Resistive Interchange Instability Research Articles

Resistive instabilities in toroidal anisotropic plasmas

Resistive singular layer equations are developed by applying the magnetohydrodynamic (MHD) model to toroidal anisotropic plasmas. This work extends the previous ideal MHD theory [Shi et al. Phys. Plasmas 23, 082121 (2016)] to the resistive case. These layer equations can be used to investigate resistive localized MHD instabilities, such as tearing instability and resistive interchange instability. Compared to existing resistive theory [Johnson and Hastie, Phys. Fluids 31, 1609 (1988)], our model includes plasma compressibility, allowing for a study of the coupling between parallel motion to perpendicular one, which is known as the apparent mass effect. In addition, these obtained equations are valid for low n modes, where n is the toroidal mode number. The dispersion relation is derived in a reduced model. We find that the anisotropic pressure effect (when p⊥ > p‖) not only increases the stable threshold of the resistive interchange mode but also raises the critical value Δc of the tearing mode stability index Δ′, which represents the logarithmic jump of the radial magnetic field perturbation across the rational surface. This discovery holds significant practical implications for mitigating neoclassical tearing modes in high confinement plasmas, particularly those characterized by a low aspect ratio (such as spherical tokamaks) or low magnetic shear (as designed in ITER hybrid scenarios). However, it enhances the growth rate of the tearing mode in a low growth rate region, where p‖ and p⊥ denote the pressure components parallel and perpendicular to the magnetic fields, respectively.

Suppression of resistive interchange instability by external RMP

We experimentally investigate the effect of external resonant magnetic perturbation (RMP) on resistive interchange MHD instability which is typically observed in the Large Helical Device. We apply the m/n = 1/1 external RMP to discharges with the m/n = 1/1 interchange instability. We find that the electron density fluctuation as well as the magnetic field one is clearly reduced without a reduction of the pressure gradient by imposing the external RMP. Moreover, the achieved beta value as well as the beta gradient at the resonant surface is a little improved under certain conditions. Next, we investigate the responses of interchange instability to the external RMP under some different operational conditions. We find that the amplitude of the external RMP to completely suppress the instability with the shielding of the external RMP has a higher correlation with the volume-averaged beta value than other plasma parameters.

Approaching the investigation of plasma turbulence through a rigorous verification and validation procedure: A practical examplea)

In the present work, a Verification and Validation procedure is presented and applied showing, through a practical example, how it can contribute to advancing our physics understanding of plasma turbulence. Bridging the gap between plasma physics and other scientific domains, in particular, the computational fluid dynamics community, a rigorous methodology for the verification of a plasma simulation code is presented, based on the method of manufactured solutions. This methodology assesses that the model equations are correctly solved, within the order of accuracy of the numerical scheme. The technique to carry out a solution verification is described to provide a rigorous estimate of the uncertainty affecting the numerical results. A methodology for plasma turbulence code validation is also discussed, focusing on quantitative assessment of the agreement between experiments and simulations. The Verification and Validation methodology is then applied to the study of plasma turbulence in the basic plasma physics experiment TORPEX [Fasoli et al., Phys. Plasmas 13, 055902 (2006)], considering both two-dimensional and three-dimensional simulations carried out with the GBS code [Ricci et al., Plasma Phys. Controlled Fusion 54, 124047 (2012)]. The validation procedure allows progress in the understanding of the turbulent dynamics in TORPEX, by pinpointing the presence of a turbulent regime transition, due to the competition between the resistive and ideal interchange instabilities.

Characteristics of magnetic island formation due to resistive interchange instability in helical plasma

Focusing attention on the magnetic island formation, we investigate the characteristics of the resistive interchange magnetohydrodynamics instabilities, which would limit a high beta operational regime in helical type fusion reactors. An introduction of a new index, i.e., the ratio of the magnetic fluctuation level to the radial displacement, enables us to make a systematic analysis on the magnetic island formation in the large helical device-like plasmas during the linear growth phase; (i) the interchange instability with the second largest growth rate makes the magnetic island larger than that with the largest growth rate when the amplitude of the radial displacement in both cases is almost the same as each other; (ii) applied to a typical tearing instability, the index is smaller than that for the interchange instability with the second largest growth rate.

