I-mode Regime Research Articles

Experimental evidence for the drift wave nature of the weakly coherent mode in ASDEX Upgrade I-mode plasmas

The improved energy confinement mode (I-mode) is a potential candidate for future fusion power plants, as it combines ELM-free operation with good confinement. The unusual edge transport and turbulence in this regime is still not fully understood. This study analyzes the turbulent structure of the weakly coherent mode (WCM) in ASDEX Upgrade. Measurements from Doppler back-scattering and a thermal helium beam diagnostic are used to determine velocities of the background plasma and the WCM over multiple discharges. A phase velocity of the WCM of the order of 2–5 km s−1 in the electron diamagnetic drift direction is found, quantitatively close to a drift wave assuming negligible temperature fluctuations. A good agreement with a previously proposed mechanism behind the I-mode regime is observed. This marks the first experimental verification of a specific understanding of the WCM and the I-mode regime.

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.

Edge turbulence measurements in L-mode and I-mode at ASDEX Upgrade

The I-mode confinement regime is promising for future reactor operation due to high energy confinement without high particle confinement. However, the role of edge turbulence in creating I-mode's beneficial transport properties is still unknown. New measurements of edge turbulence (ρpol=0.9−1.0) in L-modes and I-modes at low and high densities at ASDEX Upgrade are presented in this paper. A high radial resolution correlation electron cyclotron emission radiometer measures the broadband turbulence throughout the L-mode and I-mode edge and pedestal. The weakly coherent mode (WCM) is measured in both L-mode and I-mode near the last closed flux surface with Te fluctuation levels of 2.3%–4.2%, with a frequency shift between the two phases related to a deeper Er well in I-mode. An neTe phase diagnostic captures a change of the WCM neTe phase between L-mode and I-mode from −171° to −143°. The thermal He beam diagnostic measures a WCM wavenumber range of −0.5 to −1.0 cm−1. A low-frequency edge oscillation (LFEO) appears in the I-mode phase of these discharges and displays coupling to the WCM, but the LFEO does not appear in the L-mode phase. Linear gyrokinetic simulations of the outer core and pedestal top turbulence indicate that while the dominant turbulent modes in the outer core are ion directed and electrostatic, the turbulence becomes increasingly electron directed and electromagnetic with increasing radius. Collisionality is not found to impact characteristics of the L-mode and I-mode edge turbulence with respect to the presence of the WCM; however, the quality of global confinement decreases with collisionality.

I-mode in non-deuterium plasmas in ASDEX Upgrade

The I-mode confinement regime in non-deuterium plasmas has been investigated in the ASDEX Upgrade tokamak. We report the first experimental observations on the existence and the main characteristics of this regime in hydrogen and helium plasmas and compare them with deuterium I-modes. Hydrogen features a higher power threshold to enter I-mode and a higher electron edge pressure at the L- to I-mode transition with respect to deuterium. Furthermore, all the hydrogen I-modes obtained exhibit pedestal relaxation events (PRE). The I-mode power window in hydrogen is found to be 2–3 times larger than in deuterium. This property allows a better characterization of PRE and to differentiate them from type-III ELMs. Helium I-modes feature properties which are similar to those of deuterium I-modes. The analysis on the minimum of the edge radial electric field E r shows a correlation between the E r minimum, the net input power and the ion diamagnetic term in the ion radial force balance. Indications of the dominant role of the edge ion temperature in the evolution of the radial electric field with increasing input power are also reported.

I-mode pedestal relaxation events at ASDEX Upgrade

The I-mode confinement regime can feature small edge temperature drops that can lead to an increase in the energy deposited onto the divertor targets. In this work, we show that these events are associated with a relaxation of both electron temperature and density edge profiles, with the largest drop found at the pedestal top position. The relative energy loss is about 1 %, and is thus lower than that of type-I ELMs for the same pedestal top collisionality. Stability analysis of edge profiles reveals that the operational points are far from the ideal peeling-ballooning boundary. Also, we show that these events appear close to the H-mode transition in the typical I-mode operational space in ASDEX Upgrade, and that no further enhancement of energy confinement is found when they occur. Moreover, scrape-off layer transport during these events is found to be very similar to type-I ELMs, with regard to timescales (≈ 800 µs), filament propagation, toroidally asymmetric energy effluxes at the midplane and asymmetry between inner and outer divertor deposited energy. In particular, the latter reveals that more energy reaches the outer divertor target. Lastly, first measurements of the divertor peak energy fluence are reported, and projections to ARC—a reactor that could potentially operate in I-mode—are drawn.

