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DOE OSTI2020

Machine learning control for disruption and tearing mode avoidance

In this work, real-time feedback control based on machine learning algorithms (MLA) was successfully developed and tested on DIII-D plasmas to avoid tearing modes and disruptions while maximizing the plasma performance, which is measured by normalized plasma beta. Control uses MLAs that were trained with ensemble learning methods using only the data available to the real-time Plasma Control System (PCS) from several thousand DIII-D discharges. A `tearability' metric that quantifies the likelihood of the onset of 2/1 tearing modes (TM) in a given time window, and a 'disruptivity' metric that quantifies the likelihood of the onset of plasma disruptions were first tested o -line then implemented on the PCS. A real-time control system based on these MLAs was successfully tested on DIII-D discharges, using feedback algorithms to maximize β Ν while avoiding tearing modes and to dynamically adjust ramp down to avoid high-current disruptions in ramp down.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

Nonlinear coupling of tearing modes in reversed field pinch plasmas with stepped pressure profiles

A theory of the three-wave coupling of triplets of tearing modes in toroidal pinches [i.e., either reversed field pinches (RFPs) or tokamaks] was proposed by R. Fitzpatrick [Phys. Plasmas 6, 1168 (1999)]. However, this theory only applies to toroidal pinches with negligible equilibrium plasma pressure gradients. Such a limitation is particularly inappropriate to RFPs. This paper generalizes the analysis of R. Fitzpatrick [Phys. Plasmas 6, 1168 (1999)] in order to take the equilibrium pressure gradient into account. However, for the sake of simplicity, a stepped pressure profile, rather than a continuous profile, is employed. In the limit in which the number of steps becomes very large, the results obtained from the generalized theory are presumably equivalent to those that would have been achieved using a continuous pressure profile. The generalized theory is used to investigate the formation of the characteristic toroidally localized pattern of phase-locked m = 1 and m = 0 tearing modes in RFP plasmas that is known as the “slinky” pattern. The incorporation of the equilibrium plasma pressure into the analysis is found to be of crucial importance when determining the properties of the pattern. This is the case because the plasma pressure controls the number of unstable m = 1 and m = 0 tearing modes, and also significantly affects the strength of three-wave coupling, as well as the phase relation between the phase-locked m = 1 and m = 0 modes.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2026

Chaos as the cause of randomness in tearing mode onset times in DIII-D ITER baseline scenario plasmas

The first evidence of widespread chaotic plasma dynamics relevant to the onset of disruptive tearing modes is found in DIII-D tokamak discharges. This evidence is obtained by calculating positive maximal Lyapunov exponents from Mirnov signals using the Rosenstein algorithm, implying the chaotic growth and/or rotation of magnetohydrodynamic modes in DIII-D [Luxon, Nucl. Fusion 42, 614 (2002)] plasmas. Such chaotic dynamics offer an explanation for the random tearing mode onset times previously observed in ITER baseline scenario discharges. Further, the Lyapunov timescales associated with this chaos could inhibit reliable prediction of tearing mode onset beyond the angular momentum confinement timescale; this constraint should inform the design of plasma control systems on ITER.

Chaotic dynamics↗

DOE OSTI2021

Numerical investigation of active control of tearing mode by magnetic coils and the role of Δ'

Magnetic feedback stabilization of the tearing mode (TM) is numerically investigated, utilizing the MARS-F code (Liu et al 2000 Phys. Plasmas 7 3681) for toroidal tokamak equilibria. With control coil configurations assumed in this study, magnetic feedback partially or fully stabilizes the TM, with either vanishing or finite equilibrium pressure. The best control is achieved by the combination of internal active coils and internal poloidal sensors. The internal and external tearing indices are evaluated for the close-loop system, based on the MARS-F computed mode eigenvalue and eigenfunction, respectively. In the absence of the favorable curvature effect, these two indices are real-valued and quantitatively agree well with each other. For the equilibrium with finite pressure gradient at the mode rational surface, the favorable average curvature effect becomes important and the close-loop tearing index also becomes complex-valued, partly due to interaction of the feedback system with the dissipative wall eddy current response. Isolating the inner layer and outer region response to magnetic feedback, with either proportional or proportional-derivative actions, allows to establish that feedback stabilization of the TM occurs mainly due to modification of the behavior of the external ideal solution, further confirming the analytic result reported in He et al 2021 Phys. Plasmas 28 012504.

