Low Toroidal Mode Number Research Articles

From L-mode to the L–H transition, experiments on ASDEX upgrade and related gyrokinetic simulations

This work combines experimental observations from the ASDEX Upgrade tokamak with related gyrokinetic simulations of the turbulence moving from L-mode toward, and beyond, the L–H transition. Dedicated experiments have been performed with slow steps of increasing electron cyclotron heating power. Gyrokinetic simulations of the edge turbulence of these plasmas highlight the key roles of the non-linear electromagnetic effects and the external flow shear (E × B shear), both related to the evolution of the plasma pressure profile with increasing heating power. The increase in the plasma βe destabilizes turbulence at low toroidal mode numbers, that, in turn, is strongly suppressed by the external flow shear. This allows the plasma pressure profiles to evolve without a sharp rise in the turbulent fluxes. When all the experimentally measured plasma parameters are consistently included as inputs of the local gyrokinetic simulations, both the experimental electron and ion heat fluxes are quantitatively reproduced on the whole L-mode phase of the selected discharge. Simulations carried out with edge parameters of an ELM-free H-mode phase still show the importance of the mechanisms discussed earlier while also indicating possible limitations of the local approach.

Observation of a new pedestal stability regime in MAST Upgrade H-mode plasmas

The first pedestal stability and structure analysis on the new MAST Upgrade (MAST-U) spherical tokamak H-mode plasmas is presented. Our results indicate that MAST-U pedestals are close to the low toroidal mode number (n) peeling branch of the peeling-ballooning instability, in contrast with MAST H-mode pedestals which were deeply in the high-n ballooning branch. This offers the possibility of reaching the ELM-free quiescent H-mode (Burrell et al 2005 Plasma Phys. Control. Fusion 47 B37–B52) or high-performance super H-mode (Snyder et al 2015 Nucl. Fusion 55 083026; Snyder et al 2019 Nucl. Fusion 59 086017) regimes. In addition, the coupling between the peeling and ballooning branches is weak in MAST-U, suggesting that a path to very high pedestal pressure gradient at high density may exist with sufficient heating power. A possible explanation for the differences between MAST and MAST-U pedestal stability is given in terms of plasma shaping parameters, in particular squareness and elongation, as well as the pedestal top temperature and collisionality.

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.

Tungsten transport due to the neoclassical toroidal viscosity induced by resonant magnetic perturbation in the EAST tokamak

The impact of neoclassical toroidal viscosity (NTV) induced by resonant magnetic perturbations (RMPs) on tungsten has been studied in EAST. Modeling results from NTVTOK show that the NTV effect on low charge state tungsten ions is greater than that on high charge state tungsten ions, and the effective transport coefficient of W20+ is only on the order of 10−4–10−3 m2/s, while the effective transport coefficient of W1+ can reach 0.1–1 m2/s, which is close to the 2D neoclassical diffusion coefficient of W1+. The flux of W1+ exhibits a clear phase dependence on the RMP spectrum, and the W1+ flux obtained from NTVTOK is higher at low toroidal mode numbers compared to high toroidal mode numbers of RMPs, which is qualitatively consistent with EAST experiments.

Excitation of toroidal Alfvén eigenmode by barely circulating energetic electrons in low density plasmas

Toroidal Alfvén eigenmodes (TAEs) associated with runaway electrons are observed in low density EAST Ohmic discharges (Zhu et al 2022 Phys. Plasmas 29 062504), which motivate the present work to explore the possible destabilization mechanism using simplified hybrid MHD-kinetic simulations. We show that the barely circulating energetic electrons can satisfy the resonance condition with the TAE, mainly due to vanishing transit frequency near the phase space circulating/trapped separatrix. In addition, the nonlinear saturation study suggests that the phase space resonance structure plays an important role in the eventual saturation amplitude, where a low toroidal mode number is favored in this scenario.

