Weak Magnetic Shear Research Articles

Hypersonic drift-tearing magnetic islands in tokamak plasmas

A two-fluid theory of long wavelength, hypersonic, drift-tearing magnetic islands in low-collisionality, low-β plasmas possessing relatively weak magnetic shear is developed. The model assumes both slab geometry and cold ions, and neglects electron temperature and equilibrium current gradient effects. The problem is solved in three asymptotically matched regions. The “inner region” contains the island. However, the island emits electrostatic drift-acoustic waves that propagate into the surrounding “intermediate region,” where they are absorbed by the plasma. Since the waves carry momentum, the inner region exerts a net force on the intermediate region, and vice versa, giving rise to strong velocity shear in the region immediately surrounding the island. The intermediate region is matched to the surrounding “outer region,” in which ideal magnetohydrodynamic holds. Isolated hypersonic islands propagate with a velocity that lies between those of the unperturbed local ion and electron fluids, but is much closer to the latter. The ion polarization current is stabilizing, and increases with increasing island width. Finally, the hypersonic branch of isolated island solutions ceases to exist above a certain critical island width. Hypersonic islands whose widths exceed the critical width are hypothesized to bifurcate to the so-called “sonic” solution branch.

Low-q resonances, transport barriers, and secondary electrostatic convective cells

Recent experimental observations have suggested key characteristics of internal transport barrier (ITB) formation near low-q surfaces in off-axis minimum-q (OAMq) discharges. These observations identify mean profile flattening localized to the low-q surface as a transition precursor in the absence of observable magnetic field perturbations. This observation suggests an electrostatic model of ITB formation which accounts for strong transport in the immediate vicinity of the low-q surface, as well as the formation of an ITB nearby the surface. Here, a low-m electrostatic convective cell driven by modulational instability of the background drift wave turbulence is discussed in the context of ITB formation near low-q resonances in OAMq discharges. Unlike pure m=n=0 zonal flows, convective cells are capable of intense mixing localized around low-q resonant surfaces, thus relaxing ∇T and ∇n profiles at the k∙B=0 resonance. However, nearby, but off the low-q resonant surface the magnitude of convective cell shear is maximal, providing an effective means of triggering a transport barrier there. Field line bending coupled with collisional viscosity are found to strongly damp the intensity of the vortical flows except in the case of weak magnetic shear. Furthermore, collisionless nonlinear saturation mechanisms such as nonlinear wave trapping are largely circumvented due to the strong mixing of the convective cell. This suggests that low-m convective cells may play a key role in the regulation of turbulent transport near low-q resonances for OAMq discharges.

Current profile control and optimization under dominant electron heating in HL-2A

The establishment of the current profile as in the hybrid scenario is studied under the condition of dominant electron heating in HL-2A. The scenarios with injecting lower hybrid (LH) and electron cyclotron (EC) waves are under numerical study. Carefully adjusting the position of non-inductive current driven by two groups of gyrotron, an optimized q-profile was obtained with qa = 3.78 and a weak shear region extending to ρ ∼ 0.45 (where ρ is the square-root of toroidal flux normalized to its value at the plasma boundary) in low-density discharges of . When 0.5 MW LH power in the current drive mode and 0.95 MW EC power mainly for plasma heating are used to control the current profile, a hybrid discharge scenario with a weak magnetic shear region extended to ρ = 0.6 and qa = 3.21 is established by controlling the EC absorption position. The mechanism of the LH wave absorption in the HL-2A plasma causes interplay of the distribution of the LH driven current with the modification of the plasma configuration, which constitutes non-linearity in the LH wave deposition. Due to the non-linearity the LH wave deposition position changes spontaneously or oscillates. The oscillatory behaviour caused by the non-linear effect of the LH wave deposition is analysed.

Role of magnetic shear in flow shear suppression

The interplay between flow shear and magnetic shear is studied in the three-dimensional reduced magnetohydrodynamic turbulence. It is analytically shown that near the resonance surface, transport quenching by flow shear is weakened by magnetic shear as the latter interferes with shearing process. In particular, anomalous particle transport becomes more efficient in the regime with stronger magnetic shear for a given flow shear while self-regulation of zonal flows becomes less effective. The results suggest that weak magnetic shear could be favorable for the formation of transport barrier.

Self-organization in electron temperature gradient driven turbulence

Based on first principle gyrokinetic calculations, a zonal flow generation mechanism in the slab electron temperature gradient driven (ETG) turbulence with weak magnetic shear is identified as self-organization via the turbulent spectral cascade in the two dimensional rotating fluid turbulence. The inverse energy cascade and the scaling of a zonal flow wavenumber, which is consistent with the Rhines scale length, are confirmed. An impact of the scaling, which depends on the density gradient, on the turbulent structure and transport is demonstrated for the slab ETG turbulence.

