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Various types of AlfvĂ©n eigenmodes (AEs) have been destabilized by fast ions over a broad frequency range from ∼80 kHz to ∼700 kHz in a series of JET experiments in mixed Dâ€"3He plasmas heated with the three-ion ICRF scenario (2020 Nocente et al Nucl. Fusion 60 124006). In this paper, we identify the radial localization of AEs using an X-mode reflectometer, a multiline interferometer and soft x-ray diagnostics. The analysis is focused on the most representative example of these measurements in JET pulse #95691, where two different types of AlfvĂ©n cascade (AC) eigenmodes were observed. These modes originate from the presence of a local minimum of the safety factor q min. In addition to ACs with frequencies below the frequency of toroidal AlfvĂ©n eigenmodes (TAEs), ACs with frequencies above the TAE frequency were destabilized by energetic ions. Both low- (f ≈ 80â€"180 kHz) and high-frequency (f ≈ 330â€"450 kHz) ACs were localized in the central regions of the plasma. The characteristics of the high-frequency ACs are investigated in detail numerically using HELENA, CSCAS and MISHKA codes. The resonant conditions for the mode excitation are found to be determined by passing ions of rather high energy of several hundred keV and similar to those established in JT-60U with negative-ion-based NBI (2005 Takechi et al Phys. Plasmas 12 082509). The computed radial mode structure is found to be consistent with the experimental measurements. In contrast to low-frequency ACs observed most often, the frequency of the high-frequency ACs decreases with time as the value of q min decreases. This feature is in a qualitative agreement with the analytical model of the high-frequency ACs in Breizman et al (2003 Phys. Plasmas 10 3649). The high-frequency AC could be highly relevant for future ITER and fusion reactor plasmas dominated by ∼MeV energetic ions, including a significant population of passing fast ions. [ABSTRACT FROM AUTHOR]

Recently, stationary plasma with a world-record pulse length of 1056 s was achieved on the Experimental Advanced Superconducting Tokamak (EAST). In this work, the core magnetohydrodynamics (MHD) events as well as mode coupling processes have been investigated in EAST long pulse operation with electron heating dominant and pure radio frequency wave heating low collisionality, by using several diagnostics and the nonlinear numerical code M3D together. A saturated m / n = 1/1 kink mode was observed in the core region, where a stable internal transport barrier was found in the electron temperature channel. The frequencies and 2D structures of these modes were studied by a combination of soft X-ray (SXR) imaging and electron cyclotron emission diagnostics. The frequency of the m / n = 1/1 mode exhibited a feature of chirping down with time, and this chirping rate corresponds to the rate of electron diamagnetic drift frequency change. A twisted pattern ('Taichi structure in shape') was reconstructed by SXR tomography of the m / n = 1/1 mode. The perturbations of electron temperature and density caused by m / n = 1/1 are different in size, the latter one being much smaller. The destabilization of m / n = 1/1 was due to the strong central heating combined with electron cyclotron resonance heating and lower hybrid current drive. In the presence of the m / n = 1/1 mode, a negative current was generated on the magnetic axis, which anomalously broadened the core current profile. A m / n = 3/2 tearing mode triggered by m / n = 1/1 mode was also observed. The m / n = 3/2 mode has a smaller frequency than the m / n = 1/1 mode, and carries an m / n = 3/2 island with detectable size. A novel 3D MHD model that separately evolves the plasma density and temperature is applied to the m / n = 3/2 triggered by m / n = 1/1. It is found that a toroidal current density at the q = 1.5 surface, caused by non-axisymmetric density perturbation during the m / n = 1/1 nonlinear growth phase, was generated and hence the destabilization of the m / n = 3/2 tearing mode. Both the modeled electron temperature and density perturbations agree well with experimental observations. In the last section of this paper, the interaction between the m / n = 1/1 mode and fast electrons as well as the active control of this mode are also presented. [ABSTRACT FROM AUTHOR]