Electron temperature fluctuation measurements with Correlation Electron Cyclotron Emission in L-mode and I-mode plasmas at ASDEX Upgrade

The Correlation Electron Cyclotron Emission (CECE) diagnostic at ASDEX Upgrade (AUG) is used to investigate the features of outer core and pedestal (ρpol = 0.85-1.0) turbulence across confinement regime transitions. The I-mode confinement regime is a promising operational scenario for future fusion reactors because it features high energy confinement without high particle confinement, but the nature of the edge and pedestal turbulence in I-mode plasmas is still under investigation. The edge Weakly Coherent Mode (WCM) appears in the I-mode pedestal and may play a role in transport. In this work we explore electron temperature (Te) fluctuations in the plasma outer core and pedestal using a 24-channel high radial resolution CECE radiometer. CECE measurements provide turbulence information including the Te fluctuation amplitude, turbulent spectra, and radial localization of turbulent features. With CECE measurements we show that the WCM is localized in the pedestal region in both L-mode and I-mode and is measured in optically thick plasmas with a Te fluctuation amplitude of 2.3%. Broadband drift wave turbulence is measured in the outer core with a Te fluctuation amplitude of <1%. A second CECE system recently installed at AUG allowed for non-standard fluctuation measurements during L-mode and I-mode experiments. The second CECE system was toroidally separated from the primary system, allowing measurements of the long-range toroidal correlation of the WCM indicating its low toroidal mode number. A reflectometer sharing a line of sight with the second CECE system enabled density-temperature cross-phase (αne Te ) measurements. The WCM αne Te changes between L-mode and I-mode as the Te gradient steepens.

Multi-scale analysis of global electromagnetic instabilities in ITER pre-fusion-power operation plasmas

Global electromagnetic gyrokinetic simulations are performed with the particle-in-cell code ORB5 for an ITER pre-fusion-power-operation plasma scenario, with half-field (2.65 T) and half-current (7.5 MA). We report on a ‘multi-scale‘ analysis of the discharge, considering eigenmodes and instabilities across three scale-lengths (n < 35, 45 < n < 70, n > 100). Although the scenario will nominally have neutral beam heating with particles injected with 1 MeV, Alfvén eigenmodes are investigated in the absence of such source, and reversed shear, toroidal and elliptical Alfvén eigenmodes are found with weak damping for moderately low toroidal mode numbers (10 ⩽ n ⩽ 35). At higher toroidal mode numbers (40 ⩽ n ⩽ 70), unstable Alfvénic modes have been observed close to rational surfaces and are labelled as beta-induced Alfvén eigenmodes (BAEs)/Alfvénic ion temperature gradient modes, since their frequency is associated with the BAE gap and they are driven by the bulk plasma on the Alfvénic continuum. These modes are unstable in the absence of energetic particles (EPs), and adding a species of EPs (with an isotropic 1 MeV slowing down distribution) has negligible impact on their growth rate. At higher toroidal mode numbers (n ⪅ 200), low frequency microscale instabilities are observed.

Kink–ballooning mode in circular tokamak plasma

Peeling–ballooning modes, which are driven by gradients of parallel current and pressure in the pedestal, are widely accepted as the instability triggering large Edge Localized Modes (ELMs). However, the current-driven mode related to ELMs is not fully understood. This paper is about comparing the kink mode to the peeling mode, and the modified current profiles are specifically made to be simultaneously kink stable/peeling unstable or vice versa so that the two modes (or the modes coupled to peeling modes) can be compared. Caltrans-Corsica is used to generate a series of equilibria with modified edge current profiles. Based on these equilibria, the effects of edge current density on plasma instabilities are studied with the three-field BOUT++ elm-pb code. The results suggest that kink–ballooning modes can drive ELMs in some peeling-stable regions. Compared to the peeling–ballooning mode, kink–ballooning modes have comparatively lower poloidal resonant modes and growth rates at low toroidal mode numbers.

Linear gyrokinetic simulations of reversed shear Alfvén eigenmodes and ion temperature gradient modes in DIII-D tokamak

Global linear gyrokinetic simulations using realistic DIII-D tokamak geometry and plasma profiles find co-existence of unstable reversed shear Alfvén eigenmodes (RSAE) with low toroidal mode number n and electromagnetic ion temperature gradient (ITG) instabilities with higher toroidal mode number n. For intermediate n = [10, 12], RSAE and ITG co-exist and overlap weakly in the radial domain with similar growth rates but different real frequencies. Both RSAE and ITG growth rates decrease less than 5% when compressible magnetic perturbations are neglected in the simulations. The ITG growth rates increase less than 7% when fast ions are not included in the simulations. Finally, the effects of trapped electrons on the RSAE are negligible.