Analysis Method for the Low-Order Resistive Interchange Instability in LHD with Stochastic Magnetic Field Line Structure

Analysis Method for the Low-Order Resistive Interchange Instability in LHD with Stochastic Magnetic Field Line Structure

Rotation of Interchange Instability in the Large Helical Device

The rotation of resistive interchange instabilities excited in the periphery of plasmas compared to plasma flows under various plasma conditions in the Large Helical Device. The observed magnetohydrodynamic modes exhibit nominal rotation in the electron diamagnetic direction in the laboratory frame. We assumed that the ion (electron) flows consist of the E × B and ion (electron) diamagnetic drift flows. These drift flows were individually evaluated and geometrically compensated using a finite beta equilibrium. Experiments with different neutral beam injection conditions and different electron densities show that the frequencies of the observed modes were quantitatively consistent with those of the electron flow. c

Pressure-driven, resistive magnetohydrodynamic interchange instabilities in laser-produced high-energy-density plasmas

Recent experiments using proton backlighting of laser-foil interactions provide unique opportunities for studying magnetized plasma instabilities in laser-produced high-energy-density plasmas. Time-gated proton radiograph images indicate that the outer structure of a magnetic field entrained in a hemispherical plasma bubble becomes distinctly asymmetric after the laser turns off. It is shown that this asymmetry is a consequence of pressure-driven, resistive magnetohydrodynamic (MHD) interchange instabilities. In contrast to the predictions made by ideal MHD theory, the increasing plasma resistivity after laser turn-off allows for greater low-mode destabilization (m>1) from reduced stabilization by field-line bending. For laser-generated plasmas presented herein, a mode-number cutoff for stabilization of perturbations with m> approximately [8pibeta(1+D_{m}k_{ perpendicular};{2}gamma_{max};{-1})];{1/2} is found in the linear growth regime. The growth is measured and is found to be in reasonable agreement with model predictions.

MHD study of the reactor-relevant high-beta regime in the Large Helical Device

In the Large Helical Device, the volume averaged beta value ⟨βdia⟩ of 5%, which is the highest value in all heliotron/stellarators and relevant to the reactor requirement, was achieved by optimizing the magnetic configuration from the viewpoint of magneto-hydrodynamic (MHD) characteristics, transport and heating efficiency of the neutral beam. This beta value was instantaneously obtained by pellet injection and maintained for more than 10τE, whereas the steady-state plasma with a maximum ⟨βdia⟩ of 4.8% was sustained for 85τE by gas-puff fueling. While it is theoretically predicted that stochastization of the peripheral magnetic field structure develops with an increment of ⟨βdia⟩, no serious degradation of the global confinement has been observed in the present ⟨βdia⟩ range. The several low-order MHD activities located in the periphery were enhanced with the beta value and sometimes affect the local profiles. The amplitude of the mode in the periphery strongly depends on the magnetic Reynolds number, which is close to that of the growth rate and/or the radial mode width of the resistive interchange instability.

Magnetoconvection in sheared magnetic fields

The development of magnetoconvection in a sheared magnetic field is investigated. The equilibrium magnetic field B0 is horizontal and its orientation varies linearly along the vertical axis. Preliminary consideration of the transition from the inertial to the viscous regime of the gravitational resistive interchange instability, reveals that the latter is characterized by the existence of viscoresistive boundary layers of vertical width which scales as Q−1∕6, where Q is the Chandrasekhar number. The situation is analogous to the one encountered in magnetically confined laboratory plasmas, where convective flows are constrained by the magnetic shear to develop in boundary layers located around resonant magnetic surfaces in order to fulfill the “interchange condition” k⋅B0=0, where k is the wave vector of the magnetic perturbation. It follows that when the effect of thermal diffusion is taken into account in the process, convection can only occur above a certain critical value of the Rayleigh number which scales as Q2∕3 for large Q. At the onset, the convection pattern is a superposition of identically thin convective rolls everywhere aligned with the local magnetic field lines and which therefore adopt the magnetic field geometry, a situation also reminiscent of the penumbra of sunspots. Using this degeneracy, equations describing the weakly nonlinear state are obtained and discussed. A reduced magnetohydrodynamic description of magnetoconvection is introduced. Since it is valid for arbitrary magnetic field configurations, it allows a simple extension to the case where there exists an inclination between the direction of gravity and the plane spanned by the equilibrium magnetic field. These reduced magnetohydrodynamic equations are proposed as a powerful tool for further investigations of magnetoconvection in more complex field line geometries.

Critical transition for the edge shear layer formation: Comparison of model and experiment

The experimental results for the emergence of the plasma edge shear flow layer in TJ-II [C. Alehaldre et al.Fusion Technol. 17, 131 (1990)] can be explained using a simple model for a second-order transition based on the sheared flow amplification by Reynolds stress and turbulence suppression by shearing. In the dynamics of the model, the resistive interchange instability is used. This model gives power dependence on density gradients before and after the transition, consistent with experiment.

