Ballooning Modes Research Articles

Buoyancy Modes in a Low Entropy Bubble

AbstractIn the nightside region of Earth's magnetosphere, braking oscillations or buoyancy modes have been associated with the occurrence of low entropy bubbles. These bubbles form in the plasma sheet, particularly during geomagnetically disturbed times, and because of interchange, move rapidly earthward and may eventually come to rest in the inner plasma sheet or inner magnetosphere. Upon arrival, they often exhibit damped oscillations with periods of a few minutes and are associated with Pi2 pulsations. Previously we used the thin filament approximation to compare the frequencies and modes of buoyancy waves using magnetohydrodynamic (MHD) ballooning and classic interchange theory. Interchange oscillations differ from the more general MHD oscillations by assuming constant pressure along a magnetic field line. It was determined that MHD ballooning and interchange modes are similar for plasma sheet field lines but differ for field lines that map to the inner magnetosphere. This suggested that the classic interchange formulation was only valid in the plasma sheet. This paper tests the hypothesis that the agreement between MHD ballooning and classic interchange could be restored inside a bubble. We create a small region of entropy depletion in the magnetotail and compare the buoyancy mode properties. At some locations inside the bubble, the MHD ballooning buoyancy modes resemble interchange modes but with lower frequencies than those of the unperturbed background. Unstable modes are found on the earthward edge of the bubble, while at the tailward edge, MHD ballooning predicts a slow mode wave solution not seen in the pure interchange solution.

Implementation of magnetic compressional effects at arbitrary wavelength in the global version of GENE

The global tokamak code GENE has been extended including the effect of magnetic compression caused by B1,|| turbulent fluctuations of the magnetic field parallel to the equilibrium one. This paper outlines the basic structure of the algorithm, valid at arbitrary wavelengths of the gyrokinetic fluctuations, with emphasis on the numerical construction of the so-called “gyrodisk-integral” operators necessary for the model. The numerical implementation is successfully verified against radially local simulations, recovering excellent agreement. Global tokamak simulations are presented as well. The upgrade enables studying a large variety of new physical scenarios at high plasma-β, such as kinetic ballooning modes, MHD-like modes or the interaction of B1,|| with fast particle modes, reducing the gap between gyrokinetic models and physically realistic systems.

First access to ELM-free negative triangularity at low aspect ratio

Abstract A plasma scenario with negative triangularity (NT) shaping is achieved on MAST-U for the first time. While edge localized modes (ELMs) are eventually suppressed as the triangularity is decreased below δ ≲ − 0.06 , an extended period of H-mode operation with Type-III ELMs is sustained at less negative δ even through access to the second stability region for ideal ballooning modes is closed. This documents a qualitative difference from the ELM-free access conditions documented in NT scenarios on conventional aspect ratio machines. The electron temperature at the pedestal top drops across the transition to ELM-free operation, but a steady rise in core temperature as δ is decreased allows for similar normalized β in the ELM-free NT and H-mode positive triangularity shapes.

Non-thermal fusion burning processes, relevant collective modes and gained perspectives

Abstract New tridimensional plasma structures, that are oscillatory and classified as non-separable ballooning modes, can emerge in inhomogeneous plasmas and undergo resonant mode-particle interactions, e.g. with a minority population, that can lead them to modify their spatial profiles. Thus, unlike the case of previously known ballooning modes their amplitudes are not separable functions of time and space. The relevant resonance conditions are intrinsically different from those of the well-known Landau conditions for (ordinary) plasma waves: they involve the mode geometry and affect different regions of the distribution in momentum space at different positions in configuration space. A process for a transfer of energy among different particle populations is envisioned.

