide and thin gaps which can separate from or merge into open neutral–stability curves. Alternatively, CDNCs can also morph into open neutral stability curves as the rotation rate ratio is changed. CDNCs are observed to be sensitive to changes in control parameters, and their appearance/disappearance is shown to induce discontinuous jumps in the critical Taylor number. Finally, for both wide and thin gaps, the fastest-growing modes found in the pure corotation case are shown to have their origins in the instability islands at smaller values of rotation rate ratios.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Quantitative comparisons of electron-scale turbulence measurements in NSTX via synthetic diagnostics for high-k scattering.

Two synthetic diagnostics are implemented for the high-k scattering system in NSTX [D. R. Smith, E. Mazzucato, W. Lee, H. K. Park, C. W. Domier, and N. C. Luhmann Jr., Rev. Sci. Instrum., 79, 123501 (2008)] allowing direct comparisons between synthetic and experimentally detected frequency and wavenumber spectra of electron-scale turbulence fluctuations. Synthetic diagnostics were formulated in real-space and in wavenumber space, and were deployed to realistic electron-scale simulations carried out with the GYRO code [J. Candy and R. E. Waltz, J. Comput. Phys. 186 (2003) 545]. A highly unstable ETG regime (electron temperature gradient mode) in a modest beta NSTX NBI-heated H-mode discharge was chosen for the analysis. Mapping the measured wavenumbers to field aligned coordinates showed that the high-k system is sensitive to fluctuations that are closer to the spectral peak in the density fluctuation wavenumber spectrum (streamers) than originally predicted. Analysis of synthetic spectra show that the frequency response of the detected fluctuations is dominated by Doppler shift and insensitive to the turbulence drive. The shape of the high-k density fluctuation wavenumber spectrum is sensitive to the ETG turbulence drive conditions, and can be reproduced in a sensitivity scan of the most pertinent turbulent drive terms in the simulation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

A Novel Protection Scheme for Unbalanced Faults in Inverter Dominated Networks: A Computationally Efficient Algorithm for Entry-Level Relays

Microgrids are now a common practice in distribution systems to increase resilience and reliability. However, microgrid protection remains a critical challenge, considering its requirement to operate in both grid connected and islanded, and the variability in fault characteristics under each mode of operation. This paper presents unbalanced power (S unb ) based fault detection algorithm, which considers local voltage and current unbalances to determine faults in the system. S unb is a computationally efficient fault detection algorithm that is suitable for implementation in the programmable logic of entry level protective relays. In addition, the difference in current and voltage unbalance (D n ) is used to determine the fault type. The proposed method demonstrates high sensitivity and selectivity for line-to-ground (LG), line-to-line (LL), and double line-to-ground (LLG) faults, representing the most common faults in distribution systems. It also allows relay coordination with upstream and downstream protection devices in both island and grid connected operation, while preserving grading margins. The same pickup and time multiplier settings of a particular relay for both modes of operation eliminates the need for adaptive settings, which rely on communication networks. Validation was performed with a hardware-in-the-loop (HIL) setup using Typhoon HIL real time simulator interfaced with three entry-level, SEL 751 relays. Results confirmed the algorithm’s ability to discriminate fault conditions, and determine the fault type under both operating modes, maintain fast detection times, and ensure proper protection coordination.

fault classification↗
DOE OSTI2022

Numerical Simulation of Vibrational Sum Frequency Generation Intensity for Non-Centrosymmetric Domains Interspersed in an Amorphous Matrix: A Case Study for Cellulose in Plant Cell Wall

Vibrational sum frequency generation (SFG) spectroscopy can specifically probe molecular species non-centrosymmetrically arranged in a centrosymmetric or isotropic medium. This capability has been extensively utilized to detect and study molecular species present at the two-dimensional (2D) interface at which the centrosymmetry or isotropy of bulk phases is naturally broken. The same principle has been demonstrated to be very effective for the selective detection of non-centrosymmetric crystalline nanodomains interspersed in three-dimensional (3D) amorphous phases. However, the full spectral interpretation of SFG features has been difficult due to the complexity associated with the theoretical calculation of SFG responses of such 3D systems. This paper describes a numerical method to predict the relative SFG intensities of non-centrosymmetric nanodomains in 3D systems as functions of their size and concentration as well as their assembly patterns, i.e., the distributions of tilt, azimuth, and rotation angles with respect to the lab coordinate. We applied the developed method to predict changes in the CH and OH stretch modes characteristic to crystalline cellulose microfibrils distributed with various orders, which are relevant to plant cell wall structures. As a result, the same algorithm can also be applied to any SFG-active nanodomains interspersed in 3D amorphous matrices.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Constructing protein polyhedra via orthogonal chemical interactions