A first-of-its-kind, inductively driven micro-particle (Pellet) accelerator and injector have been developed and operated successfully in ADITYA-U circular plasma operations, which may ably address the critical need for a suitable disruption control mechanism in ITER and future tokamak. The device combines the principles of electromagnetic induction, pulse power technology, impact, and fracture dynamics. It is designed to operate in a variety of environments, including atmospheric pressure and ultra-high vacuum. It can also accommodate a wide range of pellet quantities, sizes, and materials and can adjust the pellets' velocities over a coarse and fine range. The device has a modular design such that the maximum velocity can be increased by increasing the number of modules. A cluster of lithium titanate/carbonate (Li2TiO3/Li2CO3) impurity particles with variable particle sizes, weighing ∼50–200 mg are injected with velocities of the order of ∼200 m s−1 during the current plateau in ADITYA-U tokamak. This leads to a complete collapse of the plasma current within ∼5–6 ms of triggering the injector. The current quench time is dependent on the amount of impurity injected as well as the compound, with Li2TiO3 injection causing a faster current quench than Li2CO3 injection, as more power is radiated in the case of Li2TiO3. The increase in radiation due to the macro-particle injection starts in the plasma core, while the soft x-ray emission indicates that the entire plasma core collapses at once. [ABSTRACT FROM AUTHOR]

Dedicated experiments were performed in JET DTE2 plasmas for obtaining an α -particle bump-on-tail (BOT) distribution aiming at exciting Alfvén eigenmodes (AEs). Neutral beam injection-only heating with modulated power was used so that fusion-born α -particles were the only ions present in the MeV energy range in these DT plasmas. The beam power modulation on a time scale shorter than the α -particle slowing down time was chosen for modulating the α -particle source and thus sustaining a BOT in the α -particle distribution. High-frequency modes in the toroidicity-induced Alfven eigenmode (TAE) frequency range and multiple short-lived modes in a wider frequency range have been detected in these DT discharges with interferometry, soft x-ray cameras, and reflectometry. The modes observed were localised close to the magnetic axis, and were not seen in the Mirnov coils. Analysis with the TRANSP and Fokker-Planck FIDIT codes confirms that α -particle distributions with BOT in energy were achieved during some time intervals in these discharges though no clear correlation was found between the times of the high-frequency mode excitation and the BOT time intervals. The combined magneto-hydrodynamic (MHD) and kinetic modelling studies show that the high-frequency mode in the TAE frequency range is best fitted with a TAE of toroidal mode number n = 9. This mode is driven mostly by the on-axis beam ions while the smaller drive due to the pressure gradient of α -particles allows overcoming the marginal stability and exciting the mode (Oliver et al 2023 Nucl. Fusion submitted). The observed multiple short-lived modes in a wider frequency range are identified as the on-axis kinetic AEs predicted in Rosenbluth and Rutherford (1975 Phys. Rev. Lett. 34 1428). [ABSTRACT FROM AUTHOR]

Off-axis sawtooth oscillations during the presence of nonlinear coupling between toroidal Alfvén eigenmodes (TAEs) and tearing mode are firstly observed in the plasma without two q = 2 rational surfaces on HL-2A tokamak. Those low frequency oscillations always take place followed by nonlinear interaction processes and the off-axis features have been confirmed by multiple diagnostics, such as soft x-ray arrays and electron cyclotron emission imaging systems. A possible physical mechanism is proposed for interpretation of those off-axis oscillations. That is, nonlinear interaction between TAEs and tearing mode causes significant losses of fast ions though the spacial overlapped global mode structure, then makes a drop in torque and leads to rotation braking or even mode locking. When magnetic fluctuation becomes large enough during braking or locking, the resulting high amplitude saturated mode leads to subsequent or immediate collapse at the q = 2 rational surface. [ABSTRACT FROM AUTHOR]

This paper describes a new method to derive, from soft x-ray (SXR) tomography, robust estimates of the core displacement, growth rate and frequency of a 1/1 sawtooth crash precursor. The method is valid for very peaked SXR profiles and is robust against both the inversion algorithm and the presence of tungsten in a rotating plasma. Three typical ASDEX Upgrade crashes are then analysed. In all cases a postcursor is observed, suggesting incomplete reconnection. Despite different dynamics, in all three cases the growth rate of the core displacement shows similar features. First, it is not constant, supporting the idea of non-linear growth. Second, it can be divided into clearly identified phases with quasi-constant growth rates, suggesting sudden change of growth regime rather than smooth transitions. Third, its evolution is non-monotonic, with phases of accelerated growth followed by damped phases. This damping is interpreted for two cases respectively as an effect of fast ions and of mode coupling, based on the result of a MHD simulation. The mode frequency is observed in all cases to be closely related to the plasma bulk rotation profile, with little or no visible effect of the electron diamagnetic drift frequency. The onset criterion could not be clearly identified and it is shown that the role of the pressure gradient is not as expected from a naive extrapolation of the linear stability theory. [ABSTRACT FROM AUTHOR]