Interchange and infernal fishbone modes in plasmas with tangentially injected beams

New energetic particle mode instabilities of fishbone type are predicted. The considered instabilities are driven by circulating energetic ions. They can arise in plasmas of tokamaks and spherical tori with weak magnetic shear in the wide core region and strong shear at the periphery, provided that the central safety factor is close to the ratio m∕n, where m and n are the poloidal mode number and toroidal mode number, respectively. The instability with m=n=1 has a mainly interchange-like radial structure, whereas the radial structure of instabilities with m∕n>1 is mainly similar to that of the infernal magnetohydrodynamics (MHD) mode; the differences between the fishbone mode structures and MHD mode structures are considerable only in the vicinity of the local Alfvén resonance.

Overview of the latest HT-7 experiments

An overview of the progress with experiments in the HT-7 during 2003–4 is presented. The H-mode, negative reversed shear and high li operational scenarios were investigated for quasi-steady-state high performance plasma discharges. Ion Bernstein wave (IBW) heating at 30 MHz produced a typical edge H-mode plasma. Transport in both electron and ion channels were reduced in the outer half portion of the plasma. H-mode was produced in off-axis lower hybrid current drive (LHCD) plasmas by launching a lower hybrid wave (LHW) with a greater parallel refractive index, , of 3.1. The improved confinement status in such plasma discharges could be sustained for more than 400τE. A high inductance, li, plasma was created using a fast plasma current ramp down and sustained by central LHCD and IBW heating for a duration of >1 s with a strongly peaked electron temperature profile. The highest central electron temperature obtained was 4.5 keV. An increase in the energy confinement time with li was observed. It was found that the IBW heating could improve the plasma confinement at the same li if part of the LHW power was replaced by IBW. Stationary internal transport barriers with normalized performance H89βN > 1–3 were obtained with combined injection of LHW and IBW for a duration of several hundred energy confinement times in the weak negative magnetic shear (RS). Increasing the total injection power to 1 MW did not degrade the plasma confinement significantly in the RS operational scenario. Long pulse discharges were performed, using three feedback controls for the plasma current and position, the central line-averaged electron density and the magnetic swing flux of the transformer. The longest plasma discharge, with a duration of 240 s, Te(0) ∼ 1 keV and the central electron density > 0.8 × 1019 m−3 was achieved in 2004. The wall saturation and refreshment (wall pumping) were first observed in such long pulse discharges. A fully LHW current driven plasma without using ohmic current in the central solenoid coils was sustained for 80 s. The main limitation for the pulse length was due to the recycling, which caused an uncontrollable rise in the electron density.

Global Gyrokinetic Stability of Pressure-Gradient-Driven Electromagnetic Modes in Tokamaks with Regions of Low Shear

Tokamaks with large pressure gradients (alpha(max)) formed in regions of weak magnetic shear are shown to be susceptible to novel, low-n, global, kinetic, electromagnetic modes with a toroidal mode number n in the range 2</=n</=12. For a weakly varying monotonic safety factor profile q with its minimum q(min)>1 on the magnetic axis and alpha(max) near q(min), new, global kinetic infernal modes with a strong mode rotation omega(r) and a finite growth rate gamma<|omega(r)| are found. For equilibria with reverse shear where q(min) is off axis and alpha(max) near q(min), the existence of an unstable low-n global branch of Alfve n ion temperature gradient modes is revealed with an oscillatory gamma as a function of n. The addition of trapped electron dynamics is shown to be further destabilizing.

Short wavelength ion temperature gradient instability in toroidal plasmas

Series of ion temperature gradient (ITG or ηi) driven modes in the short wavelength region, ∣k⊥ρi∣&amp;gt;1, are investigated with a gyrokinetic integral equation code in toroidal plasmas. These instabilities exist even if electrons are assumed adiabatic. However, nonadiabatic electron response can influence these short wavelength ITG (SWITG) modes, especially the fundamental l=0 mode. At typical parameters, excitation of the l=0 mode requires that both ηi and ηe exceed thresholds, while the l=1 and l=2 modes with higher harmonic eigenfunctions persist unstable even at ηe=0. Dependence of the SWITG modes on other parameters is also investigated. The l=1 mode with an odd potential eigenfunction grows faster than the l=0 mode and may be dominant in low ηe, high β, weak positive magnetic shear, and/or weak toroidicity regions.

