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All sourcesNASA NTRSDOE OSTI
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 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 NTRS1990

Tearing modes in solar coronal loops

It is shown that solar coronal-like magnetic loops, that is loops emerging from and reentering heavy plasma, are unstable to tearing modes. In particular, the previously made assumption of line tying to the heavy plasma, resulting in stabilization, is shown to be inapplicable because the growth rate is sub-Alfvenic in the entire loop, including the submerged part. In fact, it is shown that the tearing mode may grow faster than ordinarily surmised because the growth rate is determined by the average resistivity along an entire flux line rather than by the resistivity in the corona alone.

Hassam, A. B.↗
NASA NTRS1977

Nonlinear evolution of the collisionless tearing mode

For a broad k vector spectrum, the collisionless tearing mode grows linearly until the Landau electrons become magnetized by the wave field. The electrons then spatially diffuse as a result of turbulent magnetic-gradient drifts which leads to a nonlinearly enhanced growth rate. At large amplitudes the nonlinear growth rate is dominated by ions.

Coroniti, F. V.↗
NASA NTRS1994

Tearing mode instability in a multiple current sheet system

The tearing mode and magnetic reconnection are studied for multiple current sheet systems by two-dimensional magnetohydrodynamic (MHD) simulations. Both the linear and nonlinear evolution of this process are anaylsed for laminar perturbations. The results illustrate the existence of a linear regime with a symmetric and antisymmetric mode and agree with previous analytic results (Otto and Birk, 1992). The nonlinear evolution shows a number of interesting new features and may explain some properties in corresponding studies of turbulent reconnection. For wavelengths larger than twice the current sheet separation the evolution of antisymmetric modes leads to an entire reconfiguration of the magnetic field and converts a major portion of the magnetic energy into kinetic energy. Antisymmetric modes with smaller wavelengths and symmetric modes are found to saturate. The influence of the value of the resistivity on the reconnection rate decreases in the nonlinear evolution, and the ratio of current sheet separation to wavelength seems to be of major importance. A comparion of the dynamics of periodic current sheets with the evolution of only two current sheets indicates that some of the results for the periodic system also apply to the evolution of only two interacting current sheets. The results are discussed with respect to observations of large-scale plasma and magnetic field reconfigurations in the magnetosheath and near the Earth's bow shock.

Yan, M.↗
NASA NTRS1981

Tearing modes at the magnetopause

This paper examines the possible occurrence of tearing modes in the dayside magnetopause. First, the expected magnetic signature of tearing, as obtained from existing theory, is reviewed. Magnetometer data from one terrestrial magnetopause crossing of Jupiter's magnetopause are then examined in detail. Magnetic field oscillations are found in three subsegments of the terrestrial crossing at a frequency of 0.1-0.2 Hz and with peak amplitudes of 5-10 nanotesla (nT), and in one segment of the Jovian crossing, at 0.05-0.1 Hz and with 2-nT amplitude. The frequency range, as well as the orientation of the magnetic field perturbation vectors, agrees with a model in which tearing-produced magnetic islands are convected past the satellite with the plasma flow in the current layer. In both cases the magnetopause structure was of the rotational discontinuity type with a nonvanishing normal magnetic field component. Hence, if the tearing structures were active, i.e., growing, at the observation site, ion tearing (or perhaps resistive tearing, with the resistivity provided by microturbulence) must be invoked. But it is also possible that the structures were passive, consisting of 'debris' from active tearing elswhere on the magnetopause surface, this debris being convected along the magnetopause past the observation site.

Greenly, J. B.↗
NASA NTRS1990

Collisionless drift-tearing modes in the magnetopause

The linear stability properties of collisionless drift-tearing modes are analyzed in a modified Harris equilibrium model of the magnetopause. Particular attention is paid to the relevance of the parametric behavior of growth rates to the 'magnetic percolation' theory of flux transfer event formation (Galeev et al., 1986). Numerical methods are used to solve the drift-tearing eigenmode equations and the results are compared with those previously obtained by analytical methods. The analytical results are found to correctly model important parametric dependencies but to typically overestimate the rate of growth. The eigenmode equations are numerically difficult, and an integration scheme utilizing Ricatti transforms is developed to affect their solution.