Verification of the kinetic electron role in the microinstabilities in a negative triangularity model equilibrium

Effect of kinetic electrons on negative triangularity plasmas has been investigated and compared against the corresponding positive triangularity plasmas, using the global gyrokinetic code X-point Gyrokinetic Code with scale-separated delta-f option without Coulomb collisions. Our model magnetic equilibria have strong positive and negative triangularities and weak magnetic shear. However, unusually large ρi/a and low density plasmas are chosen to maximize the nonlocal effect to investigate the finite ρi effect and to be clearly away from kinetic ballooning modes. Similar conclusions to previous flux tube and global simulations have been obtained in this highly nonlocal model plasma: it is essential to include kinetic electrons in the micro-instability study of negative triangularity plasmas. Most physics findings agree with existing reports, with some disagreement. We offer a new “effective trapping fraction” concept that can add to the explanation of the growth rate difference between NT and PT plasmas, pointing to the significant variation in trapped particle fractions that have turning points in the mode growth regions.

New millimeter-wave diagnostics to locally probe internal density and magnetic field fluctuations in National Spherical Torus Experiment-Upgrade (invited).

A set of new millimeter-wave diagnostics will deliver unique measurement capabilities for National Spherical Torus Experiment-Upgrade to address a variety of plasma instabilities believed to be important in determining thermal and particle transport, such as micro-tearing, global Alfvén eigenmodes, kinetic ballooning, trapped electron, and electron temperature gradient modes. These diagnostics include a new integrated intermediate-k Doppler backscattering (DBS) and cross-polarization scattering (CPS) system (four channels, 82.5-87GHz) to measure density and magnetic fluctuations, respectively. The system can access reasonably large normalized wavenumbers kθρs ranging from ≤0.5 to 15 (where ion sound gyroradius ρs = 1cm and kθ is the binormal density turbulence wavenumber). The system addresses the challenges for making useful DBS/CPS measurements with a remote control of launch polarization (X- or O-mode), probed wavenumber, polarization match of the launch beam with the edge magnetic field pitch angle, and beam steering of the launched beam for wave-vector alignment. In addition, a low-k DBS system consisting of eight fixed frequencies (34-52GHz) and four tunable frequencies (55-75GHz) for low-k density turbulence and fast ion physics will be located at a nearby port location. The combined systems cover the near LCFS and pedestal regions (34-52GHz), the pedestal or mid-radius (50-75GHz), and core plasmas (82.5-87GHz).

On the importance of parallel magnetic-field fluctuations for electromagnetic instabilities in STEP

This paper discusses the importance of parallel perturbations of the magnetic-field in gyrokinetic simulations of electromagnetic instabilities and turbulence at mid-radius in the burning plasma phase of the conceptual high-β, reactor-scale, tight-aspect-ratio tokamak STEP. Previous studies have revealed the presence of unstable hybrid kinetic ballooning modes (hKBMs) and subdominant microtearing modes at binormal scales approaching the ion Larmor radius. In this STEP plasma it was found that the hKBM requires the inclusion of parallel magnetic-field perturbations to be linearly unstable. Here, the extent to which the inclusion of fluctuations in the parallel magnetic-field can be relaxed is explored through gyrokinetic simulations. In particular, the frequently used MHD approximation (dropping δB∥ and setting the ∇B drift frequency equal to the curvature drift frequency) is discussed and simulations explore whether this approximation is useful for modelling STEP plasmas. It is shown that the MHD approximation can reproduce some of the linear properties of the full STEP gyrokinetic system, but is too stable at low ky and nonlinear simulations using the MHD approximation result in very different transport states. It is demonstrated that the MHD approximation is challenged by the high β′ values in STEP, and that the approximation improves considerably at lower β′ . Furthermore, it is shown that the sensitivity of STEP to δB∥ fluctuations is primarily because the plasma sits close to marginality and it is shown that in slightly more strongly driven conditions the hKBM is unstable without δB∥. Crucially, it is demonstrated that the state of large transport typically predicted by local electromagnetic gyrokinetic simulations of STEP plasmas is not solely due to δB∥ physics.