Theory and Simulation Basis for Magnetohydrodynamic Stability in DIII-D

Theory and simulation have provided one of the critical foundations for many of the significant achievements in magnetohydrodynamic (MHD) stability in DIII-D over the past two decades. Early signature achievements included the validation of tokamak MHD stability limits, beta and performance optimization through cross-section shaping and profiles, and the development of new operational regimes. More recent accomplishments encompass the realization and sustainment of wall stabilization using plasma rotation and active feedback, a new understanding of edge stability and its relation to edge-localized modes, and recent successes in predicting resistive tearing and interchange instabilities. The key to success has been the synergistic tie between the theory effort and the experiment made possible by the detailed equilibrium reconstruction data available in DIII-D and the corresponding attention to the measured details in the modeling. This interaction fosters an emphasis on the important phenomena and leads to testable theoretical predictions. Also important is the application of a range of analytic and simulation techniques, coupled with a program of numerical tool development. The result is a comprehensive integrated approach to fusion science and improving the tokamak approach to burning plasmas.

Study of Type III ELMs in JET

This paper presents the results of JET experiments aimed at studying the operational space of plasmas with a Type III ELMy edge, in terms of both local and global plasma parameters. In JET, the Type III ELMy regime has a wide operational space in the pedestal ne – Te diagram, and Type III ELMs are observed in standard ELMy H-modes as well as in plasmas with an internal transport barrier (ITB). The transition from an H-mode with Type III ELMs to a steady state Type I ELMy H-mode requires a minimum loss power, PTypeI. PTypeI decreases with increasing plasma triangularity. In the pedestal ne – Te diagram, the critical pedestal temperature for the transition to Type I ELMs is found to be inversely proportional to the pedestal density (Tcrit ∝ 1/n) at a low density. In contrast, at a high density, Tcrit, does not depend strongly on density. In the density range where Tcrit ∝ 1/n, the critical power required for the transition to Type I ELMs decreases with increasing density. Experimental results are presented suggesting a common mechanism for Type III ELMs at low and high collisionality. A single model for the critical temperature for the transition from Type III to Type I ELMs, based on the resistive interchange instability with magnetic flutter, fits well the density and toroidal field dependence of the JET experimental data. On the other hand, this model fails to describe the variation of the Type III ne – Te operational space with isotopic mass and q95. Other results are instead suggestive of a different physics for Type III ELMs. At low collisionality, plasma current ramp experiments indicate a role of the edge current in determining the transition from Type III to Type I ELMs, while at high collisionality, a model based on resistive ballooning instability well reproduces, in term of a critical density, the experimentally observed q95 dependence of the transition from Type I to Type III ELMs. Experimental evidence common to Type III ELMs in standard ELMy H-modes and in plasmas with ITBs indicates that they are driven by the same instability.

Physics of the L-H Transition and Type III-ELMs Phenomena (Scaling Properties and Dimensionless Analysis)

The stability theory of Alfven drift-waves shows that with increasing plasma pressure electron drift waves become strongly coupled with Alfven waves thus damping radial perturbations. The Alfven drift turbulence suppression at the plasma edge was suggested as a triggering mechanism for the L to H transition [1]. After the transition the resistive interchange in-stability emerges as a dominant phenomenon which reveals itself in the form of Type III ELMs. Magnetic flutter provides the resistive driver for the interchange instability and, together with the stability condition caused by the electric shear stabilisation, creates the right dependence of the marginal temperature on density and other plasma parameters seen in experiments.

Ideal and resistive interchange instabilities in negative shear tokamaks and currentless heliotron plasmas

For tokamaks the ideal localized interchange mode does not play a role for cases of q (safety factor) >1 over the whole plasma region, whereas in heliotron plasmas the mode becomes unstable in the edge region owing to the magnetic hill. However, for negative shear tokamaks, the resistive localized interchange mode becomes unstable where q0 is much larger than qmin, where q0 (qmin) is the central (minimum) q value. With the appropriate ellipticity and triangularity the stability against the resistive interchange mode is significantly improved. It is also shown that ideal and resistive non-resonant global interchange modes appear easily in the central region of heliotrons and in negative shear tokamaks; the modes are similar to the infernal mode in low shear tokamaks.

Characterization of coherent structures in tokamak edge turbulence.

A statistical test for extracting and identifying coherent structures in the scrape-off layer turbulence is used to analyze Langmuir probe data from the ADITYA and ASDEX tokamaks. This method, the biorthogonal decomposition, allows one to characterize large-scale coherent structures in plasma turbulence in an unambiguous manner. It is shown that such structures effectively contribute to radial transport and to intermittency. Results from numerical simulations of turbulence driven by the resistive interchange instability in the scrape-off layer are compared to the observed statistical properties.