Energetic electrons driving low-frequency magnetohydrodynamic instabilities, e.g., electron fishbone (eFB) modes and electron beta-induced Alfvén eigenmodes (eBAEs), are found in co- and counter-current drive low hybrid current drive (LHCD) plasma in HL-2A, respectively. The eBAEs are found in LHCD plasma for the first time. Two branches eFB modes are observed in the core of plasma, and they can transit from the high-frequency one to the low-frequency one continuously. The different mode structures and positions are obtained by tomography of soft x-ray arrays. The frequency jump phenomena of eFB modes are also found. Two eBAEs, with poloidal and toroidal mode numbers m/n = 3/1 and 5/2, are found in the edge of the plasma. The single m/n = 3/1 mode is found when the LHCD power (PLHCD) is 0.44 MW. The strong m/n = 5/2 mode coexists with the weak 3/1 mode when PLHCD = 0.52 MW. Although the current drive direction of LHCD is opposite to the plasma current, the two eBAEs also propagate in the electron diamagnetic drift direction poloidally, which is the same direction as the eFB modes in co-current drive LHCD plasma. With increasing PLHCD (or changed current profile), the value of the edge safety factor (q) decreases. The evolutions of the mode numbers of eBAEs may be related to changes in the edge q factors. [ABSTRACT FROM AUTHOR]

The optimised superconducting stellarator W7-X generates its rotational transform by means of external coils, therefore no toroidal current is necessary for plasma confinement. Electron cyclotron current drive experiments were conducted for strikeline control and safe divertor operation. During current drive experiments periodic and repetitive crashes of the central electron temperature, similar to sawtooth crashes in tokamaks, were detected. Measurements from soft x-ray tomography and electron cyclotron emission show that the crashes are preceded by weak oscillating precursors and a displacement of the plasma core, consistent with a (m, n) = (1, 1) mode. The displacement occurs within , followed by expulsion and redistribution of the core into the external part of the plasma. Two types of crashes, with different frequencies and amplitudes are detected in the experimental program. For these non-stationary parameters a strong dependence on the toroidal current is found. A 1-D heuristic model for current diffusion is proposed as a first step to explain the characteristic crash time. Initial results show that the modelled current diffusion timescale is consistent with the initial crash frequency and that the toroidal current rise shifts the position where the instability is triggered, resulting in larger crash amplitudes. [ABSTRACT FROM AUTHOR]

A pulsed oscillating power amplifier has been developed to apply high frequency biasing voltage to an electrode at the edge of the STOR-M tokamak plasma. The power amplifier can deliver a peak-to-peak oscillating voltage ±60 V and current 30 A within the frequency range 1 kHz–50 kHz. The electrode is located in the equatorial plane at radius ρ = 0.88. The frequency of the applied voltage has been varied between discharges. It is observed that the plasma density and soft x-ray intensity from the plasma core region usually increase at lower frequency regime 1 kHz–5 kHz as well as relatively higher frequency regime 20 kHz–25 kHz but seldom increase in between them. Increment of τ\!E has been observed 40% and 20% for the frequency regimes of 1 kHz–5 kHz and 20 kHz–25 kHz, respectively, and τ\!p increment is 25% for both frequency regimes. Transport simulation has been carried out using the ASTRA simulation code for STOR-M tokamak parameters to understand the physical process behind experimental observations at the higher frequency branch. The model is based on geodesic acoustic mode(GAM) excitement at resonance frequency associated with Ware-pinch due to the oscillating electric field produced by biasing voltage, which can suppress anomalous transport. Simulation results reproduce the experimental trends quite well in terms of the density, particle confinement, as well as energy confinement time evolution. All the results indicate that high frequency biasing is capable of improving confinement efficiently. [ABSTRACT FROM AUTHOR]