Influence of the shape of a conducting chamber on the stability of rigid ballooning modes in a mirror trap

MHD stabilization of flute and ballooning modes in an axisymmetric mirror trap is studied under the assumption of strong finite Larmor radius effect that suppresses all perturbations with azimuthal numbers m⩾2 and makes the m = 1 mode ‘rigid’. The rigid mode can be effectively suppressed using perfectly conducting lateral wall without any additional means of stabilization or in combination with end MHD anchors. Numerical calculations were carried out for an anisotropic plasma produced in the course of neutral beam injection into the minimum of the magnetic field at the right angle to the trap axis. The stabilizing effect of the conducting shell made of a straightened cylinder is compared with a proportional chamber, which, on an enlarged scale, repeats the shape of the plasma column. It is confirmed that for convincing wall stabilization of the rigid modes, the plasma beta (β, the ratio of the plasma pressure to the magnetic field pressure) must exceed some critical value βcr2 . When conducting lateral wall is combined with conducting end plates imitating MHD end anchors, there are two critical betas and, respectively, two stability zones β<βcr1 and β>βcr2 that can merge, making the entire range 0<β<1 of betas allowable for stable plasma confinement. The dependence of the critical betas on the plasma anisotropy, mirror ratio, width of the vacuum gap between the plasma column and the lateral wall, radial pressure profile and the axial magnetic field profile is examined.

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.

On electromagnetic turbulence and transport in STEP

In this work, we present first-of-their-kind nonlinear local gyrokinetic (GK) simulations of electromagnetic turbulence at mid-radius in the burning plasma phase of the conceptual high-β, reactor-scale, tight-aspect-ratio tokamak Spherical Tokamak for Energy Production (STEP). A prior linear analysis in Kennedy et al (2023 Nucl. Fusion 63 126061) reveals the presence of unstable hybrid kinetic ballooning modes (KBMs), where inclusion of the compressional magnetic field fluctuation, δB∥ , is crucial, and subdominant microtearing modes (MTMs) are found at binormal scales approaching the ion-Larmor radius. Local nonlinear GK simulations on the selected surface in the central core region suggest that hybrid KBMs can drive large turbulent transport, and that there is negligible turbulent transport from subdominant MTMs when hybrid KBMs are artificially suppressed (through the omission of δB∥ ). Nonlinear simulations that include perpendicular equilibrium flow shear can saturate at lower fluxes that are more consistent with the available sources in STEP. This analysis suggests that hybrid KBMs could play an important role in setting the turbulent transport in STEP, and possible mechanisms to mitigate turbulent transport are discussed. Increasing the safety factor or the pressure gradient strongly reduces turbulent transport from hybrid KBMs in the cases considered here. Challenges of simulating electromagnetic turbulence in this high-β regime are highlighted. In particular the observation of radially extended turbulent structures in the absence of equilibrium flow shear motivates future advanced global GK simulations that include δB∥ .

Effect of hyper-resistivity on ballooning modes with resonant magnetic perturbations

The impact of hyper-resistivity on non-ideal ballooning modes (BMs) is studied in the presence of resonant magnetic perturbation (RMP) through considering the hyper-resistivity, resistivity and diamagnetic effect in the BM model with an equilibrium distorted by RMP, which is stable for ideal BMs. Similar to the resistivity, the hyper-resistivity is also destabilizing for the BMs, but RMPs make the mode spectrum of the BMs destabilized by the hyper-resistivity move towards the low toroidal mode number side on the flux surface with a safety factor slightly larger than the RMP resonance safety factor, where the growth rates of the BMs destabilized by the resistivity decrease due to RMP. When both the hyper-resistivity and the resistivity are considered, there is a sort of competitive relationship between them in determining the properties of BMs. If either of the hyper-resistivity term and the resistivity term is much larger than the other one, the instability of BMs is mainly determined by the larger one, and the effect of the smaller one is masked. The destabilizing mechanisms of the hyper-resistivity and the resistivity on BMs are similar, namely, the diffusion and dissipation of current and magnetic field weaken the stabilizing effect of magnetic field line bending. The research results may be important for understanding the enhancement of plasma transport and the mechanism of small edge localized mode (ELM) during ELM control with RMP.

