Negative Central Magnetic Shear Research Articles

Predictive modeling of operation scenarios with negative central magnetic shear and large-radius ITBs on EAST

Negative central magnetic shear or magnetic shear reversal is an attractive aspect for advanced operation scenarios in tokamaks as it suppresses turbulence and facilitates the formation of internal transport barriers (ITBs). The advanced operation scenario with negative magnetic shear, which is associated with high confinement quality, a large bootstrap fraction, ITBs, and so on, is one of the future goals of the experiments on EAST. In this work, modeling efforts have been made to find the operation regimes on EAST with negative central shear and large-radius ITBs. The modeling results indicate that negative central shear and large-radius ITBs can be achieved when the electron density is 〈ne〉/nG > 0.7 and the off-axis deposited electron cyclotron heating (ECH) power is 2 MW. Additionally, scenarios with lower ECH power (∼1.5 MW) have been studied since at present, the maximum ECH power that can be provided on EAST is 1.5 MW. With a lower off-axis ECH power of 1.5 MW, scenarios with negative central shear and large-radius ITBs but with a higher electron density of 〈ne〉/nG > 0.8 are obtained. The same as the first case, if the electron density is reduced to 〈ne〉/nG = 0.8 in this case, large-radius ITBs disappeared in the predicted scenario. This reveals that high electron density and large off-axis deposited ECH power are important for scenarios that have q-profiles with negative central shear and large-radius ITBs since lower hybrid current drive (LHCD) tends to peak near the axis at lower electron density, and hence, it helps to increase the temperature gradient near the axis, which will promote bootstrap in this region, leading to a centrally peaked total current density profile. Higher off-axis deposited ECH power helps to obtain scenarios with strong negative central shear and large-radius ITBs at a lower density. Scenarios predicted in this work will guide future experiments on EAST.

Robust control of q-profile and βp using data-driven models on EAST

• A novel H ∞ robust control scheme is developed for the current profile control using data-driven models. • A decoupling technique enables the control scheme to exhibit multi-functional characteristics. • An anti-windup technique can compensate the effects from moderate time-delays and actuator dynamics. • An efficient procedure is provided to support the H-mode steady-state operation on EAST. • Three general performance indexes are proposed to characterize the current profile control performance. A new robust feedback controller for the safety factor profile and poloidal plasma pressure parameter has been developed using a two-time-scale data-driven model. The model describes the linear plasma responses of the ι profile and β p with respect to auxiliary heating & current drive (H&CD) powers, around a typical plasma equilibrium in an H-mode steady-state plasma discharge on EAST. The feedback controller comprises a carefully designed low-pass filter for the timescale separation, a decoupling module and three local controllers synthesized from the H ∞ norm optimization and the singular value decomposition. The actuators are the lower hybrid current drive (LHCD) system at 4.6 GHz and the ion cyclotron resonance heating (ICRH) system at 33 MHz. Taking into account the actuation dynamics, an anti-windup technique is employed to condition the controller online aiming to attenuate the negative effects from moderate time delays and power saturations. Extensive nonlinear closed-loop simulations with the METIS code suggest that high β p and negative central magnetic shear that characterize advanced tokamak plasma scenarios can be achieved and sustained on EAST with good tracking performance and reasonable robustness via the proposed control scheme. The feedback control of the core ι profile and β p with a range of time delays, power saturations and varying weighting functions are evaluated numerically, compared and discussed. The control robustness to plasma parameter uncertainties including the line-averaged plasma density 〈 n ¯ e 〉 , the H-mode enhancement factor H factor and the effective charge number Z eff are assessed and analyzed.

Transport modeling of the DIII-D high scenario and extrapolations to ITER steady-state operation

Transport modeling of a proposed ITER steady-state scenario based on DIII-D high poloidal-beta () discharges finds that ITB formation can occur with either sufficient rotation or a negative central shear q-profile. The high scenario is characterized by a large bootstrap current fraction (80%) which reduces the demands on the external current drive, and a large radius internal transport barrier which is associated with excellent normalized confinement. Modeling predictions of the electron transport in the high scenario improve as approaches levels similar to typical existing models of ITER steady-state and the ion transport is turbulence dominated. Typical temperature and density profiles from the non-inductive high scenario on DIII-D are scaled according to 0D modeling predictions of the requirements for achieving a steady-state fusion gain in ITER with ‘day one’ heating and current drive capabilities. Then, TGLF turbulence modeling is carried out under systematic variations of the toroidal rotation and the core q-profile. A high bootstrap fraction, high scenario is found to be near an ITB formation threshold, and either strong negative central magnetic shear or rotation in a high bootstrap fraction are found to successfully provide the turbulence suppression required to achieve .

