Engineering topics

Mahajan, S. M.

Publications and source records attributed to Mahajan, S. M..

15 records

DOE OSTI2024

Transport Barriers in magnetized plasmas- general theory with dynamical constraints

Abstract A fundamental dynamical constraint—that fluctuation induced charge-weighted particle flux must vanish- can prevent instabilities from accessing the free energy in the strong gradients characteristic of Transport Barriers (TBs). Density gradients, when large enough, lead to a violation of the constraint and hence preclude unstable modes and turbulent transport. This mechanism, then, broadens the class of configurations (in magnetized plasmas) where these high confinement states can be formed and sustained. The need for velocity shear, the conventional agent for TB formation, is obviated. The most important ramifications of the constraint is to permit a charting out of the domains conducive to TB formation and hence to optimally confined fusion worthy states; the detailed investigation is conducted through new analytic methods and extensive gyrokinetic simulations.

Physics↗

DOE OSTI2024

Modeling electron temperature profiles in the pedestal with simple formulas for ETG transport

Abstract This paper reports on the refinement (building on (Hatch D.R. et al 2022 Phys. Plasmas 29 062501)) and application of simple formulas for electron heat transport from electron temperature gradient (ETG) driven turbulence in the pedestal. The formulas are improved by (1) improving the parameterization for certain key parameters and (2) carefully accounting for the impact of geometry and shaping in the underlying gyrokinetic simulation database. Comparisons with nonlinear gyrokinetic simulations of ETG transport in the MAST pedestal demonstrate the model’s applicability to spherical tokamaks in addition to standard aspect ratio tokamaks. We identify bounds for model applicability: the model is accurate in the steep gradient region, where the ETG turbulence is largely slab-like, but accuracy decreases as the temperature gradient becomes weaker in the pedestal top. We use the formula to model the electron temperature profile in the pedestal for four experimental scenarios while extensively varying input parameters to represent uncertainties. In all cases, the predicted electron temperature profile exhibits extreme sensitivity to separatrix temperature and density, which has implications for core-edge integration. The model reproduces the electron temperature profile for high η e = L n e / L T e scenarios but not for low η e scenarios in which microtearing modes (MTMs) have been identified. We develop a proof-of-concept model for MTM transport and explore the relative roles of ETG and MTM in setting the electron temperature profile.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2023

ETG turbulent transport in the Mega Ampere Spherical Tokamak (MAST) pedestal

The results of a gyrokinetic analysis of turbulent transport driven by the electron temperature gradient (ETG) in the MAST pedestal are presented. Local nonlinear simulations from the gyrokinetic code, GENE, show that heat flux produced by ETG turbulence is 10%–30% of the total applied heating power in the upper pedestal and pedestal top during both the pre-edge-localized mode (ELM) (80%–99% inter-ELM period) and post-ELM (0%–20%) periods. Increasing strongly with the ETG, the ETG transport appears to be stiff. Considering radiation losses, ion thermal transport, and the strong sensitivity of the transport to the ETG, we propose that ETG transport is a plausible mechanism mediating the inter-ELM temperature profile on MAST. Cognizant of the possibility that sharp variations in the pedestal profiles may violate the local approximation, we conducted global nonlinear simulations; the results are in good agreement with local simulations except near the pedestal top, where extended radial structures and high transport levels (far beyond experimental) develop in the local simulations. We quantify and parameterize the discrepancy between local and global simulations by calculating the ratio of the radial correlation length to a length scale representative of the profile curvature. When this ratio is sufficiently small, local and global simulations agree as expected.

ETG↗

DOE OSTI2023

Ballooning theory for micro-tearing mode in tokamak

This paper aims to investigate the impact of magnetic drift on the linear micro-tearing mode by using a kinetic approach to derive a reduced two-field eigen system in real space. Here, since the magnetic drift in real space has derivatives, it is more efficient to solve the mode equations in a Fourier-ballooning representation using the two-dimensional (2D) ballooning transform. The lowest-order eigen system in the Fourier-ballooning representation consists of two integral equations, which are numerically solved using the finite difference method for both eigenvalues and wave functions. The main results will be presented through graphical eigenvalue scans for each parameter. Furthermore, we present a graphical comparison between the predictions of the ballooning theory and GENE gyrokinetic code simulation in the pedestal region.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

Gyrokinetic simulations compared with magnetic fluctuations diagnosed with a Faraday-effect radial interferometer-polarimeter in the DIII-D pedestal