Quasi-mode evolution in a stochastic magnetic field

We present a multi-scale model of quasi-mode evolution in a stochastic magnetic field. The similarity between a quasi-mode and a ballooning mode enables us to address the challenges arising from the disparate geometries in the theories of ballooning modes in the presence of resonant magnetic perturbations. We obtain useful insights into our understanding of ballooning mode dynamics in a stochastic background. To maintain quasi-neutrality at all scales, the beat between the quasi-mode and the stochastic magnetic field drives microturbulence, which drives the turbulent background that promotes mixing and damps the quasi-mode. As a result of the broad mode structure of the quasi-mode, the turbulent viscosity and the turbulent diffusivity produced by the microturbulence are larger than those in our related study on resistive interchange modes. The stochastic magnetic field can also enhance the effective plasma inertia and reduce the effective drive, thereby slowing the mode growth. A nontrivial correlation between the microturbulence and the magnetic perturbations is shown to develop. This could account for the reduction in the Jensen–Shannon complexity of pedestal turbulence in the Resonant Magnetic Perturbation Edge-Localized Mode suppression phase observed in recent experiments. Directions for future experimental and theoretical studies are suggested.

Investigation on the roles of equilibrium toroidal rotation during edge-localized mode mitigated by resonant magnetic perturbations

The effects of equilibrium toroidal rotation during edge-localized mode (ELM) mitigated by resonant magnetic perturbation (RMP) are studied with the experimental equilibria of the EAST tokamak based on the four-field model in the BOUT++ code. As the two main parameters to determine the toroidal rotation profiles, the rotation shear and magnitudes were separately scanned to investigate their roles in the impact of RMPs on peeling–ballooning (P-B) modes. On one hand, the results show that strong toroidal rotation shear is favorable for the enhancement of the self-generated shearing rate with RMPs, leading to significant ELM mitigation with RMP in the stronger toroidal rotation shear region. On the other hand, toroidal rotation magnitudes may affect ELM mitigation by changing the penetration of the RMPs, more precisely the resonant components. RMPs can lead to a reduction in the pedestal energy loss by enhancing the multimode coupling in the turbulence transport phase. The shielding effects on RMPs increase with the toroidal rotation magnitude, leading to the enhancement of the multimode coupling with RMPs to be significantly weakened. Hence, the reduction in pedestal energy loss by RMPs decreased with the rotation magnitude. In brief, the results show that toroidal rotation plays a dual role in ELM mitigation with RMP by changing the shielding effects of plasma by rotation magnitude and affecting by rotation shear. In the high toroidal rotation region, toroidal rotation shear is usually strong and hence plays a dominant role in the influence of RMP on P-B modes, whereas in the low rotation region, toroidal rotation shear is weak and has negligible impact on P-B modes, and the rotation magnitude plays a dominant role in the influence of RMPs on the P-B modes by changing the field penetration. Therefore, the dual role of toroidal rotation leads to stronger ELM mitigation with RMP, which may be achieved both in the low toroidal rotation region and the relatively high rotation region that has strong rotational shear.

Effects of Impurity, Safety Factor, and Magnetic Shear on Kinetic Ballooning Mode in Tokamak Plasmas With Positive Impurity Density Gradient

Effects of Impurity, Safety Factor, and Magnetic Shear on Kinetic Ballooning Mode in Tokamak Plasmas With Positive Impurity Density Gradient

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.

Enhanced Transport at High Plasma Pressure and Subthreshold Kinetic Ballooning Modes in Wendelstein 7-X.

High-performance fusion plasmas, requiring high pressure β, are not well understood in stellarator-type experiments. Here, the effect of β on ion-temperature-gradient-driven (ITG) turbulence is studied in Wendelstein 7-X (W7-X), showing that subdominant kinetic ballooning modes (KBMs) are unstable well below the ideal MHD threshold and get strongly excited in the turbulence. By zonal-flow erosion, these subthreshold KBMs (stKBMs) affect ITG saturation and enable higher heat fluxes. Controlling stKBMs will be essential to allow W7-X and future stellarators to achieve maximum performance.

