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Results for “SAFETY FACTOR”

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 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Nonlinear control of the minimum safety factor in tokamaks by optimal allocation of spatially moving electron cyclotron current drive

The minimum value of the safety factor profile is related to the magnetohydrodynamic (MHD) stability of the plasma confined in a tokamak. Therefore, active control of the minimum safety factor may mitigate MHD instabilities that can degrade or even terminate plasma confinement. Typically, in most tokamak scenarios, the minimum safety factor evolves spatially with time, i.e., the location at which the safety factor achieves the minimum value changes with time. In addition to the inherent nonlinearities in the minimum safety factor evolution, its spatial variation makes the control design challenging. In particular, complexity in control design may arise from the need for time-dependent nonlinear models that account for spatial variation of the minimum safety factor. Furthermore, the minimum safety factor may drift to locations where the actuator authority is low. The problem of minimum safety factor control with target location tracking and moving electron cyclotron current drive (ECCD) is addressed in this work. A nonlinear time-dependent model that incorporates the spatial variation of the minimum safety factor is presented. A nonlinear controller based on optimal feedback linearization is developed to track a target minimum safety factor. The proposed controller treats the ECCD position as a controllable variable. In other words, the controller prescribes the ECCD position (in addition to the non-inductive powers) in real time based on an optimal criterion that is defined a priori. This work also presents the steps necessary to integrate the minimum safety factor controller with a total energy controller to achieve multiple control objectives simultaneously. In conclusion, the proposed integrated control algorithm is tested using nonlinear simulations in the Control Oriented Transport SIMulator (COTSIM) for a DIII-D tokamak scenario.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Nonlinear control of safety factor gradient in tokamaks using spatially variable electron cyclotron current drives

Active control of plasma properties may be necessary to achieve stable operation of next-generation tokamaks over large time scales. Such control algorithms can regulate the plasma properties to avoid the onset of magnetohydrodynamic (MHD) instabilities. For instance, the global and local properties of the safety factor profile are linked to the onset of neoclassical tearing modes (NTMs). This work proposes a model-based control approach for deterring/delaying NTMs through active modulation of one of the safety factor properties - the gradient of the safety factor profile at a particular rational safety factor surface. In particular, a novel control-oriented model for the local safety factor gradient is developed. The nonlinear control model is governed by a nonautonomous ordinary differential equation that accounts for a given rational safety factor surface’s spatial variation over time. Further, to improve the controllability of the spatially evolving parameter, the control model treats ECH&CD positions, along with noninductive powers, as controllable variables. A nonlinear control algorithm based on feedback linearization with optimization is synthesized to achieve the objective of regulating the safety factor gradient around a given target. The proposed algorithm allocates optimal ECH&CD positions, in addition to auxiliary powers, at each time instant as the rational safety factor surface drifts to locations with a low control authority. Stability guarantees of the proposed control law are also discussed in this work. The proposed algorithm is tested for a DIII-D tokamak scenario in nonlinear simulations carried out using the Control Oriented Transport SIMulator (COTSIM). Both fixed and moving ECH&CD cases are studied, and their outcomes are compared. Simulation results demonstrate that enthusiastic regulation of the safety factor gradient can be achieved during the ramp-up and flat-top phases of tokamak operation in both fixed and moving ECH&CD cases. However, real-time updates of ECH&CD positions can prevent the saturation of auxiliary powers.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Self-organized magnetic equilibria in tokamak plasmas with very low edge safety factor

Tokamak plasmas often exhibit self-organizing behavior in which internal modes shape the toroidal current density profile, a common example being the sawtooth instability. However, such behavior has not been studied in detail for edge safety factor below 2 due to disruptive kink instabilities that typically prevent operation in this regime. Now, steady tokamak plasmas with an edge safety factor down to 0.8 have been created in the Madison Symmetric Torus, where disruptions are prevented due to a thick, conductive wall and a feedback power supply that sustains the plasma current. Internal measurements and nonlinear magnetohydrodynamic modeling reveal a family of safety factor profiles with a central value clamped near unity as the edge safety factor decreases, indicating current profile broadening through a relaxation process. Furthermore, as the safety factor decreases, the magnetic fluctuations become irregular, and the electron energy confinement time decreases.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

X-point effects on the ideal MHD modes in tokamaks in the description of dual-poloidal-region safety factor