Physics↗

DOE OSTI2024

Tearing Stable Stationary ITER Baseline Operation in DIII-D

We present a tearing stable, stationary and reproducible operating solution for DIII-D plasmas characterized by the ITER Baseline Scenario normalized parameter set and shape. In these plasmas low differential rotation (Δf1,2) between the core and edge is identified as the single root cause of the onset of the primary limiting instability, the 2,1 Neoclassical Tearing Mode (NTM), while a group of other examined parameters have a much weaker impact on the stability. Explanation is offered by drift kinetic simulations, which show a six-fold reduction in the NTM onset threshold due to diminished stabilizing ion polarization currents when the seed island drift frequency ceases in the local plasma frame. Based on the experimental observation and the explanation provided by the theory, a new method is developed to sustain Δf1,2 by modifying the edge neoclassical potential through neutral gas fueling. This method enables stationary ITER baseline operation free of disruptive 2,1 tearing modes.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1978

Explosive tearing mode reconnection in the magnetospheric tail

A speculative model for the nonlinear phase of the collisionless tearing instability is developed for the case of a single long wavelength tearing mode. Using an energy principle formalism, we find that the nonlinear growth rate is linearly proportional to the mode amplitude. Hence in the nonlinear phase, the tearing mode grows explosively in time, and saturates when the width of the magnetic islands become comparable to the thickness of the current sheet. For typical plasma sheet parameters, the explosive phase lasts 5-10 minutes, and develops cross-tail emf's of several 100 KV.

Galeev, A. A.↗

NASA NTRS1979

The energetics of resistive magnetic tearing

A new treatment of the energetics of resistive magnetic tearing is presented. This instability is the only known field-reconnection mechanism which develops in time, and is thus a primary candidate for a number of astrophysical 'flare' processes occurring in stressed magnetic fields. The tearing process is elucidated by a subdivision into magnetic regions of different characteristics: first, as dominated by resistive or highly conductive dynamics, and then by function as a source or sink of the energy flux. Matching conditions between these zones provide a determination of the growth rate and its physical-parameter dependence. The observable plasma energy outputs, due mainly to two distinct magnetically driven acceleration mechanisms, are estimated and their directive spatial properties shown. Finally, the generality of resistive tearing is demonstrated by an application of the previous considerations to realistic sheared-field configurations, including the case of a solar coronal loop, for which flare-instability thresholds and energy-deposition sites are described.

Van Hoven, G.↗

NASA NTRS1980

On the tearing mode in quasi-neutral sheets

The paper examines the stability of the tearing mode in a quasi-neutral sheet which contains electron pitch angle scattering wave turbulence (or collisions). It is found that the pitch angle scattering dissipation destabilizes the tearing mode and that the tearing growth rate is proportional to the pitch angle diffusion coefficient. The results are discussed with reference to theories of the plasma sheet.

Coroniti, F. V.↗

NASA NTRS1983

The effects of Ohmic heating and stable radiation on magnetic tearing

A study is made of the effect of a temperature-dependent Coulomb-like resistivity on the planar tearing mode. The local evolution of the temperature is described by an energy equation which includes Joule heating and optically thin radiation. The resulting system of coupled linear magnetohydrodynamic equations is solved numerically, and eigenfunctions and growth rates are obtained. In the absence of radiation, there are two distinct solutions above a critical value of the magnetic Reynolds number S, a tearing-like mode and a Joule-heating mode. Below this point, the growth rates coalesce into a conjugate-complex pair. When stable radiation (dR/dT greater than 0) is added, the heating mode disappears and a modified tearing excitation exists to much lower values of S before its growth is cut off by Ohmic heating. Examples are given for solar coronal parameters, and for those characteristic of fusion-research devices. The introduction of an effective value for the resistivity, in the presence of energy transport, allows a simple qualitative discussion of the different modes.