Abstract Experimental data on electromagnetic fluctuations in DIII-D, made available by the Faraday-effect radial interferometer-polarimeter (RIP) diagnostic Chen (2016 Rev. Sci. Instrum. 87 11E108), is examined in comparison with detailed gyrokinetic simulations using gyrokinetic electromagnetic numerical experiment (GENE). The diagnostic has the unique capability of making internal measurements of fluctuating magnetic fields ∫ n e δ B r d R ∫ n e d R . Local linear simulations identify microtearing modes (MTMs) over a substantial range of toroidal mode numbers (peaking at n = 15) with frequencies in good agreement with the experimental data. Local nonlinear simulations reinforce this result by producing a magnetic frequency spectrum in good agreement with that diagnosed by RIP. Simulated heat fluxes are in the range of experimental expectations. However, magnetic fluctuation amplitudes are substantially lower than the experimental expectations. Possible sources of this discrepancy are discussed, notably the fact that the diagnostics are localized at the mid-plane—the poloidal location where the simulations predict the fluctuation amplitudes to be smallest. Despite some discrepancies, several connections between simulations and experiments, combined with general criteria discriminating between potential pedestal instabilities, strongly point to MTMs as the source of the observed magnetic fluctuations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

Reduced models for ETG transport in the tokamak pedestal

This paper reports on the development of reduced models for electron temperature gradient (ETG) driven transport in the pedestal. Model development is enabled by a set of 61 nonlinear gyrokinetic simulations with input parameters taken from pedestals in a broad range of experimental scenarios. The simulation data have been consolidated in a new database for gyrokinetic simulation data, the multiscale gyrokinetic database (MGKDB), facilitating the analysis. The modeling approach may be considered a generalization of the standard quasilinear mixing length procedure. The parameter η, the ratio of the density to temperature gradient scale length, emerges as the key parameter for formulating an effective saturation rule. With a single order-unity fitting coefficient, the model achieves an error of 15%. A similar model for ETG particle flux is also described. We also present simple algebraic expressions for the transport informed by an algorithm for symbolic regression.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

A survey of pedestal magnetic fluctuations using gyrokinetics and a global reduced model for microtearing stability

This article presents a global reduced model for slab-like microtearing modes (MTMs) in the H-mode pedestal, which reproduces distinctive features of experimentally observed magnetic fluctuations, such as chirping and discrete frequency bands at noncontiguous mode numbers. Our model, importantly, includes the global variation of the diamagnetic frequencies, which is necessary to reproduce the experimental observations. The key insight underlying this model is that MTM instability is enabled by the alignment of a rational surface with the peak in the profile of the diamagnetic frequency. Conversely, MTMs are strongly stabilized for toroidal mode numbers for which these quantities are misaligned. This property explains the discrete fluctuation bands in several DIII-D and JET discharges, which we survey using our reduced model in conjunction with global gyrokinetic simulations. A fast yet accurate reduced model for MTMs enables rapid interpretation of magnetic fluctuation data from a wide range of experimental conditions to help assess the role of MTM in the pedestal.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Identifying the microtearing modes in the pedestal of DIII-D H-modes using gyrokinetic simulations

Recent evidence points toward the microtearing mode (MTM) as an important fluctuation in the H-mode pedestal for anomalous electron heat transport. A study of the instabilities in the pedestal region carried out using gyrokinetic simulations to model an ELMy H-mode DIII-D discharge (USN configuration, 1.4 MA plasma current, and 3 MW heating power) is presented. The simulations produce MTMs, identified by predominantly electromagnetic heat flux, small particle flux, and a substantial degree of tearing parity. The magnetic spectrogram from Mirnov coils exhibits three distinct frequency bands—two narrow bands at lower frequency (~35–55 kHz and ~70–105 kHz) and a broader band at higher frequency (~300–500 kHz). Global linear GENE simulations produce MTMs that are centered at the peak of the ω* profile and correspond closely with the bands in the spectrogram. The three distinctive frequency bands can be understood from the basic physical mechanisms underlying the instabilities. For example (i) instability of certain toroidal mode numbers (n) is controlled by the alignment of their rational surfaces with the peak in the ω* profile, and (ii) MTM instabilities in the lower n bands are the conventional collisional slab MTM, whereas the higher n band depends on curvature drive. While many features of the modes can be captured with the local approximation, a global treatment is necessary to quantitatively reproduce the detailed band gaps of the low-n fluctuations. Notably, the transport signatures of the MTM are consistent with careful edge modeling by SOLPS.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Global Theory of Microtearing Modes in the Tokamak Pedestal

The pedestal of H-mode tokamaks displays strong magnetic fluctuations correlated with the evolution of the electron temperature. The microtearing mode (MTM), a temperature-gradient-driven instability that alters magnetic topology, is compatible with these observations. Here we extend the conventional theory of the MTM to include the global variation of the temperature and density profiles. The offset between the rational surface and the location of the pressure gradient maximum (μ) emerges as a crucial parameter for MTM stability. In conclusion, the extended theory matches observations on the Joint European Torus tokamak.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

The effect of curvature induced broken potential vorticity conservation on drift wave turbulences

Abstract The correlation theory of turbulence suppression (Zhang and Mahajan 1993 Phys. Fluids B5 2000) by velocity shear was constructed by invoking the ansatz of potential vorticity conservation (PVC) that holds for relatively simple (slab) models of drift wave turbulence. It is, therefore, surprising that a detailed modern simulation of the H mode pedestal, using the gyrokinetic code GENE (Hatch et al 2018 Plasma Phys. Control. Fusion 60 084003), found ‘striking agreement’ with the predictions of the analytic model. To understand the reasons for this remarkable agreement, an extended theory that contains finite (magnetic) curvature, and which does not conserve potential vorticity, is developed and ‘solved’ by calculating an inhomogeneous Green function reflecting the fact that the new system has a potential vorticity source. It is, then, demonstrated that the effect of the broken PVC is insignificant for the normal operation parameters in tokamaks; the correction due to curvature is at the order of 2 L 0 / R , where L 0 is the scale length of the local gradient and R is the major radius. The excellent agreement between simulation and slab model 1993 theory is therefore not accidental; the latter can be applied with confidence to the tokamak pedestal.