Fishbone instability excited by energetic electrons during electron cyclotron resonant heating (ECRH) is identified on HL-2A.With high-power ECRH, periodic frequency jump phenomena are observed by soft x-ray arrays. Soft x-ray tomography shows that the poloidal and toroidal mode numbers are 1/1 and 2/2 with the frequency jump. There is an ECRH power threshold for the frequency jump phenomena, which is generally about 0.9MW. The frequencies of the two modes increase with the ECRH power. Experiments show that trapped particles are dominant in the low-density high-power ECRH plasma. The precessional frequency of the energetic trapped electrons is calculated with different discharge parameters. The results indicate that the energy of resonant electrons is in agreement with the hard x-ray measurement. [ABSTRACT FROM AUTHOR]

The study of electron temperature profiles of quasi-single helical states (QSH) in RFX-Mod (and, in general, in other RFP machines) was carried out in the past mainly using Thomson scattering, thus being limited to a time resolution of the order of some milliseconds and to the collection of single, isolated cases, which displayed clear transport barriers. A new multichord double filter SXR spectrometer was developed and installed. Temperature profiles are now measured up to a frequency of some kHz, allowing one to determine the entire time evolution of electron temperature during a QSH cycle. A mapping technique, originally developed for Thomson temperature profiles, is adapted to deal with the line-integrated nature of the SXR diagnostic. In particular, temperature gradients related to the presence of transport barriers are reconstructed and analysed in a helical reference system, coherently with the underlying plasma equilibrium. The method is discussed in its capabilities and limits and then applied to a wide QSH database. As a result, a clear difference in temperature gradient behaviour between the rising phase of QSH and the saturated (or flattop) phase is observed. In the rising phase the expected correlation of temperature gradient with magnetic spectrum is confirmed, showing a positive trend between dominant mode amplitude and thermal structure dimension, as well as a negative correlation of secondary mode amplitudes and temperature gradient. On the other hand, in the flattop phase the presence of a thermal structure is intermittent, and much less influenced by the magnetic dynamics. This suggests the simultaneous presence of different mechanisms that enhance energy transport. [ABSTRACT FROM AUTHOR]

The Keda Torus eXperiment (KTX) is still operated in the commissioning phase, and preparation for the operation capability of the KTX phase II upgrade is underway. The diagnostics in the KTX have been greatly developed: (1) the terahertz interferometer has been upgraded to seven chords for electron density profile inversion; (2) a Thomson scattering system with a 5 Joule laser has been installed and commissioning is in progress; (3) a 3D movable probe system has been developed for the electromagnetic turbulence measurement; (4) double-foil soft x-ray imaging diagnostics have been set up and a bench test has been completed; (5) an edge capacitive probe has been installed for the radial electrical field measurement; (6) a multi-channel spectrograph system has been built for detecting impurities of carbon and oxygen. In addition, the design of a new compact torus injection system has been completed for feeding and momentum driving. Pilot research, such as the 3D reversed field pinch physics and electromagnetic turbulence, etc, have been conducted in the discharge status of the KTX. The 3D spectra characters of electromagnetic turbulence are firstly measured using a classical two-point technique by Langmuir probe arrays set on the 3D movable probe system and edge magnetic sensors. The forward scattering is collected by the interferometer system, which shows the potential for turbulence research. The electromagnetic turbulence is tentatively investigated in the KTX. The formation of a quasi-single-helicity state in the KTX regime is also preliminarily explored in simulation. [ABSTRACT FROM AUTHOR]

The 2D gas electron multiplier (GEM) is used to measure the chord-integrated soft x-ray radiation in the direction tangential to the magnetic field. With the Tikhonov tomography algorithm, the soft x-ray emissivity is derived considering the soft x-ray air transmission factor. The cooling factors are also determined according to the continuum and impurity line radiations. The impurity concentration is then obtained from the measured emissivity. In the dominant electron heating scenario, iron is the main impurity of which the high ionization states contribute to the total counting rate of GEM. The up-down asymmetry of concentrated impurity is observed before the plasma confinement conversion from edge localized mode (ELM)-free high confinement mode (H-mode) to ELMy H-mode. A large scale perturbation is observed which is radially elongated on the tomography plots as the electron temperature profile shows in–out asymmetry. The perturbation drives outward impurities and energy transport, reducing the impurity concentration and the electron temperature gradient in the core. The underlying instability is also discussed which shows the relevance of the macroscopic mode with the iron impurity density and electron temperature profiles. [ABSTRACT FROM AUTHOR]