Tachi, T.↗

NASA NTRS1984

Nonlinear evolution of magnetopause tearing modes

Since the magnetosheath plasma is highly turbulent, reconnection at the dayside magnetopause is likely to be temporally unsteady. The tearing mode can be viewed as a model for the unsteady development of a reconnecting magnetic topology. Magnetopause tearing occurs in the guide-field limit and has a wave packet spatial structure in the east-west direction. This paper solves for the nonlinear evolution of a single wavelength guide-field tearing mode including the effects of finite transit time on the Landau resonant electrons. Short wavelength modes evolve algebraically in time with perturbation amplitudes proportional to t-squared. Long wavelength modes are fully nonlinear, and the amplitude grows linearly in time.

Coroniti, F. V.↗

NASA NTRS1984

Radiative tearing - Magnetic reconnection on a fast thermal-instability time scale

Two energy modification mechanisms which are known to occur in sheared magnetic fields are the tearing and thermal instabilities. These processes can be studied separately with formalisms incorporating just the effective driving mechanism of interest (finite resistivity for the tearing mode and unstable radiation for the thermal mode). A model which includes both effects, and a temperature-dependent resistivity, indicates that modified forms of these two instabilities may coexist for identical physical conditions. When they are isolated computationally, one can show that their limiting growth rates are approximately those of the uncoupled instabilities. The spatial structure and energy content of these two new hybrid processes are then individually examined and are found to differ considerably from those obtained from separate treatments of the driving mechanisms. The faster radiative instability, which has a hydromagnetically scaled growth rate like the condensation mode of the thermal instability, is shown to involve a substantial amount of magnetic field reconnection. This can be partially explained by a large temperature drop (or resistivity rise) at the X-point. The island width of the Coulomb-coupled radiative mode is 30 percent of that produced by a comparable level of the slower tearing instability. In addition, the perturbed magnetic energy in the radiative instability is 5 times that of the perturbed thermal energy, indicating an appreciable modification of the initial magnetic structure.

Steinolfson, R. S.↗

NASA NTRS1984

The nonlinear tearing mode

A series of nonlinear computations of tearing-mode development have been performed which achieve higher values of the magnetic Reynolds number and larger wavelengths than previously considered. A prime candidate for the realization of dynamic reconnection is the resistive magnetic tearing mode, a spontaneous instability of a stressed magnetic field. Typical simulations are described for a magnetic Lundquist number S of 10 to the 4th and wavelength parameters alpha from 0.05 to 0.5. In all cases, the nonlinear mode initially evolves at the linear growth rate, followed by a period of reduced growth. Another common feature is the formation of secondary flow vortices, near the tearing surface, which are opposite in direction to the initial linear vortices.

Van Hoven, G.↗

NASA NTRS1986

Polyimide Film of Increased Tear Strength

High-temperature linear aromatic polyimide with improved resistance to tearing made by new process that incorporates elastomer into polyimide. Linear aromatic condensation polyimides are materials of prime choice for use as films and coatings on advanced spacecraft and aircraft where durability at temperatures in range of 200 to 300 degree C required. Elastomer-containing polyimide film with improved toughness proves useful for applications where resistance to tearing and long-term thermal stability necessary. Desired resistance to tearing achieved by careful control of amount and chemical composition of added elastomer.

St. Clair, A. K.↗

NASA NTRS1991

Does ion tearing exist?

Theoretical models of reconnection in the geomagnetic tail and its relationship to the collisionless tearing mode are examined analytically. The focus is on attempts to remove the stabilizing effects of electron compressibility in the quasi-neutral sheet. It is shown that this goal can be achieved by introducing spatial diffusion of electrons across the magnetic-flux surfaces, but not by wave-turbulent pitch-angle scattering (Coroniti, 1980) or nonadiabatic stochastic first-invariant diffusion (Buechner and Zelenyi, 1988). Hence the ion tearing mode does not exist, but the electron tearing mode does.

Pellat, R.↗

NASA NTRS1993

Nonlinear evolution of resistive tearing mode instability with shear flow and viscosity

The effect of shear flow on the nonlinear evolution of the tearing mode is investigated via numerical solutions of the resistive MHD equations in slab geometry, using a finite-difference alternative-direction implicit method. It was found that, when the shear flow is small (V less than 0.3), the tearing mode saturates within one resistive time, whereas for larger flows the nonlinear saturation develops on longer time scales. The magnetic energy release decreases and the saturation time increases with increasing values of V for both small and large resistivity. Shear flow was found to decrease the saturated magnetic island width and to generate currents far from the tearing layer. Results suggest that equilibrium shear flow may improve the confinement of tokamak plasma.

