Resistive Ballooning Modes Research Articles

Predictive modeling of NSTX discharges with the updated multi-mode anomalous transport module

The objective of this study is twofold: firstly, to demonstrate the consistency between the anomalous transport results produced by updated Multi-Mode Model (MMM) version 9.0.4 and those obtained through gyrokinetic simulations; and secondly, to showcase MMM’s ability to predict electron and ion temperature profiles in low aspect ratio, high beta NSTX discharges. MMM encompasses a range of transport mechanisms driven by electron and ion temperature gradients, trapped electrons, kinetic ballooning, peeling, microtearing, and drift resistive inertial ballooning modes. These modes within MMM are being verified through corresponding gyrokinetic results. The modes that potentially contribute to ion thermal transport are stable in MMM, aligning with both experimental data and findings from linear CGYRO simulations. The isotope effects on these modes are also studied and higher mass is found to be stabilizing, consistent with the experimental trend. The electron thermal power across the flux surface is computed within MMM and compared to experimental measurements and nonlinear CGYRO simulation results. Specifically, the electron temperature gradient modes (ETGM) within MMM account for 2.0 MW of thermal power, consistent with experimental findings. It is noteworthy that the ETGM model requires approximately 5.0 ms of computation time on a standard desktop, while nonlinear CGYRO simulations necessitate 8.0 h on 8 K cores. MMM proves to be highly computationally efficient, a crucial attribute for various applications, including real-time control, tokamak scenario optimization, and uncertainty quantification of experimental data.

Finite pedestal width formation from early L-H transition stage with a strong edge safety-factor dependence through the resistive ballooning mode

An approximate modeling of the low- to high-confinement (L-H) transition dynamics is given using the method, similar to that by Hinton et al. [Phys. Fluid B 5, 1281 (1993)], but considering more explicitly the L-mode edge turbulence which is here assumed to be dominated by the resistive ballooning mode (RBM) near the separatrix, while the ion temperature gradient (ITG) mode in the inner edge–core region. It is shown that the L-H transition can then be initiated from an inner edge near the ITG-RBM transition point with a finite width. Especially, this width is found to have a strong edge safety-factor or poloidal field dependence, similar to that shown by the EPED1 model. Meanwhile, unlike the pedestal width, the H-mode threshold power appears to be much less sensitive to the edge safety-factor, in qualitative agreement with the observed weak dependence of the threshold power on plasma current (IP). From an additional brief check, these dependences on IP are also found to be quite different from the behavior of other parameters (ion mass, toroidal field, plasma density, and effective Z-number) where the threshold power depends relatively strongly while the initial width depends somewhat weakly on most of them, except the effective Z-number.

Experimental characterization of the quasi-coherent mode in EDA H-Mode and QCE scenarios at ASDEX Upgrade

The quasi-coherent mode (QCM), appearing in enhanced D α high confinement mode (EDA H-mode) and quasi-continuous exhaust (QCE) plasmas has been analysed in detail at ASDEX Upgrade via thermal helium beam spectroscopy under various discharge parameters. In both scenarios the QCM appears to be localized close to the separatrix and to propagate in ion diamagnetic direction in the plasma frame. The poloidal wavenumber of the QCM is about 0.025<kθρs<0.075 and the radial wavenumber is kr≈0 cm−1 . It was found that the plasmas are generally below the ideal MHD limit at the separatrix. All the properties are consistent with ideal, resistive or kinetic ballooning modes. Simultaneous to the appearance of the QCM, higher harmonic modes can be observed in EDA H-modes, which are exclusively visible in magnetic pick-up coils and have toroidal mode numbers of up to n = 10. By performing a bicoherence analysis it was found that the higher harmonic modes and the QCM are coupling, but are disjoint phenomena. Qualitatively, the bandwidth of the QCM serves as a promising distinctive feature between QCE plasmas and EDA H-modes.