Gyrokinetic analysis of turbulent transport by electromagnetic turbulence in finite β plasmas with weak magnetic shear on HL-2A

Turbulent transport and zonal flow (ZF) dynamics in the mixed kinetic ballooning mode (KBM) and ion temperature gradient (ITG) mode dominated turbulence states are analyzed by gyrokinetic simulations based on the experimental observations of KBMs in the HL-2A Internal Transport Barrier (ITB) plasmas with weak magnetic shear configuration. Results have shown that KBMs and ITGs are the main candidates for turbulent transport and the inclusion of fast ions (FIs) can destabilize both instabilities, which is resulted by the decrease of ballooning parameter αMHD hence reduced Shafranov shift stabilization due to the negative FI density gradient, making them more unstable according to the ŝ-αMHD diagram. In addition, the ITGs are suppressed by both dilution and finite-β stabilization effects caused by FIs. Nonlinear simulations excluding the effects of FIs indicate that the transport is minimum at βe=βeexp as the turbulence predominated by ITGs is strongly suppressed by the nonlinear electromagnetic (EM) stabilization and enhancement of ZFs. However, the transport is further increased with β e although the ZFs become stronger due to the transition from ITG to KBM dominated turbulence state. The presence of FIs can modify the relation between ZF shearing rate and β e. The transport level is insensitive to β e when βe⩽βeexp but increases significantly because of the KBM destabilization. Meanwhile, the ZF amplitude reaches maximum at βe=βeexp whereas it suffers an erosion at higher values, implying that the plasma might be a self-organized critical state owning to the interactions among ZFs, KBMs and FI effects hence setting the plasma β around β exp. The results have also provided a possible explanation that the destabilization of EM turbulence is responsible for the ion heat transport stiffness under weak magnetic shear configurations in the off-axis neutral beam injection heated ITB plasmas on HL-2A.

Experimental Validation of a Kinetic Ballooning Mode in High-Performance High-Bootstrap Current Fraction Fusion Plasmas.

We report the observation of a set of coherent high frequency electromagnetic fluctuations that leads to a turbulence induced self-regulating phenomenon in the DIII-D high bootstrap current fraction plasma. The fluctuations have frequency of 130-220 kHz, the poloidal wavelength and phase velocity are 16-30 m^{-1} and ∼30 km/s, respectively, in the outboard midplane with the estimated toroidal mode number n∼5-9. The fluctuations are located in the internal transport barrier (ITB) region at large radius and are experimentally validated to be kinetic ballooning modes (KBM). Quasilinear estimation predicts the KBM to be able to drive experimental particle flux and non-negligible thermal flux, suggesting its significant role in regulating the ITB saturation.

An adjoint-based method for optimising MHD equilibria against the infinite-n, ideal ballooning mode

We demonstrate a fast adjoint-based method to optimise tokamak and stellarator equilibria against a pressure-driven instability known as the infinite- $n$ ideal ballooning mode. We present three finite- $\beta$ (the ratio of thermal to magnetic pressure) equilibria: one tokamak equilibrium and two stellarator equilibria that are unstable against the ballooning mode. Using the self-adjoint property of ideal magnetohydrodynamics, we construct a technique to rapidly calculate the change in the eigenvalue, a measure of ideal ballooning instability. Using the SIMSOPT optimisation framework, we then implement our fast adjoint gradient-based optimiser to minimise the eigenvalue and find stable equilibria for each of the three originally unstable equilibria.

Dynamic stability of concrete structures with varying sections to underwater contact explosion: A case study of gravity dams

Concrete structures with varying sections are widely used in the fields of ocean engineering, hydraulic engineering and civil engineering. And the damage mechanism of variable-section structures to underwater contact explosion, which involves localized damage by explosion impact and instability by overall structural vibration, is very complex. The gravity dam is taken as an example, the coupled analysis model for gravity dams under underwater contact blast is established, a prototype test on the dynamic response of a gravity dam under underwater explosion is conducted to verify the reliability of the fluid-solid interaction method, and the reliability of the concrete dynamic damage model adopted in this paper is validated by a small-scale field test on the internal blast damage of a gravity dam. The damage mechanism of gravity dams subjected to underwater contact explosion is analyzed. A stability analysis method for gravity dams to underwater contact explosion is proposed, which allows simultaneous consideration of the dam stability in the blast-induced vibration phase and the static phase after damage. The dynamic stability performance of gravity dams to underwater contact explosion is analyzed. And a stability assessment criterion that could be used to assess the safety level of dams at various stages is presented.