Global gyrokinetic nonlinear simulations of kinetic infernal modes in reversed shear tokamaks

The nonlinear evolution of electromagnetic instabilities in reversed shear plasmas is investigated by means of global gyrokinetic simulations. It is found that the kinetic infernal mode (KIM), which is a pressure-driven instability with low to intermediate toroidal mode number excited in a region of low magnetic shear, is unstable at high β, while the ion temperature gradient mode is unstable at low β, where β is the ratio of the plasma kinetic pressure to the magnetic pressure. The β threshold of the KIM is much lower than that of the kinetic ballooning mode (KBM) appearing in a normal shear plasma, while both the KIM and KBM are strong at the unfavorable curvature region, and the KIM has the same parity as the KBM. Nonlinear simulations show that the KIM gets saturated by exciting strong zonal flows and fluctuations of low toroidal mode number. The amplitude of the KIM turbulence is similar to that of the KBM turbulence in spite of the fact that the linear growth rate of the KIM is much higher than that of the KBM. This is because the excitation of zonal flows and fluctuations at low toroidal mode number is stronger in the reversed shear plasma than that of the normal shear plasma. On the other hand, the energy flux and particle flux due to the KIM turbulence are about two or three times larger than those by the KBM turbulence.

Validation of Alfvén eigenmode simulations on DIII-D and projection for CFETR scenario

Alfvén eigenmodes (AEs) are driven unstable by on-axis neutral beam (NB) injection in DIII-D reversed magnetic shear discharges #166496 and #159243, a high-beta steady-state demonstration discharge and an L-mode current ramp discharge, respectively. The experimental results are used to validate the ideal MHD code with kinetic extensions NOVA-K and the gyro-Landau-fluid code TGLFEP. Both codes predict low toroidal mode number (n = 1–2) toroidal Alfvén eigenmode (TAE) instability in the former discharge and low-n (n = 2–6) reverse shear Alfvén eigenmode (RSAE) instability in the latter discharge, consistent with observations. Discrepancies between the two codes are discussed. The same two codes are also employed to predict linear AE instabilities driven by α particles in the China fusion engineering test reactor (CFETR). For the CFETR reversed shear q profile, the growth rates of AEs oscillate with increasing toroidal mode number, depending on the dominant AE type, and the RSAEs near a rational surface always have larger growth rates than TAEs. AEs are found to be further destabilized by the addition of 500 keV off-axis injected NB. The effects of q-profile variation on AE stability in CFETR are also investigated and the results show that raising qmin can further destabilize RSAEs, while increasing q0 with fixed qmin, to create stronger negative magnetic shear, is stabilizing. Increasing plasma density is beneficial for AE stability due to reduced fast ion drive because of shorter slowing down time and higher electron collisional damping.

Access to pedestal pressure relevant to burning plasmas on the high magnetic field tokamak Alcator C-Mod

Experiments on the Alcator C-Mod tokamak have utilized reactor-relevant magnetic fields to sustain substantially higher pedestal pressure than in other devices and allow close approach to the ITER H-mode baseline target pedestal pressure of 90 kPa. The EPED model, which couples the physics of transport driven by kinetic ballooning modes and MHD instabilities arising from peeling-ballooning modes, predicts the pressure profile at the onset of edge-localized modes (ELMs), and yields to lowest order a critical-βN like behavior for the pedestal: ( for fixed edge q). C-Mod routinely accesses edge plasma pressure in excess of 30 kPa, often by using a high-density () approach to high confinement, taking advantage of a regime known as enhanced D-alpha (EDA) H-mode. In the EDA H-mode, plasma transport regulates both the pedestal profiles and the core impurity content, thus holding the pedestal stationary at just below the peeling-ballooning stability boundary. This stationary ELM-suppressed regime has approached the maximum pedestal predicted by EPED at these densities: 60 kPa. This in turn gives rise to volume-averaged core plasma pressure in excess of 0.2 MPa, a world record value for a magnetic fusion device. Another approach to achieving high pressure utilizes a pedestal limited by current-driven modes at low collisionality, in which pressure increases with density and which allows access to a higher EPED solution, termed ‘super-H’. C-Mod experiments at reduced density () and strong plasma shaping () accessed this regime, producing pedestals with pressures up to 80 kPa (approximately 90% of the ITER target) and temperatures of nearly 2 keV. In a number of these hot H-modes, we observe strong edge instabilities at low toroidal mode number (n = 1) when pedestal pressure approaches predicted values from EPED, showing that current-driven MHD modes can serve as a limit on the pedestal in a metal-walled tokamak at high pressure and low collisionality.