Impact of toroidal rotation on the resistive ballooning modes in ASDEX Upgrade tokamak

In this work, we investigate the behavior of instabilities appearing between type-I edge localized modes (ELMs), with increasing neutral beam injection (NBI) power concomitant increase in toroidal rotation, and compare it to the modeling result of the linear magneto-hydrodynamic (MHD) code CASTOR3D. An injection of one NBI beam, increasing toroidal rotation, results in the mode slowing down from 12 kHz to 7 kHz, and its associated radial displacement decreases from 5 mm to 3.5 mm. In addition, modes shift radially outwards towards higher q, decreasing their poloidal mode numbers. The mode velocity is measured to be close to the E × B velocity with significant uncertainties. Through a set of CASTOR3D simulations with varying profiles, resistivity has been identified as the primary contributor to the growth rates. Only a small stabilizing effect due to toroidal rotation has been observed. While experimental results show a decrease of mode frequency with rotation, the opposite trend is observed in modeling. Reasons for discrepancies between modeling and experiment are discussed. Nevertheless, a main contributor to the mode frequency has been identified to be rotation velocity. CASTOR3D classifies modes as resistive ballooning modes as they do not appear unstable in ideal MHD.

Effect of triangularity on plasma turbulence and the SOL-width scaling in L-mode diverted tokamak configurations

The effect of triangularity on tokamak boundary plasma turbulence is investigated using global, flux-driven, three-dimensional, two-fluid simulations. The simulations show that negative triangularity (NT) stabilizes boundary plasma turbulence, and linear investigations reveal that this is due to a reduction of the magnetic curvature driven by interchange instabilities, such as the resistive ballooning mode (RBM). As a consequence, the pressure decay length L p , related to the scrape-off layer (SOL) power fall-off length λ q , is found to be affected by triangularity. Leveraging considerations on the effect of triangularity on the linear growth rate and nonlinear evolution of the RBM, the analytical theory-based scaling law for L p in L-mode plasmas, derived by Giacomin et al (2021 Nucl. Fusion 61 076002), is extended to include the effect of triangularity. The scaling is in agreement with nonlinear simulations and a multi-machine experimental database, which includes recent TCV discharges dedicated to the study of the effect of triangularity in L-mode diverted discharges. Overall, the present results highlight that NT narrows the L p and considering the effect of triangularity is important for a reliable extrapolation of λ q from present experiments to larger devices.

Understanding the negative triangularity ELM trigger and ELM free state on DIII-D with ECE-imaging

The Electron Cyclotron Emission Imaging (ECEI) diagnostic was used to observe a finite-n interchange mode structure in the edge of negative triangularity shaped plasmas on DIII-D. At a small negative triangularity (δu = −0.2), the plasma is in the H-mode with ELMs that are triggered by a low-n interchange mode. At a larger negative triangularity (δu = −0.4) and low NBI power (2 MW), a dithering oscillation is observed that is triggered by a low-n interchange mode, whereas at higher NBI power (&amp;gt;2 MW), the edge reverts to L-mode and the low-n interchange mode is present continuously. In all cases, the edge pressure gradient is clamped when the interchange mode is present. It is concluded that the low-n interchange mode prevents the plasma from transitioning to H-mode at a large negative triangularity. This agrees with linear BOUT++ simulations which suggest that the interchange-type MHD can be a resistive ballooning mode whereby resistivity can significantly increase the finite-n ballooning mode growth rate. The absence of H-mode at large negative triangularity can, thus, be explained by the excitation of low-n pressure driven resistive ballooning modes in the plasma edge.

Probing non-linear MHD stability of the EDA H-mode in ASDEX Upgrade

Regimes of operation in tokamaks that are devoid of large edge localised modes have to be better understood to extrapolate their applicability to reactor-relevant devices. This paper describes non-linear extended magnetohydrodynamic (MHD) simulations that use an experimental equilibrium from an enhanced D-alpha (EDA) H-mode in ASDEX Upgrade. Linear ideal MHD analysis indicates that the operational point lies slightly inside of the stable region. The non-linear simulations with the visco-resistive extended MHD code, JOREK, sustain non-axisymmetric perturbations that are linearly most unstable with toroidal mode numbers of , but non-linearly higher and lower n become driven and the low-n become dominant. The poloidal mode velocity during the linear phase is found to correspond to the expected velocity for resistive ballooning modes. The perturbations that exist in the simulations have somewhat smaller poloidal wavenumbers (–) than the experimental expectations for the quasi-coherent mode in EDA, and cause non-negligible transport in both the heat and particle channels. In the transition from linear to non-linear phase, the mode frequency chirps down from approximately 35 kHz to 13 kHz, which corresponds approximately to the lower end of frequencies that are typically observed in EDA H-modes in ASDEX Upgrade.