Physical mechanism behind and access to the I-mode confinement regime in tokamaks

The I-mode is an attractive confinement regime for future tokamak based fusion reactors. A model is presented which explains the I-mode regime by the reduction of ITG turbulence near the separatrix at low collisionality, where the separatrix ion temperature can exceed the electron temperature. Drift-Alfvén-turbulence develops, with large and small-scale fluctuations being suppressed by phase randomization and finite-Larmor-radius effects, respectively. The intermediate scales form a broad peak in the frequency spectrum, which features the same properties as the characteristic weakly coherent mode. The model, which is studied by means of gyro-fluid simulations, reproduces a number of other experimental I-mode observations, such as decoupled energy and particle transport, intermittent turbulent bursts with precursors, an operational window widening with magnetic field strength, and the challenges met when detaching the plasma.

Power threshold and confinement of the I-mode in the EAST tokamak

Sixty-five discharges have been confirmed as I-mode discharges after searching the EAST database from 2016 to 2018, and some additional I-mode discharges were obtained in 2019. The I-mode regime features no edge localized modes (ELMs), high energy confinement, and a steep temperature pedestal, while particle confinement remains at L-mode levels. The I-mode regime has been obtained over a small parameter space (BT = 2.4 – 2.7 T, Ip = 0.4 – 0.6 MA, q95 = 4 – 6) using a configuration with drift away from the active X-point. Most of the discharges in EAST are dominated by lower hybrid wave (LHW) heating. In addition, some are heated with both LHW and neutral beam injection (NBI) heating, and a few discharges are heated by NBI and electron cyclotron resonance heating (ECRH). Turbulence suppression in density perturbation has been defined as signaling the onset of the L-I transition. The power threshold of the I-mode is slightly larger than that of the 2008 ITPA scaling law of H-mode. The minimum L-I power threshold varies only weakly with BT, and the power range for the I-mode increases with increasing BT. The I-mode is superior to the L-mode in terms of energy confinement but is still slightly inferior to the H-mode under similar conditions, although the energy confinement time decreases more slowly with increasing heating power than it does in the typical H-mode case. NBI has some benefit for achieving higher confinement. The I-mode is very sensitive to the density near the edge. Under a constant high heating power, a small enhancement in the density will terminate the I-mode, sometimes leading to the I-H transition.

Experimental energy confinement time scaling with dimensionless parameters in C-Mod I-mode plasmas

The dependence of energy confinement time on gyroradius, , and normalized collisionality in I-mode plasmas is investigated through dedicated C-Mod experiments scanning dimensionless parameters with constant safety factor. The gyroradius scaling is calculated to be , which suggests core transport may scale with gyro–Bohm physics, indicating favorable extrapolation of the I-mode regime to future devices at low . The scaling exponent for is calculated to be small, but positive (), and the exponent for is deemed inconclusive () due to high correlation with the other two dimensionless variables in the dataset, and therefore requires further investigation. The individual dimensionless parameter scaling is compared to calculations from larger C-Mod I-mode datasets as well as multi-machine scaling laws for ELMy H-mode and L-mode plasmas. Multiple regression techniques and principal component analysis are used to clarify the single parameter scalings and analyze parameter significance within the dataset.

Radiative heat exhaust in Alcator C-Mod I-mode plasmas

In order to more completely demonstrate the I-mode regime as a compelling fusion reactor operating scenario, the first dedicated attempts at I-mode radiative heat exhaust and detachment were carried out on Alcator C-Mod. Results conclusively show that within the parameter space explored, an I/L back-transition is triggered prior to meaningful reductions in parallel heat flux, , target temperature, and target pressure, at the outer divertor. The exact mechanism for the I/L trigger remains uncertain, but a multi-diagnostic investigation suggests the pedestal regulation physics is impacted promptly by small amounts of N2 seeded into the private flux region. The time delay between when N2 contacts the plasma and the I/L transition is triggered varied from 30–120 ms, approximately 0.7–, and the delay varied inversely with I-mode pedestal-top pressure, p e,95. Power and nitrogen influx scans indicate that the I/L transitions are not linked to excessive bulk-plasma impurity radiation. It is also shown that in the subsequent L-mode following nitrogen seeding, and can be reduced by factors of 10. The I/L transition and L-mode exhaust results using N2 are compared to similar attempts using Ne where such and reductions in L-mode are limited to factors of 2–3. Implications for the I-mode regime are discussed, including needs for follow-up experiments on other facilities.