MHD and resonant instabilities in JT-60SA during current ramp-up with off-axis N-NB injection

The excitation of magnetohydrodynamic (MHD) and resonant instabilities and their effect on the plasma profiles during the current ramp-up phase of a beam-driven JT-60SA tokamak plasma is studied using the MHD-PIC hybrid code MEGA. In the simple scenario considered, the plasma is only driven by one negative-ion-based neutral beam, depositing 500 keV deuterons at 5 MW power off-axis at about mid-radius. The beam injection starts half-way in the ramp-up phase. Within 1 s, the beam-driven plasma current and fast ion pressure produce a configuration that is strongly unstable to rapidly growing MHD and resonant modes. Using MEGA, modes with low toroidal mode numbers in the range n = 1–4 are examined in detail and shown to cause substantial changes in the plasma profiles. The necessity to develop reduced models and incorporate the effects of such instabilities in integrated codes used to simulate the evolution of entire plasma discharges is discussed.

Gyrokinetic analysis of low-n shear Alfvén and ion sound wave spectra in a high-beta tokamak plasma

Using the linear gyrokinetic code LIGKA, we study the structure of the continuous spectra of shear Alfvén waves (SAW) and ion sound waves (ISW) in a high-beta JT-60U tokamak plasma and look for evidence of Alfvén acoustic couplings or mode conversion. Here, is the complex local eigenfrequency, ρ is a radial coordinate, and we consider waves with low toroidal mode number . We focus on the frequency range between the beta-induced and toroidicity-induced Alfvén frequency gaps. The real frequencies of the gyrokinetic ISW continua are remarkably similar to MHD results. The kinetic damping rates are of order for , and reduce to when the temperature ratio is raised to . It is shown that SAW and ISW continua can be simultaneously excited with an antenna and that the global response of the ISWs is significantly enhanced when the on-axis beta value is raised from to 3.6% while keeping . In contrast, when the ion temperature is increased such that , ISW branches become undetectable in spite of higher . At the same time, a large part of the SAW continuum is locally destabilized by ion temperature gradients and a set of discrete global modes was found, some of which are weakly damped or unstable and interpreted as kinetic beta-induced Alfvén eigenmodes. It is estimated that the kinetic damping of such low-n Alfvénic modes contributes much more to the anomalous bulk ion heating than the excitation of nearby ISW continua, so that Alfvén acoustic couplings in the frequency band are irrelevant within the scope of the model used.

Stabilizing effects of enhanced resistivity due to lithium-conditioning on low-n edge localized modes in NSTX

The stabilizing effects of enhanced edge resistivity on edge-localized instabilities in high confinement discharges due to lithium-conditioning in the National Spherical Torus Experiment are identified for the first time. Linear stability analysis of the experimentally constrained equilibrium suggests that the change in the equilibrium plasma density and pressure profiles alone due to lithium-conditioning may be insufficient for a complete suppression of low toroidal mode number peeling-ballooning modes. The enhanced resistivity due to the increased effective electric charge number Zeff after lithium-conditioning provides additional stabilization of the edge localized modes. Notably, this stabilizing effect by enhanced edge resistivity becomes evident only in two-fluid magnetohydrodynamic simulations.

Solitary perturbations in the steep boundary of magnetized toroidal plasma

Solitary perturbations (SPs) localized both poloidally and radially are detected within ~100 μs before the partial collapse of the high pressure gradient boundary region (called pedestal) of magnetized toroidal plasma in the KSTAR tokamak device. The SP develops with a low toroidal mode number (typically unity) in the pedestal ingrained with quasi-stable edge-localized mode (QSM) which commonly appears during the inter-collapse period. The SPs have smaller mode pitch and different (often opposite) rotation velocity compared to the QSMs. Similar solitary perturbations are also frequently observed before the onset of complete pedestal collapse, suggesting a strong connection between the SP generation and the pedestal collapse.