Finite magnetic well effects on resistive and drift-resistive ballooning modes in a shaped tokamak

The impact of plasma shaping through magnetic well modifications on the stability of resistive ballooning modes (RBMs) in tokamaks is analysed, also including finite diamagnetic flows. Various limiting cases of the dispersion relation, obtained by matching the ballooning equation across the ideal and resistive layers, are analysed. It is found that stability is generally improved by the combination of vertical elongation and positive triangularity, although, in some cases, the growth rate of the unstable mode can be enhanced by these effects. Usually, vertically elongated plasmas with no triangularity are prone to exhibit worse stability properties. A value for the critical β above which RBMs are driven unstable is identified, and a connection with type-III ELM activity is established.

Trapped-electron-mode property and role for the L-H transition in L-mode edge plasmas with relatively high electron temperature and weak ion temperature gradient

When the low-confinement mode (L-mode) edge has relatively high electron temperature and weak ion temperature gradient, for example, as observed in the ECH-heated low-density plasmas, the trapped electron mode (TEM) can play an important role in the low to high confinement (L-H) transition as well as the L-mode edge transport, instead of the resistive ballooning or ion temperature gradient mode (RBM or ITG). Motivated by this, a study is first presented about, among several types of the TEM, which one is the most dominant in the above L-mode edge condition, showing that it is dominated by a mixture of the density gradient driven and dissipative TEMs. The parameter dependence of the growth rate of this dominant TEM type is then checked, showing that it has the scaling qualitatively similar to the H-mode threshold power one observed in plasmas where the TEM can be a dominant mode. Closely related to this, a discussion is also given about the L-H transition expected in plasmas where the TEM is assumed to be dominant. Unlike the typical L-H transition that is believed to occur in the RBM-dominant plasmas, it is conjectured to take place in one-step form, with no generation or negligible role of the limit-cycle-oscillation, thus requiring a larger threshold power.

Simulations of heat fluxes in an ELMy H-mode discharge on HL-2A

In order to study the distribution and evolution of the transient heat flux on HL-2A during edge-localized-mode (ELM) bursts, the BOUT++ electromagnetic six-field two-fluid model is used to simulate the pedestal collapse under the lower single-null divertor geometry. The equilibrium profiles of HL-2A ELMy H-mode discharge No. 24 953 are adopted as the initial condition in the original case. In this case, linear analysis shows that the resistive ballooning mode (RBM) and drift-Alfven wave are unstable to this equilibrium, and RBM is the dominant instability. The evolutions of the radial heat fluxes at the outer mid-plane and heat fluxes to the inner and outer targets during the ELM event are presented. Six more equilibria are constructed based on the original case to find out the influence of the pedestal profiles on the peak electron heat flux. The results indicate that the heat flux increases with temperature and/or density, and the theoretical analysis and simulation results consistently show that the heat flux q∥e is proportional to ne0,SEPTe0,SEP32.

MHD stability of JT-60SA operation scenarios driven by passing energetic particles for a hot Maxwellian model

We analyze the effects of the passing energetic particles on the resistive ballooning modes (RBM) and the energetic particle driven modes in JT-60SA plasma, which leads to the prediction of the stability in N-NBI heated plasma. The analysis is performed using the code FAR3d that solves the reduced MHD equations describing the linear evolution of the poloidal flux and the toroidal component of the vorticity in a full 3D system, coupled with equations of density and parallel velocity moments for the energetic particle (EP) species assuming an averaged Maxwellian EP distribution fitted to the slowing down distribution, including the effect of the acoustic modes. The simulations show the possible destabilization of a TAE with a frequency (f) of 115 kHz, a TAE with f = 98 kHz and a 6/4 or 7/4 BAE with f = 57 kHz in the ITER-like inductive scenario. If the energetic particle β increases, beta induced Alfven Eigenmodes (BAE), toroidal AEs (TAE) and elliptical AEs (EAE) are destabilized between the inner-middle plasma region, leading to the overlapping of AE of different toroidal families. If these instabilities coexist in the non-linear saturation phase the EP transport could be enhanced leading to a lower heating efficiency. For a hypothetical configuration based on the ITER-like inductive scenario but an center peaked EP profile, the EP β threshold increases and several BAEs are destabilized in the inner plasma region, indicating an improved AE stability with respect to the off-axis peaked EP profile. In addition, the analysis of a hypothetical JT-60SA scenario with a resonant q = 1 in the inner plasma region shows the destabilization of fishbones-like instabilities by the off-axis peaked EP profile. Also, the EPs have a stabilizing effect on the RBM, stronger as the population of EP with low energies (below 250 keV) increases at the plasma pedestal.