An efficient technique for magnetic equilibrium reconstruction with q profile constraints and its application on the EAST tokamak

An efficient technique for building plasma equilibria with preset or constrained q profiles by solving the nonlinear Grad–Shafranov equation iteratively is proposed. The technique uses a set of dynamic virtual poloidal field probes in the plasma core region. Numerical examples are shown for monotonic q profiles and negative central magnetic shear equilibria which are obtained with this technique. As a proof of principle, the technique is applied on the EAST tokamak, to constrain the plasma equilibrium reconstruction with the experimental q = 1 surface information from the ECE diagnostic in addition to the external magnetic measurements.

Magnetic shear effects on plasma transport and turbulence at high electron to ion temperature ratio in DIII-D and JT-60U plasmas

Negative magnetic shear has been demonstrated in DIII-D and JT-60U to mitigate the confinement degradation typically observed with increasing the electron to ion temperature ratio (Te/Ti). In recent experiments in DIII-D negative central magnetic shear (NCS) discharges, the thermal transport in the internal transport barrier formed around the radius of the minimum safety factor (qmin) remained almost constant and modestly increased in the region outside of qmin compared to the positive shear (PS) case, when Te/Ti increased from about 0.8 to 1.1 through electron cyclotron heating (ECH). The benefit of NCS extending into the region outside of qmin can be explained by the lower magnetic shear in the NCS plasma over the plasma radius relative to the PS plasma. Reduced confinement degradation at high Te/Ti with NCS plasmas was commonly observed in DIII-D and JT-60U. The mechanism of the different transport responses between the NCS and PS plasmas has been assessed in terms of fluctuation measurements and gyrokinetic simulations in DIII-D; NCS gave a smaller rise in the low-wavenumber broadband turbulent fluctuations with the increase in Te/Ti compared with the PS case. This is consistent with gyrokinetic simulations, which show a smaller rise in the growth rates of the ion temperature gradient mode in the NCS plasmas, with increasing Te/Ti. Gyrokinetic simulations also showed a change in the stability of the electron modes with ECH applied, consistent with higher-wavenumber fluctuation measurements, although more detailed simulations are needed to give a quantitative explanation for the experimental observations. Control of q-profile and magnetic shear will allow confinement improvement in future machines with dominant electron heating.

Localized Turbulence Suppression and Increased Flow Shear near theq=2Surface during Internal-Transport-Barrier Formation

Broadband turbulent fluctuations in the plasma density are transiently suppressed when low-order rational q surfaces first appear in negative central magnetic shear plasmas on the DIII-D tokamak, which can lead to the formation of internal transport barriers. Increased localized flow shear is simultaneously observed. It transiently exceeds the measured turbulence decorrelation rate, providing a mechanism to trigger the formation of the transport barrier. This increased flow shear and turbulence suppression propagates radially outward, following the q=2 surface.

Access to sustained high-beta with internal transport barrier and negative central magnetic shear in DIII-D

High values of normalized β (βN∼4) and safety factor (qmin∼2) have been sustained simultaneously for ∼2s in DIII-D [J.L. Luxon, Nucl. Fusion 42, 64 (2002)], suggesting a possible path to high fusion performance, steady-state tokamak scenarios with a large fraction of bootstrap current. The combination of internal transport barrier and negative central magnetic shear at high β results in high confinement (H89P>2.5) and large bootstrap current fraction (fBS>60%) with good alignment. Previously, stability limits in plasmas with core transport barriers have been observed at moderate values of βN (<3) because of the pressure peaking which normally develops from improved core confinement. In recent DIII-D experiments, the internal transport barrier is clearly observed in the electron density and in the ion temperature and rotation profiles at ρ∼0.5 but not in the electron temperature profile, which is very broad. The misalignment of Ti and Te gradients may help to avoid a large local pressure gradient. Furthermore, at low internal inductance ∼0.6, the current density gradients are close to the vessel and the ideal kink modes are strongly wall-coupled. Simultaneous feedback control of both external and internal sets of n=1 magnetic coils was used to maintain optimal error field correction and resistive wall mode stabilization, allowing operation above the free-boundary β limit. Large particle orbits at high safety factor in the core help to broaden both the pressure and the beam-driven current profiles, favorable for steady-state operation. At plasma current flat top and β∼5%, a noninductive current fraction of ∼100% has been observed. Stability modeling shows the possibility for operation up to the ideal-wall limit at β∼6%.