Verification of GENE and GYRO with L-mode and I-mode plasmas in Alcator C-Mod

Verification comparisons are carried out for L-mode and I-mode plasma conditions in Alcator C-Mod. We compare linear and nonlinear ion-scale calculations by the gyrokinetic codes GENE and GYRO to each other and to the experimental power balance analysis. The two gyrokinetic codes' linear growth rates and real frequencies are in good agreement throughout all the ion temperature gradient mode branches and most of the trapped electron mode branches of the kyρs spectra at r/a = 0.65, 0.7, and 0.8. The shapes of the toroidal mode spectra of heat fluxes in nonlinear simulations are very similar for kyρs ≤ 0.5, but in most cases GENE has a relatively higher heat flux than GYRO at higher mode numbers. The ratio of ion to electron heat flux is similar in the two codes' simulations, but the heat fluxes themselves do not agree in almost all cases. In the I-mode regime, GENE's heat fluxes are ∼3 times those from GYRO, and they are ∼60%–100% higher than GYRO in the L-mode conditions. The GYRO under-prediction of Qe is much reduced in GENE's L-mode simulations, and it is eliminated in the I-mode simulations. This largely improved agreement with the experimental electron heat flux is offset, however, by the large overshoot of GENE's ion heat fluxes, which are 2–3 times the experimental level, and its electron heat flux overshoot at r/a = 0.80 in the I-mode. Rotation effects can explain part of the difference between the two codes' predictions, but very significant differences remain in simulations without any rotation effects.

Physics and performance of the I-mode regime over an expanded operating space on Alcator C-Mod

New results on the I-mode regime of operation on the Alcator C-Mod tokamak are reported. This ELM-free regime features high energy confinement and a steep temperature pedestal, while particle confinement remains at L-mode levels, giving stationary density and avoiding impurity accumulation. I-mode has now been obtained over nearly all of the magnetic fields and currents possible in this high field tokamak (Ip 0.55–1.7 MA, BT 2.8–8 T) using a configuration with B × ∇B drift away from the X-point. Results at 8 T confirm that the L–I power threshold varies only weakly with BT, and that the power range for I-mode increases with BT; no 8 T discharges transitioned to H-mode. Parameter dependences of energy confinement are investigated. Core transport simulations are giving insight into the observed turbulence reduction, profile stiffness and confinement improvement. Pedestal models explain the observed stability to ELMs, and can simulate the observed weakly coherent mode. Conditions for I–H transitions have complex dependences on density as well as power. I-modes have now been maintained in near-DN configurations, leading to improved divertor power flux sharing. Prospects for I-mode on future fusion devices such as ITER and ARC are encouraging. Further experiments on other tokamaks are needed to improve confidence in extrapolation.

The I-mode confinement regime at ASDEX Upgrade: global properties and characterization of strongly intermittent density fluctuations

Properties of the I-mode confinement regime on the ASDEX Upgrade tokamak are summarized. A weak dependence of the power threshold for the L-I transition on the toroidal magnetic field strength is found. During improved confinement, the edge radial electric field well deepens. Stability calculations show that the I-mode pedestal is peeling-ballooning stable. Turbulence investigations reveal strongly intermittent density fluctuations linked to the weakly coherent mode in the confined plasma, which become stronger as the confinement quality increases. Across all investigated structure sizes (–12 cm−1, with the perpendicular wavenumber of turbulent density fluctuations), the intermittent turbulence bursts are observed. Comparison with bolometry data shows that they move poloidally toward the X-point and finally end up in the divertor. This might be indicative that they play a role in inhibiting the density profile growth, such that no pedestal is formed in the edge density profile.

Multi-device studies of pedestal physics and confinement in the I-mode regime

This paper describes joint ITPA studies of the I-mode regime, which features an edge thermal barrier together with L-mode-like particle and impurity transport and no edge localized modes (ELMs). The regime has been demonstrated on the Alcator C-Mod, ASDEX Upgrade and DIII-D tokamaks, over a wide range of device parameters and pedestal conditions. Dimensionless parameters at the pedestal show overlap across devices and extend to low collisionality. When they are matched, pedestal temperature profiles are also similar. Pedestals are stable to peeling–ballooning modes, consistent with lack of ELMs. Access to I-mode is independent of heating method (neutral beam injection, ion cyclotron and/or electron cyclotron resonance heating). Normalized energy confinement H98,y2 ⩾ 1 has been achieved for a range of 3 ⩽ q95 ⩽ 4.9 and scales favourably with power. Changes in turbulence in the pedestal region accompany the transition from L-mode to I-mode. The L–I threshold increases with plasma density and current, and with device size, but has a weak dependence on toroidal magnetic field BT. The upper limit of power for I-modes, which is set by I–H transitions, increases with BT and the power range is largest on Alcator C-Mod at B > 5 T. Issues for extrapolation to ITER and other future fusion devices are discussed.