Stabilization of Short Wavelength Resistive Ballooning Modes by Ion-to-Electron Temperature and Gradient Ratios in Tokamak Edge Plasmas**Supported by the National Key R&D Program of China (Grant Nos. 2017YFE0300405 and 2017YFE0301200) and the National Natural Science Foundation of China (Grant Nos. 11775067, 11775069, 11875019, and 11805058).

We numerically investigate the effects of ion-to-electron temperature ratio Ti/Te and temperature gradient ratio ηi/ηe on resistive ballooning modes (RBMs) under tokamak edge plasma conditions. The results show that the growth rates of the RBMs exhibit the characteristic of a quite broad poloidal wavenumber spectrum in the cold ion limit. The growth rate spectrum becomes narrower and the peak of the spectrum shifts from the short to long wavelength side with increasing Ti/Te and ηi/ηe. The electron temperature gradient has a very weak effect on the stability of RBMs. However, the ion-to-electron temperature ratio and the temperature gradient ratio have strong stabilizing effects on short-wavelength RBMs, while they have relatively weak effects on long-wavelength RBMs.

Effect of precession drift motion of trapped thermal ions on ballooning modes in helical plasmas

The linear stability analysis of resistive ballooning modes in Large Helical Device plasmas has been carried out by numerical simulation based on the kinetic magnetohydrodynamic (MHD) model where thermal ions are simulated with the drift-kinetic model. Due to the curvature drift and the gradient B drift, the orbit of trapped ions not only deviates from the magnetic surface but also has the precession motion in the poloidal and toroidal directions. Even when the trapped ions remain well inside the radial profile of the MHD mode, the response of the trapped ions is weakened when the precession drift frequency of the trapped ions with respect to the mode phase is close to or larger than the linear growth rate of the instability. This results in the suppression of the ion perpendicular pressure perturbation to the magnetic field leading to the reduction of the linear growth rate.

Investigation of turbulence rotation and radial electric field in the island divertor and plasma edge at W7-X

Diverted plasmas in the stellarator W7-X are investigated using a hopping poloidal correlation reflectometer and a set of Langmuir probes to investigate the plasma edge and the scrape off layer at two different toroidal positions and poloidal cross sections, respectively. The properties of the scrape off layer are studied as function of two magnetic configurations and as function of plasma parameters. The experimentally determined radial position of the inversion point of the radial electric field is compared with calculations. For certain magnetic configurations a remnant island in the scrape off layer is observed and studied as function of the plasma current. Different methods to determine the radial electric field are applied which allow to estimate the phase velocity of the turbulence. The measured phase velocity is small and shows some evidence for the existence of resistive ballooning modes in the scrape off layer. Spectrum decomposition of coherence spectra is applied for a radial localization of modes and to determine their properties. An estimate of the radial correlation length of the broad band (BB) turbulence in the vicinity of the last closed flux surface is calculated from the decrease of BB turbulence amplitude as obtained from the coherence spectra. The obtained radial correlation length is found to be .

Penetration of filamentary structures into the divertor region of spherical tokamaks

Understanding the penetration from the midplane region towards the divertor plate of filamentary structures in the main scrape-off layer of spherical tokamaks is of interest for divertor design and plasma material interaction. Insight into this problem is gained by studying the closely related problem of the parallel structure of resistive ballooning modes, localized to a particular flux surface by a perturbed blob-like density profile. The resulting linearized equations are solved using the Arbitrary Topology Equation Reader code. A metric applied to the spatial structure of the dominant eigenmode quantifies mode penetration. Trends in this quantity are then measured by performing parameter scans over temperature and density. The results of this study are consistent with the dominant role of collisionality in limiting mode interaction with the divertor plate.

Quasi-coherent mode simulation during inter-ELM period in HL-2A

We have performed linear and nonlinear simulations to study the drive mechanism of the quasi-coherent modes (QCM) during the inter-edge localized mode period in HL-2A. With an unstable Resistive-Ballooning mode from linear simulations, the nonlinear simulation has successfully reproduced the QCM inside the separatrix at the outer mid-plane. The poloidal wave number and frequency from fluctuation analysis are almost the same as the experimental results. The phase shift between the electrical potential and the density fluctuation matches. Linear and nonlinear global profile scans show that the QCM is triggered by the density gradient. Based on these scans, some other experimental observations of the QCM are explained.