Evolution of nonlocal ideal helical perturbations in cylindrical plasma

The evolution and the stability property of a helical perturbation for arbitrary magnetic shear configurations are investigated. An analytic stability criterion has been obtained and predicts that nonlocal perturbations exhibit stronger instabilities than local perturbations. A weak positive magnetic shear is favorable to the stability, while a strong negative magnetic shear contributes little to the instability for reversed magnetic shear configurations, which do not show better stabilities than positive shear configurations. Instability is stronger in the decreasing region of the r-direction perturbation amplitude than in the increasing region and perturbations with a steep negative slope produces strong localized instabilities. A larger poloidal or toroidal mode number of the perturbations relates to a stronger instability. Instability is weaker in the core than in other regions.

Numerical study of zonal flow dynamics and electron transport in electron temperature gradient driven turbulence

The electron temperature gradient (ETG) driven turbulence in tokamak core plasmas is numerically investigated based on a three-dimensional gyrofluid model with adiabatic ion response. Attentions are focused on the zonal flow dynamics in ETG fluctuations and the resultant electron heat transport. A high electron energy confinement mode is found in the weak magnetic shear region, which is relevant to the self-organization behavior of turbulence through the enhanced zonal flow dynamics rather than the weak shear stabilization of ETG fluctuations. It is demonstrated that the weak shear favors the enhancement of zonal flows in ETG turbulence. The enhanced zonal flows may be plausibly limited by the excitation of a secondary Kelvin–Helmholtz mode, which is observed from the spatial spectral analyses and time-frequency wavelet analyses of turbulent fluctuations. Electromagnetic ETG simulations show that while the Ohkawa’s scaling of anomalous electron transport with beta, χe∝1/βe, is reproduced in the moderate shear plasma, the finite beta effect may reverse the Ohkawa’s scaling in weak shear ETG turbulence due to the reduction of zonal flow generation by the magnetic Reynolds stress. Further, it is shown that the toroidal coupling enhances the zonal flow while it destabilizes the ETG mode. Hence, the electron transport seems insensitive to the toroidicity in the weak shear plasma due to the complex destabilizing and stabilizing competitions.

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.

New interpretation of alpha-particle-driven instabilities in deuterium-tritium experiments on the Tokamak Fusion Test Reactor.

The original description of alpha particle driven instabilities in the Tokamak Fusion Test Reactor in terms of toroidal Alfvén eigenmodes (TAEs) remained inconsistent with three fundamental characteristics of the observations: (i) the variation of the mode frequency with toroidal mode number, (ii) the chirping of the mode frequency for a given toroidal mode number, and (iii) the antiballooning density perturbation of the modes. It is now shown that these characteristics can be explained by observing that cylindrical-like modes can exist in the weak magnetic shear region of the plasma that then make a transition to TAEs as the central safety factor decreases in time.

Temperature gradient driven short wavelength modes in sheared slab plasmas

The temperature gradient (ηi and ηe) driven instability in the short wavelength regime, |kyρi|&amp;gt;1, is studied in a sheared slab. An analytical analysis is performed first to clarify the physics mechanisms for the modes in a shearless slab. The correlation between the growth rate and the real frequency of the modes is discussed in detail. The electron temperature gradient is found to have strong influences on the modes in short wavelength regions. Several series of the short wavelength modes are then identified with a kinetic integral equation code in a sheared slab. The radial widths of the modes are found to be comparable with the conventional ηi modes and not short, although the poloidal wavelengths are short. The lowest odd mode usually dominates in the weak magnetic shear and low β regime. However, the fundamental mode seems to be important in tokamak plasmas because the higher order modes are easily stabilized by finite β and/or by magnetic shear. The fundamental short wavelength mode cannot be stabilized by β when the magnetic gradient drift effect is taken into account. The modes are excited by both finite ηi and ηe, and may be stabilized by magnetic shear.

Effects of flow shear on the ion temperature gradient modes in a high β plasma slab

The integral eigenmode equations derived previously for the study of drift instabilities in a sheared slab plasma with arbitrary β (plasma pressure/magnetic pressure) are extended. These equations are used to investigate the effects of flow shear on the ion temperature gradient driven (ITG) modes. It is found that the destabilizing effect of a parallel velocity shear, V0′, is weakened by the finite β effect, especially in case of weak magnetic shear. However, the perpendicular velocity shear, VE′, still effectively stabilizes these modes even in high β regions. A large enough VE′ can completely stabilize the ITG mode at arbitrary β. In addition, the effect of VE′ is highly enhanced in weak magnetic shear regions. When the parallel flow coexists with the perpendicular flow, the comprehensive flow effect depends on the relative sign of these velocity shears. The modes with higher growth rates may be stabilized by a smaller VE′ for V0′VE′&amp;gt;0.