Experimental studies of high-confinement mode plasma response to non-axisymmetric magnetic perturbations in ASDEX Upgrade

The interaction of externally applied small non-axisymmetric magnetic perturbations (MP) with tokamak high-confinement mode (H-mode) plasmas is reviewed and illustrated by recent experiments in ASDEX Upgrade. The plasma response to the vacuum MP field is amplified by stable ideal kink modes with low toroidal mode number n driven by the H-mode edge pressure gradient (and associated bootstrap current) which is experimentally evidenced by an observable shift of the poloidal mode number m away from field alignment (m = qn, with q being the safety factor) at the response maximum. A torque scan experiment demonstrates the importance of the perpendicular electron flow for shielding of the resonant magnetic perturbation, as expected from a two-fluid MHD picture. Two significant effects of MP occur in H-mode plasmas at low pedestal collisionality, : (a) a reduction of the global plasma density by up to and (b) a reduction of the energy loss associated with edge localised modes (ELMs) by a factor of up to 9. A comprehensive database of ELM mitigation pulses at low in ASDEX Upgrade shows that the degree of ELM mitigation correlates with the reduction of pedestal pressure which in turn is limited and defined by the onset of ELMs, i. e. a modification of the ELM stability limit by the magnetic perturbation.

Sensitivity study for N-NB-driven modes in JT-60U: boundary, diffusion, gyroaverage, compressibility

The sensitivity of the growth and nonlinear evolution of fast-ion-driven modes is examined with respect to the choice of particle boundary conditions, diffusion coefficients, fast ion gyroradii and bulk compressibility. The primary purpose of this work is to justify the choice of parameters to be used in the self-consistent long-time simulations of fast ion dynamics using global MHD-kinetic hybrid codes that include fast ion sources and collisions. The present study is conducted for a scenario based on the N-NB-driven JT-60U shot E039672, which is subject to abrupt large events (ALE). We use realistic geometry, a realistic fast ion distribution, and focus on experimentally observed harmonics with low toroidal mode numbers n = 1, 2, 3. The use of realistic boundary conditions and finite Larmor radii for the fast ions is shown to be essential. The usual values used for resistivity, viscosity and thermal diffusivity, and used for the specific heat ratio (controlling the effect of compressibility) are shown to be reasonable choices. Our method for performing the parameter scans around the threshold for the onset of convective amplification is proposed as a strategy for nonlinear benchmark studies.

Orbit-based analysis of nonlinear energetic ion dynamics in tokamaks. I. Effective mode number profile and resonant frequency tracking

The nonlinear interactions between shear Alfvén modes and tangentially injected beam ions in the 150–400 keV range are studied numerically in a JT-60U tokamak scenario with realistic geometry, large magnetic drifts, and strong beam drive. For this purpose, the recently developed orbit-based resonance analysis (ORA) method for circulating particles is extended, so that it can be applied to the nonlinear regime, where the spectrum of orbit-based poloidal mode numbers morb varies in time as the fast ions undergo wave-particle trapping and radial transport. In particular, the extended ORA method captures the effect of nonlinear overlaps between resonances associated with neighboring harmonics (morb,n) and (morb+1,n) that cause long-distance ballistic transport. Two cases with low toroidal mode numbers n≳1 are studied: an n = 1 mode without resonance overlap and a strongly driven n = 3 mode with resonance overlap. For both cases, an effective radial profile of the resonant poloidal mode number mres=Meff(r) is computed and used to track the effective resonant frequency ωres(t) of individual particles during their radial motion r(t). In Paper II, this frequency tracking technique will be applied to study the nonlinear frequency chirping and convective amplification of the modes.

Orbit-based analysis of nonlinear energetic ion dynamics in tokamaks. II. Mechanisms for rapid chirping and convective amplification

The nonlinear interactions between shear Alfvén modes and tangentially injected beam ions in the 150–400 keV range are studied numerically in realistic geometry for a JT-60U tokamak scenario. In Paper I, which was reported in the companion paper, the recently developed orbit-based resonance analysis method was used to track the resonant frequency of fast ions during their nonlinear evolution subject to large magnetic and electric drifts. Here, that method is applied to map the wave-particle power transfer from the canonical guiding center phase space into the frequency-radius plane, where it can be directly compared with the evolution of the fluctuation spectra of fast-ion-driven modes. Using this technique, we study the nonlinear dynamics of strongly driven shear Alfvén modes with low toroidal mode numbers n = 1 and n = 3. In the n = 3 case, both chirping and convective amplification can be attributed to the mode following the resonant frequency of the radially displaced particles, i.e., the usual one-dimensional phase locking process. In the n = 1 case, a new chirping mechanism is found, which involves multiple dimensions, namely, wave-particle trapping in the radial direction and phase mixing across velocity coordinates.