Gladd, N. T.↗
DOE OSTI2025

Integrated modeling of advanced tokamaks for tearing mode avoidance on DIII-D

Understanding the physics of the onset and evolution of tearing modes (TMs) in tokamak plasmas is crucial for high-performance steady-state operations. The onset condition of (m,n) = (2,1) tearing stability, $Δ′$ > $Δ_c^′$> 0, has been studied in DIII-D steady-state hybrid discharges with accurate equilibrium reconstruction and well-measured plasma profiles. Here, m is the poloidal mode number and n is the toroidal mode number. The onset of n = 1 TMs is carefully identified using the Mirnov array to determine in-phase signals for the onset time and using electron cyclotron emission measurements to trace back from the saturated island width in the experiments for both initial island width and its growth rate. The tearing stability index $Δ′$ at TM onset is calculated in multiple ways, using the modified Rutherford equation and using the PEST-III or resistive DCON magnetohydrodynamic codes, and the results are in reasonable agreement with each other. The calculated $Δ′$ is compared with an analytical formula of the tearing stability threshold $Δ_c^′$ to determine the condition for the mode onset, $Δ′$ > $Δ_c^′$. Finally, the local gradient effect of the plasma current and the pressure profiles on the tearing stability is investigated in terms of the difference between $Δ′$ and $Δ_c^′$ through a series of modeled equilibria with the parametric variations. A database of experimental mode instability onsets is compatible with the simulated regions of instability obtained from the parametric variations.

Linear stability analysis↗
DOE OSTI2025

Large-scale tearing-mode hazard function analysis with standard matched equilibrium reconstructions

The association between features from standard tokamak equilibrium reconstructions and the onset of n = 1 tearing modes (TMs) is analyzed at scale. The TM onset rate is directly modeled with a ‘hazard’ function which gives the expected number of onsets (per unit time spent) in a given equilibrium parameter region. In particular the different statistical modeling performance achieved for magnetics-only reconstructions and motional Stark effect (MSE) enhanced reconstructions is studied. It is observed that a better hazard model for the TM onset rate can be built with the MSE-enhanced equilibria compared to the matched magnetics-only situation. This advantage disappears if internal profile details are withheld from the matched analysis. Plausibility of the hazard function is further demonstrated with visualizations of global trends in the operational space, and time-traces from specific tokamak discharges. As a result, TMs typically degrade tokamak plasma performance and may lead to plasma termination, motivating this statistical study.

equilibrium↗
DOE OSTI2024

Analysis of neoclassical tearing mode stabilization experiment by electron cyclotron injection in KSTAR

We report the neoclassical tearing mode (NTM) stabilization experimental results by injection of the electron cyclotron (EC) beam in KSTAR, and its analysis with integrated modelling. In the KSTAR experiment, NTM was intentionally induced and the EC beam was injected by the plasma control system (PCS) to stabilize it. Here, the EC angle was controlled based on the minimum seeking algorithm for the island growth rate. Although the EC angle was not changed significantly, the island width significantly decreased towards the end of the experiment followed by the recovery of plasma performance. To assess the NTM stabilization experiment from a stability perspective, we performed integrated modelling with TRIASSIC utilizing the reconstructed equilibrium with magnetic diagnostics and motional stark effect diagnostics. As a result, we observed that the NTM is stabilized by EC.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Calculation of tearing mode stability in an inverse aspect-ratio expanded tokamak plasma equilibrium

The tearing mode stability of an inverse aspect-ratio expanded tokamak plasma equilibrium of general shape is investigated using asymptotic matching techniques. Particular emphasis is placed on the conservation of toroidal electromagnetic angular momentum. The TJ code, which is a specific implementation of the results of the investigation, is described.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Predictions of m/n = 2/1 neoclassical tearing mode stabilization via high field side lower hybrid current drive on the DIII-D tokamak

Neoclassical tearing modes (NTMs) are a class of resistive instabilities that arise in tokamaks at rational surfaces and form magnetic islands. These islands flatten the pressure gradient, reducing plasma performance and may lead to disruptions if they grow large enough. Driving current within the island can stabilize the NTM, which has been achieved with electron cyclotron current drive (ECCD) on multiple devices. An alternative to ECCD is lower hybrid current drive (LHCD), which offers the advantages of increased current drive efficiency and reduced system cost. LHCD has been viewed as poorly suited for NTM suppression due to the large spatial extent of the driven current when in the multi-pass absorption regime (as has been the case in all past LHCD experiments). However, the driven current is more localized when in the single pass absorption regime, as is predicted for the DIII-D high field side (HFS) LHCD experiment. This work evaluates the feasibility of NTM suppression with HFS LHCD on DIII-D by predicting the island growth rate for a set of representative DIII-D plasmas via the modified Rutherford equation with and without the application of LHCD. In these plasmas, NTM suppression is achieved at reasonable power levels, even with finite misalignment between LH current and the island. The effect of current condensation was included and found to be most significant at smaller island sizes, assuming an experimentally typical temperature perturbation amplitude of 10%.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1983

Hall current effect on tearing mode instability

From a linear 2-D eigenmode analysis, it is found that the Hall current effect on collisional tearing mode instability becomes important for the thin magnetic reversal layer whose width is comparable to the ion inertia length; Hall currents produce a three-dimensional field structure and increase the reconnection (growth) rate. Since the magnetaic reversal layer widths both in the magnetopause and in the magnetotail are reported to become as thin as the ion inertial length (several hundred km) when the reconnection process is supposed to occur, the Hall current effect may explain the appearance of the dawn-dusk component of the magnetic field in the magnetotail reconnection region.