Many proteins exist naturally as symmetrical homooligomers or homopolymers. The emergent structural and functional properties of such protein assemblies have inspired extensive efforts in biomolecular design2–5. As synthesized by ribosomes, proteins are inherently asymmetric. Therefore, they must acquire multiple surface patches that selectively associate to generate the different symmetry elements needed to form higher-order architectures—a daunting task for protein design. Here we address this problem using an inorganic chemical approach, whereby multiple modes of protein–protein interactions and symmetry are simultaneously achieved by selective, ‘one-pot’ coordination of soft and hard metal ions. We show that a monomeric protein (protomer) appropriately modified with biologically inspired hydroxamate groups and zinc-binding motifs assembles through concurrent Fe 3+ and Zn 2+ coordination into discrete dodecameric and hexameric cages. Our cages closely resemble natural polyhedral protein architectures and are, to our knowledge, unique among designed systems in that they possess tightly packed shells devoid of large apertures. At the same time, they can assemble and disassemble in response to diverse stimuli, owing to their heterobimetallic construction on minimal interprotein-bonding footprints. With stoichiometries ranging from [2 Fe:9 Zn:6 protomers] to [8 Fe:21 Zn:12 protomers], these protein cages represent some of the compositionally most complex protein assemblies—or inorganic coordination complexes—obtained by design.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Mobile loop dynamics in adenosyltransferase control binding and reactivity of coenzyme B 12

Cobalamin is a complex organometallic cofactor that is processed and targeted via a network of chaperones to its dependent enzymes. AdoCbl (5'-deoxyadenosylcobalamin) is synthesized from cob(II)alamin in a reductive adenosylation reaction catalyzed by adenosyltransferase (ATR), which also serves as an escort, delivering AdoCbl to methylmalonyl-CoA mutase (MCM). The mechanism by which ATR signals that its cofactor cargo is ready (AdoCbl) or not [cob(II)alamin] for transfer to MCM, is not known. In this study, we have obtained crystallographic snapshots that reveal ligand-induced ordering of the N terminus of Mycobacterium tuberculosis ATR, which organizes a dynamic cobalamin binding site and exerts exquisite control over coordination geometry, reactivity, and solvent accessibility. Cob(II)alamin binds with its dimethylbenzimidazole tail splayed into a side pocket and its corrin ring buried. The cosubstrate, ATP, enforces a four-coordinate cob(II)alamin geometry, facilitating the unfavorable reduction to cob(I)alamin. The binding mode for AdoCbl is notably different from that of cob(II)alamin, with the dimethylbenzimidazole tail tucked under the corrin ring, displacing the N terminus of ATR, which is disordered. In this solvent-exposed conformation, AdoCbl undergoes facile transfer to MCM. The importance of the tail in cofactor handover from ATR to MCM is revealed by the failure of 5'-deoxyadenosylcobinamide, lacking the tail, to transfer. In the absence of MCM, ATR induces a sacrificial cobalt–carbon bond homolysis reaction in an unusual reversal of the heterolytic chemistry that was deployed to make the same bond. Finally, the data support an important role for the dimethylbenzimidazole tail in moving the cobalamin cofactor between active sites.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2023

Stability of the modulator in a plasma-modulated plasma accelerator

We explore the regime of operation of the modulator stage of a recently proposed laser-plasma accelerator scheme [Phys. Rev. Lett. 127, 184801 (2021)], dubbed the plasma-modulated plasma accelerator (P-MoPA). The P-MoPA scheme offers a potential route to high-repetition-rate, GeV-scale plasma accelerators driven by picosecond-duration laser pulses from, for example, kilohertz thin-disk lasers. The first stage of the P-MoPA scheme is a plasma modulator in which a long, high-energy “drive” pulse is spectrally modulated by copropagating in a plasma channel with the low-amplitude plasma wave driven by a short, low-energy “seed” pulse. The spectrally modulated drive pulse is converted to a train of short pulses, by introducing dispersion, which can resonantly drive a large wakefield in a subsequent accelerator stage with the same on-axis plasma density as the modulator. In this paper we derive the 3D analytic theory for the evolution of the drive pulse in the plasma modulator and show that the spectral modulation is independent of transverse coordinate, which is ideal for compression into a pulse train. We then identify a transverse mode instability (TMI), similar to the TMI observed in optical fiber lasers, which sets limits on the energy of the drive pulse for a given set of laser-plasma parameters. We compare this analytic theory with particle-in-cell (PIC) simulations and find that even higher energy drive pulses can be modulated than those demonstrated in the original proposal.