Transport and Stability Studies in Negative Central Shear Advanced Tokamak Plasmas

Achieving high performance for long duration is a key goal of advanced tokamak research around the world. To this end, tokamak experiments are focusing on obtaining (a) a high fraction of well-aligned noninductive plasma current, (b) internal transport barriers (ITBs) in the ion and electron transport channels over a wide radial region with transport approaching neoclassical values, and (c) control of resistive wall modes and neoclassical tearing modes that limit the achievable beta. A current profile that yields a negative central magnetic shear (NCS) in the core is consistent with this focus; NCS is conducive for obtaining ITBs, a high degree of bootstrap current alignment, and reaching the second stability region for ideal ballooning modes, while being stable to ideal kink modes at high beta with wall stabilization and neoclassical tearing modes in the core NCS region. Much progress has been made in obtaining advanced performance in several tokamaks through an increasing understanding of the stability and transport properties of tokamak plasmas. Radio-frequency and neutral beam current drive scenarios are routinely developed and implemented in experiments to access new advanced regimes and control plasma profiles. Short-duration and sustained ITBs have been obtained in the ion and electron channels. The formation of an ITB is attributable to the stabilization of ion and electron temperature gradient and trapped electron modes by the negative shear and by the enhanced E × B flow shear rate and rarefaction of resonant surfaces near the rational qmin values. The progress in understanding the underlying physics in such plasmas and the development of techniques and technology would be of interest in stellarator efforts.

Overview of physics basis for ITER

ITER will be the first magnetic confinement device with burning DT plasma and fusion power of about 0.5 GW. Parameters of ITER plasma have been predicted using methodologies summarized in the ITER Physics Basis (1999 Nucl. Fusion 39 2175). During the past few years, new results have been obtained that substantiate confidence in achieving Q ⩾ 10 in ITER with inductive H-mode operation. These include achievement of a good H-mode confinement near the Greenwald density at high triangularity of the plasma cross section; improvements in theory-based confinement projections for the core plasma, even though further studies are needed for understanding the transport near the plasma edge; improvement in helium ash removal due to the elastic collisions of He atoms with D/T ions in the divertor predicted by modelling; demonstration of feedback control of neoclassical tearing modes and resultant improvement in the achievable β-values; better understanding of edge localized mode (ELM) physics and development of ELM mitigation techniques; and demonstration of mitigation of plasma disruptions. ITER will have a flexibility to operate also in steady-state and intermediate (hybrid) regimes. The ‘advanced tokamak’ regimes with weak or negative central magnetic shear and internal transport barriers are considered as potential scenarios for steady-state operation. The paper concentrates on inductively driven plasma performance and discusses requirements for steady-state operation in ITER.

Integrated, advanced tokamak operation on DIII-D

Recent experiments on DIII-D have demonstrated the ability to sustain plasma conditions that integrate and sustain the key ingredients of advanced tokamak (AT) operation: high β with 1.5<q min <2.5, good energy confinement, and high current drive efficiency. Utilizing off-axis (ρ = 0.4) electron cyclotron current drive (ECCD) to modify the current density profile in a plasma operating near the no-wall ideal stability limit with q min >2.0, plasmas with β≈2.9% and 90% of the plasma current driven non-inductively have been sustained for nearly 2 s (limited only by the duration of the ECCD pulse). Negative central magnetic shear is produced by the ECCD, leading to the formation of a weak internal transport barrier even in the presence of Type I ELMs. Separate experiments have demonstrated the ability to sustain a steady current density profile using ECCD for periods as long as 1 s with β = 3.3% and >90% of the current driven non-inductively. In addition, stable operation well above the ideal no-wall β limit has been sustained for several energy confinement times with the duration only limited by resistive relaxation of the current profile to an unstable state. Stability analysis indicates that the experimental β limit depends on the degree to which the no-wall limit can be exceeded and weakly on the actual no-wall limit. Achieving the necessary density levels required for adequate ECCD efficiency requires active divertor exhaust and reducing the wall inventory buildup prior to the high performance phase. Simulation studies indicate that the successful integration of high β operation with current profile control consistent with these experimental results should result in high β, fully non-inductive plasma operation.

Modification of the current profile in high-performance plasmas using off-axis electron-cyclotron-current drive in DIII-D.