Turbulence intermittency linked to the weakly coherent mode in ASDEX Upgrade I-mode plasmas

This letter shows for the first time a pronounced increase of extremely intermittent edge density turbulence behavior inside the confinement region related to the I-mode confinement regime in the ASDEX Upgrade tokamak. With improving confinement, the perpendicular propagation velocity of density fluctuations in the plasma edge increases together with the intermittency of the observed density bursts. Furthermore, it is shown that the weakly coherent mode, a fluctuation feature generally observed in I-mode plasmas, is connected to the observed bursts. It is suggested that the large amplitude density bursts could be generated by a non-linearity similar to that in the Korteweg–de-Vries equation which includes the radial temperature gradient.

Characterization of density fluctuations during the search for an I-mode regime on the DIII-D tokamak

The I-mode regime, routinely observed on the Alcator C-Mod tokamak, is characterized by an edge energy transport barrier without an accompanying particle barrier and with broadband instabilities, known as weakly coherent modes (WCM), believed to regulate particle transport at the edge.Recent experiments on the DIII-D tokamak exhibit I-mode characteristics in various physical quantities.These DIII-D plasmas evolve over long periods, lasting several energy confinement times, during which the edge electron temperature slowly evolves towards an H-mode-like profile, while maintaining a typical L-mode edge density profile. During these periods, referred to as I-mode phases, the radial electric field at the edge also gradually reaches values typically observed in H-mode.Density fluctuations measured with the phase contrast imaging diagnostic during I-mode phases exhibit three features typically observed in H-mode on DIII-D, although they develop progressively with time and without a sharp transition: the intensity of the fluctuations is reduced; the frequency spectrum is broadened and becomes non-monotonic; two dimensional space-time spectra appear to approach those in H-mode, showing phase velocities of density fluctuations at the edge increasing to about 10 km s−1. However, in DIII-D there is no clear evidence of the WCM.Preliminary linear gyro-kinetic simulations are performed in the pedestal region with the GS2 code and its recently upgraded model collision operator that conserves particles, energy and momentum. The increased bootstrap current and flow shear generated by the temperature pedestal are shown to decrease growth rates, thus possibly generating a feedback mechanism that progressively stabilizes fluctuations.

Fluctuating zonal flows in the I-mode regime in Alcator C-Mod

Velocity fields and density fluctuations of edge turbulence are studied in I-mode [F. Ryter et al., Plasma Phys. Controlled Fusion 40, 725 (1998)] plasmas of the Alcator C-Mod [I. H. Hutchinson et al., Phys. Plasmas 1, 1511 (1994)] tokamak, which are characterized by a strong thermal transport barrier in the edge while providing little or no barrier to the transport of both bulk and impurity particles. Although previous work showed no clear geodesic-acoustic modes (GAM) on C-Mod, using a newly implemented, gas-puff-imaging based time-delay-estimate velocity inference algorithm, GAM are now shown to be ubiquitous in all I-mode discharges examined to date, with the time histories of the GAM and the I-mode specific [D. Whyte et al., Nucl. Fusion 50, 105005 (2010)] Weakly Coherent Mode (WCM, f = 100–300 kHz, Δf/f≈0.5, and kθ≈1.3 cm−1) closely following each other through the entire duration of the regime. Thus, the I-mode presents an example of a plasma state in which zero frequency zonal flows and GAM continuously coexist. Using two-field (density-velocity and radial-poloidal velocity) bispectral methods, the GAM are shown to be coupled to the WCM and to be responsible for its broad frequency structure. The effective nonlinear growth rate of the GAM is estimated, and its comparison to the collisional damping rate seems to suggest a new view on I-mode threshold physics.

Threshold conditions for transitions to I-mode and H-mode with unfavourable ion grad B drift direction

Transitions from the L-mode regime to the I-mode regime, with an energy transport barrier, and to the H-mode regime with both an energy and particle transport barrier are studied on the Alcator C-Mod tokamak. Steady I-mode plasmas have been produced over a wide range of plasma field (3–6 T), current (0.8–1.35 MA), density and shaping in the unfavourable ion B × ∇B configuration. The power threshold for the L–I transition is higher than scalings for the L–H transition with favourable drift, and increases with plasma current as well as density. Threshold conditions for the I–H transition are more variable. In some conditions I-mode is maintained up to the maximum available ICRF power of 5 MW, nearly a factor of two above the L–I threshold, giving a robust operating window. Edge Te at the L–I transition is in the range 250–450 eV, over a range of current and density, about a factor of two higher than with favourable drift, while at the I–H transition it can be much higher (up to 1.1 keV) but is again widely variable. Heat pulses due to sawteeth may play a role in transitions. Controlled I–L back transitions indicate little power hysteresis.