Fusion Plasma Performance and Confinement Studies on JT-60 and JT-60U

Fusion plasma performance and confinement studies on JT-60 and JT-60U are reviewed. With the main aim of providing a physics basis for ITER and the steady-state tokamak reactors, JT-60/JT-60U has been developing and optimizing the operational concepts, and extending the discharge regimes toward sustainment of high integrated performance in the reactor relevant parameter regime. In addition to achievement of high fusion plasma performances such as the equivalent breakeven condition (QDTeq up to 1.25) and a high fusion triple product nD(0)τETi(0) = 1.5 × 1021 m-3skeV, JT-60U has demonstrated the integrated performance of high confinement, high βN, full non-inductive current drive with a large fraction of bootstrap current. These favorable performances have been achieved in the two advanced operation regimes, the reversed magnetic shear (RS) and the weak magnetic shear (high-βp) ELMy H modes characterized by both internal transport barriers (ITB) and edge transport barriers (ETB). The key factors in optimizing these plasmas towards high integrated performance are control of profiles of current, pressure, rotation, etc. utilizing a variety of heating, current drive, torque input, and particle control capabilities and high triangularity operation. As represented by discovery of ITBs (density ITB in the central pellet mode, ion temperature ITB in the high-βp mode, and electron temperature ITB in the reversed shear mode), confinement studies in JT-60/JT-60U have been emphasizing freedom and also restriction of radial profiles of temperature and density. In addition to characterization of confinement and analyses of transport properties of the OH, the L-mode, the H-mode, the pellet mode, the high-βp mode, and the RS mode, JT-60U has clarified formation conditions, spatial structures and dynamics of edge and internal transport barriers, and evaluated effects of repetitive MHD events on confinement such as sawteeth and ELMs. Through these studies, JT-60U has demonstrated applicability of the high confinement modes to ITER and the steady-state tokamak reactors.

Beam-driven energetic particle modes in advanced tokamak plasmas

A major goal of the DIII-D program is to study `advanced tokamak' plasmas with good confinement, large normalized β, and a large fractionof self-sustained current. Many of these plasmas have large beam pressures(≲(1/3) of the total pressure) and weak magnetic shear; Alfvén instabilities with laboratory frequencies of 100-250 kHz are oftenobserved. The instabilities correlate with reductions in the neutron ratebelow the classically expected value, complicatingdetermination of the pressure and current profiles. Quantitative analysis of onecase suggests that two types of energetic particle modes are destabilized: the resonant toroidicity-induced Alfvén eigenmode and theresonant kinetic ballooning mode. The strong dependence on neutralbeam injection parameters and the variability in mode frequency arequalitatively consistent with this identification. Further analysis andmeasurements are planned.

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.

Profile and Shape Control of the Plasmas with Transport Barriers towards the Sustainment of High Integrated Performance in JT-60U.

With the main aim of providing physics basis for ITER and the steady-state tokamak reactor, JT-60U has been optimizing the operational concepts and extending discharge regimes toward the sustainment of high integrated performance. In the two advanced operation regimes, the reversed magnetic shear (RS) and the weak magnetic shear (high-βp) ELMy H modes characterized by both internal (ITB) and edge (ETB) transport barriers, JT-60U has clarified responses of the transport barrier structure to magnetic shear, heating power, momentum, density, etc. Based on these observations, possible parameter linkages and feedback loops in the core and pedestal regimes have been proposed. With the optimization of profile and shape control, both confinement and high β stability have been enhanced and favorable integrated performance has been achieved. Such operational regimes have been extended to the reactor-relevant regime.

Power Dependence of Ion Thermal Diffusivity at the Internal Transport Barrier in JT-60U.

The formation properties of an internal transport barrier (ITB) were investigated in a weak positive magnetic shear plasma by changing the neutral beam heating power. The ion thermal diffusivity in the core region shows L-mode state, weak ITB, and strong ITB, depending upon the heating power. Two features of ITB formation were experimentally confirmed. Weak ITB was formed in spite of the absence of an apparent transition in an ion temperature profile. On the other hand, strong ITB appeared after an apparent transition from the weak ITB. In addition, the ion thermal diffusivity at the ITB is correlated to the radial electric field shear. In the case of the weak ITB, ion thermal diffusivity decreased gradually with increases in the radial electric field shear. There exists a threshold in the radial electric field shear, which allows for a change in state from that of weak to strong ITBs.