Recent DIII-D experiments using off-axis electron cyclotron current drive (ECCD) have demonstrated the ability to modify the current profile in a plasma with toroidal beta near 3%. The resulting plasma simultaneously sustains the key elements required for Advanced Tokamak operation: high bootstrap current fraction, high beta, and good confinement. More than 85% of the plasma current is driven by noninductive means. ECCD is observed to produce strong negative central magnetic shear, which in turn acts to trigger confinement improvements in all transport channels in the plasma core.

Progress towards steady-state operation and real-time control of internal transport barriers in JET

In JET, advanced tokamak research mainly focuses on plasmas with internal transport barriers (ITBs) that are strongly influenced by the current density profile. A previously developed optimized shear regime with low magnetic shear in the plasma centre has been extended to deeply negative magnetic shear configurations. High fusion performance with wide ITBs has been obtained transiently with negative central magnetic shear configuration: HIPB98(y,2) ∼ 1.9, βN = 2.4 at Ip = 2.5 MA. At somewhat reduced performance, electron and ion ITBs have been sustained in full current drive operation with 1 MA of bootstrap current: HIPB98(y,2) ∼ 1, βN = 1.7 at Ip = 2.0 MA. The ITBs were maintained for up to 11 s for the latter case. This duration, much larger than the energy confinement time (37 times larger), is already approaching a current resistive time. New real-time measurements and feedback control algorithms have been developed and implemented in JET for successfully controlling the ITB dynamics and the current density profile in the highly non-inductive current regime.

Triggering of internal transport barrier in JET

Internal transport barriers (ITBs) can be produced in JET by the application of strong additional heating during the current rise phase of the plasma discharge. Using up to 3 MW of lower hybrid power to tailor the q-profile prior to the main heating phase, a large variety of q-profiles ranging from low positive to strong negative central shear have been obtained during the current rise (0.4 MA s−1). With negative central magnetic shear s = (r/q)(dr/dq), the analysis of ITB triggering reveals a correlation between the formation of the ITB and q min reaching an integer value (q = 2 or q = 3). This observation is confirmed by the analysis of the Alfvèn cascades. The minimum power required to access regimes with ITBs is probably related to the transport and magnetohydrodynamic properties of integer magnetic surfaces. Laser ablation and shallow pellet injection have also been attempted in recent JET ITB triggering experiments.This article was scheduled to appear in issue 7 of Plasma Phys. Control. Fusion. To access this special issue on advanced Tokamak research in EFDA-JET please follow this link: http://stacks.iop.org/0741-3335/44/7

Dynamics of the formation, sustainment and destruction of transport barriers in magnetically contained fusion plasmas*

The formation of transport barriers in fusion plasmas is studied through examination of mechanisms which can stabilize plasma turbulence and, thereby, reduce turbulence-driven transport. These include the effects of E×B velocity shear, negative central magnetic shear and the Shafranov shift. Transport barriers formed at the plasma edge and in the plasma core are considered, as well as the formation of multiple barriers. The access conditions for barrier formation are examined, particularly by considering local conditions compared to global parameters. Processes that can destroy transport barriers, such as magnetohydrodynamic instabilities, are described. Plasmas with high confinement and good plasma stability then require effective control of plasma profiles and transport. Efforts towards real-time control of transport barriers are described.

Dynamics of Plasma during the Formation of a Weak Negative Central Magnetic Shear Configuration Using Counter Neutral Beam Injection in the JFT-2M Tokamak.

In the JFT-2M tokamak, discharges exhibiting good performance have been produced by counterNBI after boronization. An improved core confinement mode under an H-mode edge condition is sustained for -5~~E With H89p - 1.5 and pN - 2.0 at a line-averaged electron density of around 70%-80% of the Greenwald density limit. It is found that the q-profile changes from a monotonic one having qo ~ 1 to a zero or weak negative central magnetic shear configuration having I < qmin ~ qo < 3 during improved core confinement mode using counter-NBI under an H-mode edge condition. The central electron temperature very clearly increases when the sawtooth activity disappears, while the previous result without boronization exhibited a significant degradation of the energy confinement due to the accumulation of impurities. The mechanism governing the improved core confinement mode including the density peaking and/or ITB formation due to negative shear is presently unclear.