Edge energy transport barrier and turbulence in the I-mode regime on Alcator C-Mod

We report extended studies of the I-mode regime [Whyte et al., Nucl. Fusion 50, 105005 (2010)] obtained in the Alcator C-Mod tokamak [Marmar et al., Fusion Sci. Technol. 51(3), 3261 (2007)]. This regime, usually accessed with unfavorable ion B × ∇B drift, features an edge thermal transport barrier without a strong particle transport barrier. Steady I-modes have now been obtained with favorable B × ∇B drift, by using specific plasma shapes, as well as with unfavorable drift over a wider range of shapes and plasma parameters. With favorable drift, power thresholds are close to the standard scaling for L–H transitions, while with unfavorable drift they are ∼ 1.5–3 times higher, increasing with Ip. Global energy confinement in both drift configurations is comparable to H-mode scalings, while density profiles and impurity confinement are close to those in L-mode. Transport analysis of the edge region shows a decrease in edge χeff, by typically a factor of 3, between L- and I-mode. The decrease correlates with a drop in mid-frequency fluctuations (f ∼ 50–150 kHz) observed on both density and magnetics diagnostics. Edge fluctuations at higher frequencies often increase above L-mode levels, peaking at f ∼ 250 kHz. This weakly coherent mode is clearest and has narrowest width (Δf/f ∼ 0.45) at low q95 and high Tped, up to 1 keV. The Er well in I-mode is intermediate between L- and H-mode and is dominated by the diamagnetic contribution in the impurity radial force balance, without the Vpol shear typical of H-modes.

I-mode: an H-mode energy confinement regime with L-mode particle transport in Alcator C-Mod

An improved energy confinement regime, I-mode, is studied in Alcator C-Mod, a compact high-field divertor tokamak using ion cyclotron range of frequencies (ICRFs) auxiliary heating. I-mode features an edge energy transport barrier without an accompanying particle barrier, leading to several performance benefits. H-mode energy confinement is obtained without core impurity accumulation, resulting in reduced impurity radiation with a high-Z metal wall and ICRF heating. I-mode has a stationary temperature pedestal with edge localized modes typically absent, while plasma density is controlled using divertor cryopumping. I-mode is a confinement regime that appears distinct from both L-mode and H-mode, combining the most favourable elements of both. The I-mode regime is investigated predominately with ion ∇B drift away from the active X-point. The transition from L-mode to I-mode is primarily identified by the formation of a high temperature edge pedestal, while the edge density profile remains nearly identical to L-mode. Laser blowoff injection shows that I-mode core impurity confinement times are nearly identical with those in L-mode, despite the enhanced energy confinement. In addition, a weakly coherent edge MHD mode is apparent at high frequency ∼100–300 kHz which appears to increase particle transport in the edge. The I-mode regime has been obtained over a wide parameter space (B T = 3–6 T, I p = 0.7–1.3 MA, q 95 = 2.5–5). In general, the I-mode exhibits the strongest edge temperature pedestal (T ped) and normalized energy confinement (H 98 > 1) at low q 95 (<3.5) and high heating power (P heat > 4 MW). I-mode significantly expands the operational space of edge localized mode (ELM)-free, stationary pedestals in C-Mod to T ped ∼ 1 keV and low collisionality , as compared with EDA H-mode with T ped < 0.6 keV, . The I-mode global energy confinement has a relatively weak degradation with heating power; leading to increasing H 98 with heating power.

High confinement and high density with stationary plasma energy and strong edge radiation cooling in the upgraded Torus Experiment for Technology Oriented Research (TEXTOR-94)

An overview of the results obtained so far for the radiative I-mode regime on the upgraded Torus Experiment for Technology Oriented Research (TEXTOR-94) [Proceedings of the 16th IEEE Symposium on Fusion Engineering (Institute of Electrical and Electronics Engineers, Piscataway, NJ, 1995), Vol. 1, p. 470] is given. This regime is obtained under quasistationary conditions with edge neon seeding in a pumped limiter tokamak with circular cross section. It combines high confinement and high β (up to a normalized beta, βn=2) with low edge q values (down to qa=2.8) and high density even above the Greenwald limit together with dominant edge radiative heat exhaust, and therefore shows promise for the future of fusion research. Bulk and edge properties of these discharges are described, and a detailed account is given of the energy and particle confinement and their scaling. Energy confinement scales linearly with density as for the nonsaturated Ohmic Neo-Alcator scaling, but the usual degradation with total power remains. No deleterious effects of the neon seeding on fusion reactivity and plasma stability have been observed.