Characteristics of Electron Density Fluctuations in Heliotron E Measured Using a Wide Beam Laser Phase Contrast Method

Electron density fluctuations in Heliotron E were measured using a wide beam laser phase contrast method in a frequency range of 2.5≤ f ≤500 kHz and a wavenumber range of 0.1 ≤ k ≤1.3 rad/mm. Two branches of S ( k , f ) spectra were detected, which we have called a high speed branch and a low speed branch because of a difference in their measured phase velocities. Their characteristics were studied from spatial distributions, correlation with magnetic fluctuations, phase velocities, fluctuation levels and theoretical considerations. The high speed branch is consistent with a Magneto Hydro Dynamic (MHD) mode driven by a resistive interchange instability and mainly existed inside the limiter, and the low speed branch is explained as a microturbulence driven by a drift instability and mainly existed outside the limiter. The implications of these findings for studies of plasma confinement in Heliotron E are discussed.

Effect of a poloidal shear flow on the probability of accessing the multiple saturated states in the resistive interchange instability

A systematic study based on 400 nonlinear single-helicity calculations with random initial perturbations shows that multiple nonlinear states exist at saturation. They are characterized by different values of the poloidal wave number of the dominant mode in the spectrum. As a consequence, the saturated states have different levels of fluctuations and different self-consistent poloidal flow profiles. The presence of an external shear poloidal flow does not always directly change the saturation level of the fluctuations. For low shear flows, it can increase the probability of accessing the high saturated levels. For very high values of the flow shear, however, there is suppression of the fluctuations. A curvature poloidal flow reduces the saturation level of each state and increases the probability of accessing the low fluctuation levels. Transitions between saturated states accompanied by sudden changes in flow profile have been observed. Most of the observed transitions are from a low to a high level of fluctuations.

Beta-limiting phenomena due to global resistive interchange mode in high-aspect-ratio torsatron/heliotron

Evolutions of the local pressure gradient and the amplitude of the global resistive interchange instability are studied in torsatron/heliotron plasmas. (Torsatron/heliotron: the high-aspect-ratio toroidal helical plasma with magnetic shear and magnetic hill.) Coupled equations for the background pressure profile and a single helical mode are derived by keeping the effects of the thermal transport and ion viscosity. Three characteristic dynamic evolutions are identified; monotonic saturation relaxation oscillation and periodic limit cycle solution. As the heating power is increased, the dynamic evolution changes from monotonic saturation, to relaxation oscillation and finally to the limit cycle. The time average of the pressure gradient is limited by the critical gradient against the linear stability. Dependences of the amplitude and period of the sawtooth oscillation on the heating power are also analysed.

Effects of magnetic geometry, fluctuations, and electric fields on confinement in the Advanced Toroidal Facility

Recent experiments in the Advanced Toroidal Facility (ATF) [Fusion Technol. 10, 179 (1986)] have been directed toward investigations of the basic physics mechanisms that control confinement in this device. Measurements of the density fluctuations throughout the plasma volume have provided indications for the existence of theoretically predicted dissipative trapped electron and resistive interchange instabilities. These identifications are supported by results of dynamic configuration scans of the magnetic fields during which the magnetic well volume, shear, and fraction of confined trapped particles are changed continuously. The influence of magnetic islands on the global confinement has been studied by deliberately applying error fields which strongly perturb the nested flux-surface geometry, and the effects of electric fields have been investigated by means of biased limiter experiments.

Instabilities and vortex dynamics in shear flow of magnetized plasmas

Gradient-driven instabilities and the subsequent nonlinear evolution of generated vortices in sheared E×B flows are investigated for magnetized plasmas with and without gravity (magnetic curvature) and magnetic shear by using theory and implicit particle simulations. In the linear eigenmode analysis, the instabilities considered are the Kelvin–Helmholtz (K–H) instability and the resistive interchange instability. The presence of the shear flow can stabilize these instabilities. The dynamics of the K–H instability and the vortex dynamics can be uniformly described by the initial flow pattern with a vorticity localization parameter ε. The observed growth of the K–H modes is exponential in time for linearly unstable modes, secular for the marginal mode, and absent until driven nonlinearly for linearly stable modes. The distance between two vortex centers experiences rapid merging while the angle θ between the axis of the vortices and the external shear flow increases. These vortices proceed toward their overall coalescence, while shedding small-scale vortices and waves. The main features of vortex dynamics, the nonlinear coalescence and the tilt or the rotational instabilities of vortices, are shown to be given by using a low-dimension Hamiltonian representation for interacting vortex cores in the shear flow.