Research on beta induced Alfvén eigenmodes (BAEs) driven by energetic ions has been carried out on the HL-2A tokamak. The BAEs can be observed in the cases of being beyond or below unity. The mode frequencies are around 60–95 kHz. The radial mode structures have been detected by the multi-channel microwave reflectometer and soft x-ray arrays. The results suggest that the BAEs are highly localized at the normalized radius of –0.26. Theoretical analyses based on the general fishbone-like dispersion relation and Alfvén mode code support the experimental measurements in both mode frequencies and locations. The BAEs are found to be excited more easily in low electron density discharges. The coexistence of BAEs and reversed shear Alfvén eigenmodes enables the estimation of directly from experiments. [ABSTRACT FROM AUTHOR]

In the present work, the tolerable impurity level and composition for a reactor plasma using several sets of model assumptions are evaluated. Special care was taken to evaluate a comprehensive and consistent set of atomic data for 35 different elements, such that the impurity level for various elements may be studied as a function of their nuclear charge. The data set may not only be useful for the presented work or for system codes which design fusion reactors, but also for interpretation of bolometric measurements. Additionally, the predictions of the spectral distribution of the radiated power is of high quality such that soft x-ray broadband measurements may be interpreted. In the present work the data is used for predicting the radiated power in a reactor plasma, using a 0D, several variants of a 0.5D model and a realistic 1D ASTRA modelling of a DEMO plasma, i.e. the EU DEMO1 2015 design. The maximal or appropriate impurity content of a reactor plasma for all models can be determined, such that the predictions from a simplistic 0D model can be compared to less simplistic models and a proper reactor simulation. These comparisons suggest that with the simplistic models the impurity content may be estimated within a factor of about 1.5, independent of the realization of the reactor plasma. At the same time this study underlines the sensitivity of the reactor performance on the impurity mixture and especially of the He content of the plasma. Additionally, an extended 0.5D model is presented which is able to predict variations of the fusion yield Q and the He concentration, when both is known for a reference scenario. These predictions prove to be of high accuracy when compared to the 1D ASTRA modelling and thus, allow the net impact of an increased dilution and a simlutaneous temperature rise at constant plasma pressure to be evaluated. Furthermore, the parameter space is scanned with more than 105 model reactor plasmas demonstrating that the use of a low-Z impurity diminishes the possibility of an economical feasible reactor plasma. The main results of the parameter scan are made available via scaling formulae. [ABSTRACT FROM AUTHOR]

Destabilization of a stationary neoclassical tearing mode due impurity influx can lead to a potentially destructive disruption and is of significant concern for current and future tokamaks. A representative scenario was developed on TCV to experiment with applicable disruption avoidance techniques and produce a real time control system capable of handling such an event. Soft x-ray (SXR) radiation intensity and magnetic diagnostics analyses available in real time were used to provide plasma state information to the control system. Electron cyclotron current drive (ECCD) was employed to prevent NTM destabilization. Deposition of ECCD near the calculated q  =  2 surface was able to prevent destabilization of the NTM if a large increase in SXR radiation intensity was used as the trigger. A delay in avoidance resulted in the plasma entering a disruptive state which required over 100 ms of continuous ECCD around the q  =  2 surface to stabilize. Ramp down scenarios were studied to complete the design of a closed loop system. This system was then successfully tested using increasingly disruptive scenarios, through increased gas quantities, and the system was able to extend the discharge for a prescribed amount of time and safely ramp down the plasma current to the minimum controllable level. The system demonstrated in this work is presently limited to this specific type of disruption but this approach could be applied to other disruptive situations on the path to building a global disruption handling system. [ABSTRACT FROM AUTHOR]

Runaway currents following disruptions have an important effect on the first wall in current tokamaks and will be more severe in next generation tokamaks. The behavior of runaway currents in massive gas injection (MGI) induced disruptions have been investigated in the J-TEXT tokamak. The cold front induced by the gas jet penetrates helically along field lines, preferentially toward the high field side and stops at a location near the q  =  2 surface before the disruption. When the cold front reaches the q  =  2 surface it initiates magnetohydrodynamic activities and results in disruption. It is found that the MGI of He or Ne results in runaway free shutdown in a large range of gas injections. Mixture injection of He and Ar (90% He and 10%Ar) consistently results in runaway free shutdown. A moderate amount of Ar injection could produce significant runaway current. The maximum runaway energy in the runaway plateau is estimated using a simplified model which neglects the drag forces and other energy loss mechanisms. The maximum runaway energy increases with decreasing runaway current. Imaging of the runaway beam using a soft x-ray array during the runaway current plateau indicates that the runaway beam is located in the center of the plasma. Resonant magnetic perturbation (RMP) is applied to reduce the runaway current successfully during the disruption phase in a small scale tokamak, J-TEXT. When the runaway current builds up, the application of RMP cannot decouple the runaway beam due to the lower sensitivity of the energetic runaway electrons to the magnetic perturbation. [ABSTRACT FROM AUTHOR]