Performance, heating and current drive scenarios of ASDEX Upgrade advanced tokamak discharges

Various approaches to high performance and steady state operation are presented. Strong neutral beam heating in the current ramp leads to internal transport barriers (ITBs) in conjunction with negative central magnetic shear. To avoid the destabilizationof external kink modes this regime is limited to L mode edge operation with βN < 1.7. In high poloidal β, βp, discharges, full non-inductive current drive has been achieved transiently. At Greenwald density, values of βp = 3.1, βN = 2.8 and HITER89-P = 1.8 have been reached simultaneously. In plasmas with ITBs and L mode edge, additional ECRH and ECCD facilitates high core confinement with Te ≈ Ti. CentralECCD has been applied in low density low current discharges. For ECCD in the co-current direction a current drive fraction of 82% is calculated. In the case of counter-ECCD, negative central shear withqmin > 1 leads to the formation of an electron ITB.

Nonlinear three-dimensional self-consistent simulations of negative central shear discharges in the DIII-D tokamak

Nonlinear simulations of experimentally observed magnetohydrodynamic (MHD) bursts in DIII-D [J. Luxon and L. G. Davis, Fusion Technol. 8, 441 (1985)] L-mode negative central magnetic shear (NCS) discharges were performed with a full three-dimensional nonlinear MHD code. The effects of plasma rotation in the presence of resistivity and viscosity are included and an effectively implicit numerical scheme allows the transport profile to evolve self-consistently with the nonlinear MHD instabilities and externally applied sources and sinks. The simulations follow the MHD bursts and disruptions through the linear and nonlinear phases and identify the connections between the early MHD bursts and the ultimate disruption phase. Specific predictions of the growth and saturation of the modes are directly compared with experimental diagnostic measurements in DIII-D. The simulations show that the bursts observed in experiments are triggered by MHD instability of a resistive interchange mode and a resistive kink mode that are excited for critical plasma profiles. The critical profiles are determined by the balance between inductive and noninductive sources of current density.

Linear and nonlinear resistive magnetohydrodynamic stability of tokamak discharges with negative central shear

Linear and nonlinear magnetohydrodynamic (MHD) calculations have been performed to study the stability of tokamak discharges with reversed or negative central magnetic shear using the finite aspect ratio (FAR) suite of MHD codes [Charlton et al., J. Comput. Phys. 86, 270 (1990)]. The linear calculations confirm anew that radially localized resistive interchange modes can be unstable in the reversed or negative central magnetic shear region. The calculations further show that these resistive interchange modes are more unstable for toroidal mode numbers n higher than n=1. The nonlinear calculations do however demonstrate that toroidal mode number n=1, enhanced by the nonlinear couplings of the linearly more unstable higher n toroidal harmonics, dominates the nonlinearly saturated steady state. While the resistive interchange modes may account for the precursors detected experimentally, the saturated levels of magnetic fluctuations obtained in the nonlinear calculations do not appear large enough to cause the experimentally observed global collapse of such discharges.

Particle transport in DIII-D discharges with internal regions of enhanced confinement and counter injected neutral beams

An analysis of experimentally measured particle transport in tokamak plasmas with negative central magnetic shear is presented. The analysis is presented in terms of a simple model for turbulent transport which allows the separation of diagonal and off diagonal terms and allows the direct comparison of particle and energy transport. Comparing the measured fluxes to the fluxes predicted by a simple quasi analytical model which specifies a relation between the diagonal and off diagonal terms allows an understanding of the reason for the difference between energy and particle fluxes. In the center of discharges with a region of enhanced confinement (or internal transport barrier), the ion thermal diffusivity becomes small and comparable to neoclassical values and the particle diffusivity also becomes small and approaches the neoclassical values.

Observation of simultaneous internal transport barriers in all fourtransport channels and correlation with turbulence behaviour in NCSdischarges on DIII-D

Very steep internal transport barriers (ITBs) have been observed in allfour transport channels on DIII-D. These ITBs are among the mosthighly localized (width⩽5 cm), simultaneous core transport barriersobserved on any machine to date, and have only been observed in dischargeswith a negative central magnetic shear (NCS discharges), at power levelsabove ~8 MW. Profile gradients and scale lengths at the location ofthe core (ρ~0.3-0.4) transport barriers are similar to thoseobserved at the plasma edge during H-mode, while profiles inside thetransport barriers are flat. The spatial location of the transport barrierscoincides in all four transport channels, although the temporal evolutionof the profiles is different; very steep gradients in the electron densityand temperature profiles form after such gradients are first observed inthe ion temperature and angular momentum profiles. Turbulence measurementsduring the evolution of the core particle transport barrier show nodecrease in low-wavenumber (0-6 cm-1) turbulence levels in theplasma centre, including within the steep gradient ITB region. Severalpossible interpretations for this observation are presented.