The flux coordinates with dual-region safety factor (q) in the poloidal direction are developed in this work. The X-point effects on the ideal MHD modes in tokamaks are then analyzed using this coordinate system. Since the X-point effects mainly affect the edge region, the modes localized at the tokamak edge are particularly examined. Two types of modes are studied. The first is related to the conventional peeling or peeling-ballooning modes. The mode existence aligned with the local magnetic field in the poloidally core region as observed experimentally is confirmed. The X points are shown to contribute to a stabilizing effect for the conventionally treated modes with the surface-averaged q and with the tokamak edge portion truncated. The other is the axisymmetric modes localized in the vicinity of X points, which can affect the cross-field-line transport near the X points. The existence of axisymmetric modes points to the possibility of applying a toroidally axisymmetric resonant magnetic perturbation (RMP) in the X-point area for mitigating the edge localized modes, which can be an alternative to the current RMP design. The dual q description also has important implications for the existing non-axisymmetric RMP concept. It helps to understand why the RMP suppression of edge localized modes is difficult to achieve in the double-null tokamak configurations and points to the possibility of further improving the current RMP concept by considering the alignment to the local q.

Fourier analysis↗
DOE OSTI2024

Simultaneous control of the electron temperature and safety factor profiles in DIII-D using model-based optimal control techniques

Future tokamak power plants will likely operate using a single, well-defined plasma scenario, either in steady state or for very long pulse lengths. In order to enhance the robustness of the scenario, feedback controllers for a variety of plasma properties will be necessary to counteract any disturbances and ensure safe operation. However, only a limited set of actuators will be available to control many different quantities. Because of this, it is necessary to develop controllers that are able to regulate multiple plasma properties using a limited set of actuators. To this end, a controller has been developed for the simultaneous regulation of both the electron temperature and safety factor profiles in DIII-D. This algorithm uses a linear quadratic integral control synthesis approach based on a linearized model of the dynamics of the two profiles. Two neural network surrogate models, NubeamNet and MMMnet, are included to improve the fidelity of the model. Furthermore, the controller has been tested in simulation using COTSIM, and has demonstrated the ability to simultaneously track changes in both the electron temperature and safety factor targets, including changes in both the magnitude and the shape of the profiles.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Regulation of the central safety factor and normalized beta under low NBI torque in DIII-D

An algorithm has been designed to simultaneously control the central safety factor (q 0 ) and normalized beta (β N ) while ensuring near-zero torque from the neutral beam injection in DIII-D. Feedback control of q 0 and β N in tokamaks can be beneficial due to the close relationship that these variables have with plasma performance and magneto-hydrodynamic stability. In addition, low neutral-beam-torque conditions are of special interest in present devices because future burning-plasma tokamaks such as ITER will most likely operate at very low plasma rotation. The control synthesis of the algorithm presented in this work is based on a linearized, one-dimensional (1D) model of the current-profile dynamics coupled with a zero-dimensional (0D) plasma-energy balance. The actuators considered are neutral beam injection and electron-cyclotron heating and current drive, and discrete logic determines the neutral-beam injection powers that deliver near-zero torque. Here, the algorithm has been tested in nonlinear, 1D simulations using COTSIM (Control-Oriented Transport SIMulator) and in DIII-D experiments, demonstrating satisfactory performance.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Hybrid model predictive control techniques for safety factor profile and stored energy regulation while incorporating NBI constraints

Abstract A novel hybrid Model Predictive Control (MPC) algorithm has been designed for simultaneous safety factor ( q ) profile and stored energy ( w ) control while incorporating the pulse-width-modulation constraints associated with the neutral beam injection (NBI) system. Regulation of the q -profile has been extensively shown to be a key factor for improved confinement as well as non-inductive sustainment of the plasma current. Simultaneous control of w is necessary to prevent the triggering of pressure-driven magnetohydrodynamic instabilities as the controller shapes the q profile. Conventional MPC schemes proposed for q -profile control have considered the NBI powers as continuous-time signals, ignoring the discrete-time nature of these actuators and leading in some cases to performance loss. The hybrid MPC scheme in this work has the capability of incorporating the discrete-time actuator dynamics as additional constraints. In nonlinear simulations, the proposed hybrid MPC scheme demonstrates improved q -profile+ w control performance for NSTX-U operating scenarios.