In the non-linear phase of a sawtooth, the complete reconnection of field lines around the q  =  1 flux surface often occurs resulting in a radial displacement of the plasma core. A complete time-dependent electromagnetic model of this type of reconnection has been developed and implemented in the EBdyna_go code. This contribution aims at studying the behaviour of ions, both impurity and fast particles, in the pattern of reconnecting field lines during sawtoothing plasma experiments in the ASDEX Upgrade tokamak by using the newly developed numerical framework. Simulations of full reconnection with tungsten impurity that include the centrifugal force are achieved and recover the soft x-ray measurements. Based on this full-reconnection description of the sawtooth, a simple tool dedicated to estimate the duration of the reconnection is introduced. This work then studies the redistribution of fast ions during several experimentally observed sawteeth. In some cases of sawteeth at ASDEX Upgrade, full reconnection is not always observed or expected so the code gives an upper estimate of the actual experimental redistribution. The results of detailed simulations of the crashes are compared with measurements from various diagnostics such as collective Thomson scattering and fast-ion D-alpha (FIDA) spectroscopy, including FIDA tomography. A convincing qualitative agreement is found in different parts of velocity space. [ABSTRACT FROM AUTHOR]

Experiments on trace argon impurity transport in L-mode discharges were performed on Korea superconducting tokamak advanced research (KSTAR) with electron cyclotron resonance heating (ECH). Ar emission was measured by soft x-ray (SXR) arrays and vacuum UV (VUV) diagnostics. A significant reduction in the core Ar emissivity was observed with core ECH. The reduction was the largest with on-axis heating and became smaller with outward heating positions. The diffusivity and convection velocity of Ar were obtained by analysis of the SXR data with the SANCO impurity transport code for the on-axis ECH and the non-ECH shots. In the on-axis ECH case, both diffusivity and convection velocity increased. Furthermore, the convection changed its direction from inward to outward in the plasma core (r/a < 0.3), resulting in a hollow profile of the total Ar density. Together with the reduction in the SXR signals, the hollow impurity profile in the core and the reversal of the convection velocity consistently confirm that ECH can reduce impurity accumulation in the core region. Neoclassical impurity transport and linear stability of micro-turbulence were calculated and discussed in relation to the possible transport mechanism. [ABSTRACT FROM AUTHOR]

The effects of applied 3D resonant magnetic perturbations are modelled with and without self-consistent plasma response. The plasma response is calculated using a linear two-fluid model. A synthetic diagnostic is used to simulate soft x-ray (SXR) emission within the steep gradient region of the pedestal, 0.98 > ψ > 0.94. Two methods for simulating the SXR emission given the perturbed fields are considered. In the first method, the emission is assumed to be constant on magnetic field lines, with the emission on each line determined by the penetration depth into the plasma. In the second method, the emission is taken to be a function of the perturbed electron temperature and density calculated by the two-fluid model. It is shown that the latter method is more accurate within the plasma, but is inadequate in the scrape-off layer due to the breakdown of the linearized temperature equation in the two-fluid model. The resulting synthetic emission is compared to measured SXR data, which show helical m = 11 ± 1 displacements around the 11/3 rational surface of sizes up to 5 cm, depending on the poloidal angle. The helical displacements around the 11/3 surface are identified to be directly related to the kink response, caused by amplification of non-resonant components of the magnetic field due to plasma response. The role of different plasma parameters is investigated, but it appears that the electron rotation plays a key role in the formation of screening and resonant amplification, while the kinking appears to be sensitive to the edge current density. It is also hypothesized that the plasma response affects the edge-localized-mode (ELM) stability, i.e. the discharge's operational point relative to the peeling–ballooning stability boundary. [ABSTRACT FROM AUTHOR]