43 PARTICLE ACCELERATORS↗
DOE OSTI2025

An Open-source Llm Enhanced-tool Specialized In Helping Moose Related Problems And Tasks

MOOSEenger is an open-source, terminal-first chat application for the MOOSE ecosystem that couples specialized parsing of MOOSE documentation and “.i” input files with retrieval-augmented generation to deliver grounded answers about multiphysics modeling and workflows. It includes dedicated readers for MOOSE-style HTML and a pyhit-based parser that uses the MOOSE syntax tree to preserve block structure and attach retrieval metadata. A data-ingestion pipeline performs semantic chunking into atomic facts and stores them hierarchically in a local Chroma vector database that maintains parent–child relationships across documents; the system can ingest directories, individual files, and single-page web content, and it provides CRUD operations (insert, update, delete) to manage the corpus. At query time, relevant chunks are embedded, retrieved, and fused into the model context, with interactive features such as token streaming, persistent chat history, and dynamic RAG (retrieval triggered by user input or intermediate model output). Deployment is flexible: MOOSEenger runs with local Ollama models or remote Hugging Face/OpenAI backends—typically coordinating generation, lightweight tagging/summarization, and embeddings across three models—and it also supports a server mode and integration with the VS Code Continue interface.

Li, Mengnan [Idaho National Laboratory (INL), Idah↗
DOE OSTI2021

The efficacy of Lewis affinity scale metrics to represent solvent interactions with reagent salts in all-inorganic metal halide perovskite solutions

Solvents employed in the solution processing of metal halide perovskites are known to play a key role in defining the morphology and properties of the resulting thin film, and thus the performance of perovskite solar cell devices. Accurate metrics are needed that are capable of differentiating among candidates, finding solvents that adequately solubilize the various precursor species in solution and facilitate the nucleation and growth of these materials. Existing metrics such as the unsaturated Mayer bond order (UMBO) and the Gutmann donor number (DN) have been tested for lead iodide perovskite systems; but there has yet to be a comprehensive study on their transferability to lead-free perovskite solutions. Here, we use ab initio methods (density functional theory) and regression analysis tools to study the usefulness of DN and BF 3 affinity scales in this regard. We compared the relative effectiveness of these scales to describe interactions between solvents and BXn perovskite salts of lead (Pb 2+ ), tin (Sn 2+ and Sn 4+ ), germanium (Ge 2+ ), bismuth (Bi 3+ ), and antimony (Sb 3+ and Sb 5+ ). The DN proved to be a better representation than the BF 3 of such interactions, reflecting the closer similarity of these species to the “parent” SbCl 5 Lewis acid than to BF 3 . In addition, we have uncovered the usefulness of the lithium cation affinity metric (LCA) to describe the strength of interactions between solvents and A-site cations (e.g. Na + , K + , Rb + and Cs + ) in all-inorganic metal halide perovskite solutions. We find that the coordination strengths of solvents towards species in all-inorganic metal halide perovskite solutions are best described by two different metrics with distinct modes of action: DN differentiates among BX n salt complexes, and LCA among A-site cation species. This revelation can help guide the choice of solvent to optimize processing conditions. It also emphasizes the importance of selecting solvents whose DN and LCA optimize coordination to key Lewis acid species in all-inorganic perovskite solutions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Theory of the tertiary instability and the Dimits shift within a scalar model

The Dimits shift is the shift between the threshold of the drift-wave primary instability and the actual onset of turbulent transport in a magnetized plasma. It is generally attributed to the suppression of turbulence by zonal flows, but developing a more detailed understanding calls for consideration of specific reduced models. The modified Terry–Horton system has been proposed by St-Onge ( J. Plasma Phys. , vol. 83, 2017, 905830504) as a minimal model capturing the Dimits shift. Here, we use this model to develop an analytic theory of the Dimits shift and a related theory of the tertiary instability of zonal flows. We show that tertiary modes are localized near extrema of the zonal velocity $U(x)$ , where $x$ is the radial coordinate. By approximating $U(x)$ with a parabola, we derive the tertiary-instability growth rate using two different methods and show that the tertiary instability is essentially the primary drift-wave instability modified by the local $U'' \doteq {\rm d}^2 U/{\rm d} x^2 $ . Then, depending on $U''$ , the tertiary instability can be suppressed or unleashed. The former corresponds to the case when zonal flows are strong enough to suppress turbulence (Dimits regime), while the latter corresponds to the case when zonal flows are unstable and turbulence develops. This understanding is different from the traditional paradigm that turbulence is controlled by the flow shear $| {\rm d} U / {\rm d} x |$ . Our analytic predictions are in agreement with direct numerical simulations of the modified Terry–Horton system.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