Variation in the linear stability property of resistive ballooning mode including the parametric dependence of its growth rate in L-mode edge

Motivated by some unexpected features, like the stabilization of the density gradient driven RBM (resistive ballooning mode) by temperature gradient or the smooth transition from the RBM to the ion temperature gradient mode, observed in a recent numerical work [J. Y. Kim et al., Phys. Plasmas 24, 042503 (2017)], an additional study is presented on the linear stability of the RBM in L-mode edge-like plasmas. From an approximate analysis of the RBM dispersion relation in the local fluid limit, it is first shown that the above behaviors can be explained as due to the substantial change of the RBM linear stability, which occurs when the effects by the coupling to drift wave branch or the finite electron thermal conduction are fully considered through the generalized Ohm's law. Corresponding to this significant change in the linear stability property, a check is also presented on the parametric dependence of the RBM growth rate. It is shown that there can be also a large variation in this dependence, with the modified one apparently having a better agreement with the observed L-H threshold power scaling when we assume such a scaling is mainly determined from the RBM growth rate property.

Transition between resistive ballooning mode and toroidal drift wave mode at the edge of tokamak plasmas

The transition between the resistive ballooning mode (RBM) and toroidal drift wave (DW) mode is a possible physical mechanism triggering L-H transition in tokamaks. The two-fluid model [Rafiq et al., Phys. Plasmas 17, 082511 (2010)] developed by Rafiq et al. was improved by including ion diamagnetic effects in plasma polarization drift velocity. Based on the improved fluid model, the gyrokinetic results [Bourdelle et al., Nucl. Fusion 54, 022001 (2014)] about the transition between RBM and toroidal DW were recovered. It shows good agreement under a set of real experimental conditions. Hence the fluid theory is valid to investigate the physics of edge plasmas. A transition temperature Tmin about 80 eV, which RBM is dominant for plasma temperature Te &amp;lt; Tmin, but DW prevails for Te &amp;gt; Tmin, was found in gas puffing experiments of HL-2A tokamak. Employing the improved fluid model, we have simulated this phenomenon and the experimental result has been verified exactly.

Experimental observation of the transition between resistive ballooning modes and ion temperature gradient modes in the edge of the HL-2A tokamak

The type of edge turbulence transition from resistive ballooning modes (RBM) to drift-type ion temperature gradient (ITG) modes has been observed in the gas puffing modulation experiments and also simulations at the HL-2A tokamak. The experimental evidence on RMB and ITG characteristics is given by Langmuir probe and Doppler reflectometry data. In the low temperature region (Te < 80 eV), the variation of turbulence intensity is in phase with that of the parallel resistivity, consistent with RBM features. However, in the high temperature region (Te > 80 eV), the turbulence intensity is enhanced with increasing temperature and reduction of the parallel resistivity, implying a drive by drift wave type ITG modes. By numerical simulations with drift resistive inertial ballooning model, the dependence of the growth rate on the electron temperature for the most unstable mode has been investigated based on experimental parameters. Both experiments and simulations have suggested that the dominating instability transits from RBMs in the low Te regime to ITG modes in the high Te regime.

Simulation of density fluctuations before the L-H transition for Hydrogen and Deuterium plasmas in the DIII-D tokamak using the BOUT++ code

A six-field two-fluid model has been used to simulate density fluctuations. The equilibrium is generated by experimental measurements for both Deuterium (D) and Hydrogen (H) plasmas at the lowest densities of DIII-D low to high confinement (L-H) transition experiments. In linear simulations, the unstable modes are found to be resistive ballooning modes with the most unstable mode number n = 30 or .The ion diamagnetic drift and convection flow are balanced when the radial electric field (Er) is calculated from the pressure profile without net flow. The curvature drift plays an important role in this stage. Two poloidally counter propagating modes are found in the nonlinear simulation of the D plasma at electron density m−3 near the separatrix while a single ion mode is found in the H plasma at the similar lower density, which are consistent with the experimental results measured by the beam emission spectroscopy (BES) diagnostic on the DIII-D tokamak. The frequency of the electron modes and the ion modes are about 40 kHz and 10 kHz respectively. The poloidal wave number is about 0.2 cm−1 () for both ion and electron modes.The particle flux, ion and electron heat fluxes are ∼3.5–6 times larger for the H plasma than the D plasma, which makes it harder to achieve H-mode for the same heating power. The change of the atomic mass number A from 2 to 1 using D plasma equilibrium make little difference on the flux. Increase the electric field will suppress the density fluctuation. The electric field scan and ion mass scan results show that the dual-mode results primarily from differences in the profiles rather than the ion mass.