Terasawa, T.↗
DOE OSTI2026

Interpreting AI for fusion: An application to plasma profile analysis for tearing mode stability

Artificial intelligence models have demonstrated strong predictive capabilities for various instabilities in fusion devices such as Tokamaks, including tearing modes (TM), edge localized modes, and disruptive events, but their opaque nature raises concerns about safety and trustworthiness when applied to fusion power plants. Here, we present a physics-based interpretation framework using a TM prediction model as a demonstration that is validated through a dedicated DIII-D TM avoidance experiment. By applying Shapley analysis, we identify how profiles such as rotation, temperature, and density contribute to the model's prediction of TM stability. Our analysis shows that in our experimental scenario, core electron temperature and rotation peaking play the primary role in TM stability, while density changes have smaller effects on stability. We show that off-axis ion temperature stabilizes TMs, suggesting that off-axis neutral beam heating can further stabilize this scenario. This work presents a generalizable ML-based event prediction methodology, from training to physics-driven interpretation, bridging the gap between physics understanding and opaque ML models.

Farre-Kaga, Hiro J. [Princeton Univ., NJ (United S↗
NASA NTRS1993

Low-frequency mobility response functions for the central plasma sheet with application to tearing modes

Consideration is given to the effect of constant cross-tail magnetic field By on the collisionless conductivity produced by chaotic scattering and stochastic diffusion of particles in the current sheet for a parabolic geometry. It is shown that the correlation time scales as (By/Bz)-squared, and from this strong By scaling a strong tendency toward stabilization of the linear tearing modes with increasing values of By is inferred. This effect of increased dawn-dusk mobility is particularly dramatic when electrons are introduced in the calculation, and is in agreement with the results of kinetic particle simulations. The collisionless conductivity is expressed in terms of the ensemble-averaged power spectrum of the single particle trajectories, which makes it possible to calculate directly the linear conductivity instead of deriving it from the calculation of the irreversible heating rates.

Hernandez, J.↗
NASA NTRS1984

Nonlinear evolution of the resistive tearing mode

The nonlinear behavior of the tearing instability is investigated with the aid of numerical solutions of the resistive incompressible magnetohydrodynamic equations. This study is directed toward solar applications, such as flares. Simulations were carried out for values of the Lundquist number S from 100 to 1,000,000 and wavelength parameter alpha from 0.042 to 0.5. The influence of linear conditions, such as the constancy of psi, on nonlinear growth characteristics is investigated. For high S and low alpha, secondary-flow vortices, opposite in direction to the linear vortices, were found to generate a new magnetic island centered at the initial X point. The nonlinear spatial distributions of the physical variables differ greatly from the linear behavior, and growth slows considerably once nonlinear effects become important.

Steinolfson, R. S.↗
NASA NTRS1983

Energetics and the resistive tearing mode - Effects of Joule heating and radiation

The contribution of energy flux to the dynamics of magnetic field reconnection is analytically studied in order to determine the influence of Joule heating and radiation on the linear development of the tearing instability in slab geometry. A temperature-dependent Coulomb-like resistivity is used to provide the coupling between the dynamics and the energy equation. Analytical expressions are derived for the growth rates utilizing constant-psi and long-wavelength approximations. The solutions indicate the occurrence of several modes in addition to the usual tearing mode, several of which have relatively slow, complex growth rates. At large values of the magnetic Reynolds number, there are at least two modes with purely exponential growth when the radiative loss decreases with increasing temperature. If the radiation is neglected, the Joule heating alone also results in two modes with real, positive growth at large S. Below a particular value of S, all the modes are generally stabilized.

Steinolfson, R. S.↗
NASA NTRS1995

Investigation of spherical tearing mode

The purpose of this research was to better understand tearing and reconnection in genuinely three-dimensional configurations. We have identified an equilibrium model that should contain the required features. Three papers have been written and a fourth is in preparation. They are listed in the bibliography.

Greene, John M.↗