Physics↗
DOE OSTI2023

Reconstruction of tokamak plasma safety factor profile using deep learning

Abstract The motional Stark effect (MSE) diagnostic has been a standard measurement for the magnetic field line pitch angle in tokamaks that are equipped with neutral beams. However, the MSE data are not always available due to experimental constraints, especially in future devices without neutral beams. Here we develop a deep-learning based model (SGTC-QR) that can reconstruct the safety factor profile without the MSE diagnostic to mimic the traditional equilibrium reconstruction with the MSE constraint. The model demonstrates promising performance, and the sub-millisecond inference time is compatible with the real-time plasma control system.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2018

Mathematical Simulation of Humidification of Earth on a Slope and Calculation of Its Safety Factor

This paper presents a mathematical model of the simultaneous processes of moisture, heat, and salt transfer in a porous medium, as well as a pattern of calculation of earth stability on a slope depending on the above factors and nonlinear dependences on them of the strength characteristics of the earth. The corresponding boundary-value problem has been solved by the method of radial basis functions. A comparison has been made between the results of numerical experiments showing the relationship between the change in the value of the safety factor and the position of the slip curve depending on the heat, salt, and moisture transfer.

42 ENGINEERING↗
DOE OSTI2020

Role of fast-ion transport manipulating safety factor profile in KSTAR early diverting discharges

Magnetohydrodynamics (MHD) activity is analyzed for a particular KSTAR discharge category, the main features of which are a high-$q_\mathrm{min}$ and a broad q profile. An interesting finding in this scenario is that a steady-state high-$q_\mathrm{min}$ and broad q profile has been constructed even without a strong off-axis current drive scheme. Time traces of magnetics spectrograms and electron cyclotron emission imaging (ECEI) clearly show that Alfvénic type MHD activity appears as a high-$q_\mathrm{min}$ and broad q profile is formed. Conversely, this activity disappears as the current profiles evolve toward a low-$q_\mathrm{min}$ profile. In this study, the effect of MHD modes and accompanying fast-particle transport on the formation of various current profiles is explored. The frequency patterns of the magnetics spectrograms and ECEI coherence are compared using a NOVA analysis to determine which series of Alfvénic modes are active. Then, the kick-model is applied to potential modes, and used to estimate how much fast-ions are transported and beam driven current profiles are varied. Here, by comparing the reconstructed total current profile from the kinetic EFIT with the beam-driven current profile estimated from the kick model, it is determined how energetic particle transport is responsible for maintaining the safety factor profile and which q profile can provide high β N operation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2019

Safety factor and turbulence dynamics dependence of the L-H power threshold on DIII-D

The L-H transition power threshold (PLH) is discovered to have a vital dependence on q 95 , at n e ~ 3.2 × 10 19 m -3 on DIII-D. Comprehensive 2D turbulence and flow measurements in the plasma edge reveal the co-existence of two frequency bands of broadband modes across the L-H transition with higher flow shear at higher q 95 , which can help explain the linear decrease in PLH as q 95 is increased from 3.5 to 4.9. Density fluctuation measurements by beam emission spectroscopy at higher q 95 show that the lower frequency band (<20 kHz) of the broadband modes propagates in the ion diamagnetic direction in the lab frame (identified as an ion mode), whereas the higher frequency band (>20 kHz) propagates in the electron diamagnetic direction (identified as an electron mode). The turbulence amplitude at the plasma edge is higher at higher q 95 , implying a higher drive for a Reynolds stress driven zonal flow. At lower density, n e ~ 1.5 × 10 19 m -3 , there is little dependence of PLH on q95. Linear CGYRO kinetic simulation has shown a switch from one mode to two modes at higher q 95 at n e ~ 3.2 × 10 19 m -3 compared to lower q 95 . The ion temperature profile has been shown to strongly impact the dual mode characteristics with the increasing growth rate of the ion mode at a higher edge Ti gradient. The observations imply that it may be possible to reduce the required input power to trigger the L-H transition for ITER if both the ion and electron modes are similarly driven in the plasma edge.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Non-disruptive error field measurement in DIII-D low safety factor plasmas and projection to ITER