Physics↗

DOE OSTI2021

Pedestal magnetic turbulence measurements in ELMy H-mode DIII-D plasmas by Faraday-effect polarimetry

Internal magnetic fluctuation measurements are utilized to identify turbulence associated with micro-tearing modes (MTM) in the DIII-D Edge-Localized-Mode (ELM)-y H-mode pedestal. Using a Faraday-effect polarimeter, magnetic turbulence (150–500 kHz) is directly observed with a typical line-averaged fluctuation amplitude of ~0.8 G at peak frequency (250 kHz) and ~15 G integrated over the spectrum from 150 to 500 kHz. Frequency, poloidal wavenumber, and propagation direction of the magnetic turbulence all serve to identify as MTM. Magnetic turbulence amplitude non-monotonically correlates with collision frequency, peaks off mid-plane, and correlates with electron temperature gradient evolution between ELMs, consistent with MTM features identified from theory and gyro-kinetic simulation. The magnetic turbulence growth correlates with confinement degradation in ELMy H-mode plasmas during a slow density ramp. In conclusion, these internal measurements provide unique constraints toward developing physics understanding and validating models of the H-mode pedestal for future devices.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Microtearing modes as the source of magnetic fluctuations in the JET pedestal

Abstract We report on a detailed study of magnetic fluctuations in the JET pedestal, employing basic theoretical considerations, gyrokinetic simulations, and experimental fluctuation data to establish the physical basis for their origin, role, and distinctive characteristics. We demonstrate quantitative agreement between gyrokinetic simulations of microtearing modes (MTMs) and two magnetic frequency bands with corresponding toroidal mode numbers n = 4 and 8. Such disparate fluctuation scales, with substantial gaps between toroidal mode numbers, are commonly observed in pedestal fluctuations. Here we provide a clear explanation, namely the alignment of the relevant rational surfaces (and not others) with the peak in the ω * profile, which is localized in the steep gradient region of the pedestal. We demonstrate that a global treatment is required to capture this effect. Nonlinear simulations suggest that the MTM fluctuations produce experimentally-relevant transport levels and saturate by relaxing the background electron temperature gradient, slightly downshifting the fluctuation frequencies from the linear predictions. Scans in collisionality are compared with a simple MTM dispersion relation. At the experimental points considered, MTM growth rates can either increase or decrease with collision frequency depending on the parameters thus defying any simple characterization of collisionality dependence.

Physics↗

DOE OSTI2020

Internal measurement of magnetic turbulence in ELMy H-mode tokamak plasmas

Magnetic turbulence is directly observed internally in the pedestal of ELMy H-mode tokamak plasmas using a newly developed Faraday-effect polarimetry measurement. Fluctuation amplitude is δb r ≥ 15 G (150–500 kHz), with a ratio of magnetic to density fluctuation |δb r /B|/|δn/n|≥0.15. Here, magnetic turbulence is identified as resulting from micro-tearing-instability and mode growth accompanied by degraded plasma confinement is observed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2020

A comprehensive conductivity model for drift and micro-tearing modes

The parallel electrical conductivity is a crucial parameter in the study of the linear stability of drift-modes like the micro-tearing mode (MTM). The conductivity enters by closing the electromagnetic tearing layer equations. Recent progress in the understanding of the pedestal suggests that the MTM could play an important role in its structure and evolution. For this reason, we revisit and improve previous model conductivities. This parameter is generally derived from the linearized drift kinetic equation. In the past literature, it has been computed using either simplified collision operators or neglecting the spatial dependence away from the rational surface. Here, a fully consistent expression for the conductivity that would accurately model the pedestal has not been available. By applying a novel variational procedure and with the full Fokker Plank collision operator, including electron–electron collisions, we compute a closed expression for the parallel electrical conductivity in the form of a rational function.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2020

FY19 FES Theory Performance Target (Final Report)

Understanding the relevant turbulent transport mechanisms at the edge of a high-performance tokamak is essential for predicting and optimizing the H-mode pedestal structure in future burning plasma devices. Global electromagnetic gyrokinetic simulations will be performed based on representative experimental pedestal scenarios in order to clarify which instabilities are most important for each of the particle and heat transport channels. Edge transport modeling will be performed in order to estimate and bound the particle and heat sources—e.g., the ionization density source and the atomic energy loss channels due to ionization, charge exchange, and radiation. Comparisons will be made with data from the DIII-D, JET, C-Mod and NSTX or MAST experiments.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