Ofman, L.↗

NASA NTRS1993

Crack-tip-opening angle measurements and crack tunneling under stable tearing in thin sheet 2024-T3 aluminum alloy

The stable tearing behavior of thin sheets 2024-T3 aluminum alloy was studied for middle crack tension specimens having initial cracks that were: flat cracks (low fatigue stress) and 45 degrees through-thickness slant cracks (high fatigue stress). The critical crack-tip-opening angle (CTOA) values during stable tearing were measured by two independent methods, optical microscopy and digital image correlation. Results from the two methods agreed well. The CTOA measurements and observations of the fracture surfaces showed that the initial stable tearing behavior of low and high fatigue stress tests is significantly different. The cracks in the low fatigue stress tests underwent a transition from flat-to-slant crack growth, during which the CTOA values were high and significant crack tunneling occurred. After crack growth equal to about the thickness, CTOA reached a constant value of 6 deg and after crack growth equal to about twice the thickness, crack tunneling stabilized. The initial high CTOA values, in the low fatigue crack tests, coincided with large three-dimensional crack front shape changes due to a variation in the through-thickness crack tip constraint. The cracks in the high fatigue stress tests reach the same constant CTOA value after crack growth equal to about the thickness, but produced only a slightly higher CTOA value during initial crack growth. For crack growth on the 45 degree slant, the crack front and local field variables are still highly three-dimensional. However, the constant CTOA values and stable crack front shape may allow the process to be approximated with two-dimensional models.

Dawicke, D. S.↗

NASA NTRS1998

Buckling and Stable Tearing Responses of Unstiffened Aluminum Shells with Long Cracks

The results of an analytical and experimental study of the nonlinear response of thin, unstiffened, aluminum cylindrical shells with a long longitudinal crack are presented. The shells are analyzed with a nonlinear shell analysis code that accurately accounts for global and local structural response phenomena. Results are presented for internal pressure and for axial compression loads. The effect of initial crack length on the initiation of stable tearing and unstable crack growth in typical shells subjected to internal pressure loads is predicted using geo- metrically nonlinear elastic-plastic finite element analyses. The results of these analyses and of the experiments indicate that the pressure required to initiate stable tearing and unstable tearing in a shell subjected to internal pressure loads decreases as the crack length increases. The effects of crack length on the prebuckling, buckling and postbuckling responses of typical shells subjected to axial compression are also described. For this loading condition, the crack length is held constant. The results of the analyses illustrate the influence of crack length on shell buckling instabilities. The experimental and analytical results correlate well.

Starnes, James H., Jr.↗

NASA NTRS2021

Magnetic Reconnection in a Sheared Magnetic Flux Tube: Slippage Versus Tearing

The process of magnetic reconnection in a flux tube can occur in a time-stationary fashion as slippage reconnection or in a time-dependent manner based on, for example, the tearing instability. However, it is not well known under which conditions a system can sustain slippage reconnection. Likewise, it is unclear whether systems can exhibit slippage reconnection and time-dependent reconnection simultaneously. In order to investigate these questions, we employ a set of 3D magnetohydrodynamic simulation. Using these simulations, we model a twisted flux tube with a spatially localized resistive region in the center of the simulation box, and an applied driver on one end plane of the simulation box. As a result, the Poynting flux injected at the boundary propagates to the resistive region and dissipates there. If the driver is nearly circular, we find a predominance of slippage reconnection, which decouples the applied driver entirely from one half of the flux tube. Second, a tearing-like instability occurs with slippage reconnection in the resistive region when the resistivity is strong enough and the cross section of the flux tube, as defined by the shape of the applied velocity perturbation, is elliptical enough. In this case we find the surprising feature that magnetic field perturbation generated by the tearing-like instability radiates away from the resistive region to influence the entire flux tube shape.

Hidetaka Kuniyoshi↗