Previous experiments in DIII-D (Paz-Soldan et al 2022 Nucl. Fusion 62 126007) introduced a method to identify intrinsic error fields (EFs) in tokamaks with minimal disruption risk by promptly healing driven magnetic islands during the conventional 'compass scan'. This paper presents recent experimental and numerical advancements in extending this approach to low q 95 plasmas, and projects its applicability to ITER. Non-disruptive EF measurement is achieved at q 95 = 4.5 and 3.9 without any initial EF correction (EFC) by reducing the time between the occurrence of the locked mode (LM) and control action to 10 ms and increasing the density 50%–100%. However, 50% correction of the intrinsic EF is required to achieve island healing at q 95 = 3.2 with 10 ms delay for the control action. Nonlinear two-fluid modeling with the TM1 code reproduces the DIII-D experimental observations, indicating that promptly turning off the 3D coil current reduces both magnetic island width and electromagnetic force, while raising the density increases plasma viscosity, facilitating magnetic island healing. The simulations show that for scenarios with q 95 = 3.2, lowering the control action time to 5 ms will lead to island healing without EFC. TM1 simulations are extended to future ITER scenarios with 5 MA and 7.5 MA plasma currents, predicting the dependence of required density rise on action time and EF amplitude. These simulations indicate that, benefiting from the much longer resistive time, island healing can be successfully achieved in ITER when taking control action 100–500 ms after a LM occurrence.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Model Development for the ACME Lab Modular Wall and A-Frame Assemblies

The structural frame used for conducting large structural tests was replaced by the ACME (Applied Combined Mechanical Environments) Lab in Building 860 of Sandia National Laboratories in Albuquerque, NM. This new design required simulation and analysis to verify maximum loads and corresponding factors of safety. Two major assemblies which are part of the ACME Lab, the Modular Wall and A-Frame, were designed to operate with a multitude of components in various configurations and with varying loads. Simulations of the Modular Wall and A-Frame structures were performed through explicit analysis to determine safety factors for numerous loading scenarios. The Modular Wall had safety factors of 1.1 for the lateral, diagonal, and gusset loading conditions. The A-Frame had safety factors of 2 for all loading conditions simulated.

42 ENGINEERING↗
DOE OSTI2018

A Statistical Approach to Safety Margin Evaluation of Irradiation Experiments in the ATR

The current safety basis of the INL Advanced Test Reactor requires that irradiation experiments meet minimum safety margins to critical heat flux and flow instability during anticipated reactor fault conditions. Compliance to these requirements may be demonstrated by calculating safety margins using safety factors that account for uncertainties, or using a statistical approach to quantify the uncertainty in the safety margins. Safety margins obtained from the first approach are conservative since the individual events leading to the cumulative safety factor are assumed to occur simultaneously at their maximum uncertainty. The statistical approach is less conservative in the case where the uncertainties are not too large, and may reduce the conservatism resulting from an overabundance of safety factors. This report describes the procedure for safety margin evaluation using a statistical approach and identifies the important thermal-hydraulic variables to consider in an uncertainty analysis. In particular, safety margins to critical heat flux and flow instability are evaluated for three recent high power fueled experiments (MP-1, FSP-1 and AFIP-6) using RELAP5 coupled to RAVEN to perform statistical analysis and uncertainty quantification. The results demonstrate adequate safety margins to critical heat flux and flow instability during an anticipated loss of commercial power to the reactor.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2023

Empirical probability and machine learning analysis of m , n = 2, 1 tearing mode onset parameter dependence in DIII-D H-mode scenarios

m, n = 2, 1 tearing mode onset empirical probability and machine learning analyses of a multiscenario DIII-D database of over 14 000 H-mode discharges show that the normalized plasma beta, the rotation profile, and the magnetic equilibrium shape have the strongest impact on the 2,1 tearing mode stability, in qualitative agreement with neoclassical tearing modes (m and n are the poloidal and toroidal mode numbers, respectively). In addition, 2,1 tearing modes are most likely to destabilize when n > 1 tearing modes are already present in the core plasma. The covariance matrix of tearing sensitive plasma parameters takes a nearly block-diagonal form, with the blocks incorporating thermodynamic, current and safety factor profile, separatrix shape, and plasma flow parameters, respectively. This suggests a number of paths to improved stability at fixed pressure and edge safety factor primarily by preserving a minimum of 1 kHz differential rotation, increasing the minimum safety factor above unity, using upper single null magnetic configuration, and reducing the core impurity radiation. In addition, lower triangularity, lower elongation, and lower pedestal pressure may also help to improve stability. Furthermore, the electron and ion temperature, collisionality, resistivity, internal inductance, and the parallel current gradient appear to only weakly correlate with the 2,1 tearing mode onsets in this database.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