Negative Central Shear Discharges Research Articles

Stability of DIII-D high-performance, negative central shear discharges

Tokamak plasma experiments on the DIII-D device (Luxon et al 2005 Fusion Sci. Tech. 48 807) demonstrate high-performance, negative central shear (NCS) equilibria with enhanced stability when the minimum safety factor exceeds 2, qualitatively confirming theoretical predictions of favorable stability in the NCS regime. The discharges exhibit good confinement with an L-mode enhancement factor H89 = 2.5, and are ultimately limited by the ideal-wall external kink stability boundary as predicted by ideal MHD theory, as long as tearing mode (TM) locking events, resistive wall modes (RWMs), and internal kink modes are properly avoided or controlled. Although the discharges exhibit rotating TMs, locking events are avoided as long as a threshold minimum safety factor value is maintained. Fast timescale magnetic feedback control ameliorates RWM activity, expanding the stable operating space and allowing access to values approaching the ideal-wall limit. Quickly growing and rotating instabilities consistent with internal kink mode dynamics are encountered when the ideal-wall limit is reached. The RWM events largely occur between the no- and ideal-wall pressure limits predicted by ideal MHD. However, evaluating kinetic contributions to the RWM dispersion relation results in a prediction of passive stability in this regime due to high plasma rotation. In addition, the ideal MHD stability analysis predicts that the ideal-wall limit can be further increased to by broadening the current profile. This path toward improved stability has the potential advantage of being compatible with the bootstrap-dominated equilibria envisioned for advanced tokamak (AT) fusion reactors.

Electron cyclotron heating and current drive for maintaining minimum q in negative central shear discharges

Toroidal plasmas created with negative magnetic shear in the core region offer advantages in terms of MHD stability properties. These plasmas, transiently created in several tokamaks, have exhibited high-performance as measured by normalized stored energy and neutron production rates. A critical issue with extending the duration of these plasmas is the need to maintain the off-axis-peaked current distribution required to support the minimum in the safety factor q at large radii. We present equilibrium and transport simulations that explore the use of electron cyclotron heating and current drive to maintain this negative shear configuration. Using parameters consistent with DIII-D tokamak operation (Strait E et al 1995 Phys. Rev. Lett. 75 4421, Rice B W et al 1996 Nucl. Fusion 36 1271), we find that with sufficiently high injected power, it is possible to achieve steady-state conditions employing well aligned electron cyclotron and bootstrap current drive in fully non-inductively current-driven configurations.

Observation and analysis of a resistive mode with interchange parity in negative central shear plasmas in the DIII-D Tokamak

A magnetohydrodynamic (MHD) instability which has the characteristics that the displacement phase is in the same direction at all the affected flux surfaces (an interchange-like structure with no phase reversal across a flux surface), has been observed during the L mode in several negative central shear discharges of DIII-D tokamak [J. L. Luxon, P. Anderson, F. Baity et al., Plasma Physics and Controlled Fusion Research 1986 (International Atomic Energy Agency, Vienna, 1987), Vol. I, p. 159]. The instability occurs when the minimum safety factor is around 2.0 and the profile of the safety factor q is deeply reversed in the center. Detailed stability analyses were carried out using standard numerical codes and the high quality magnetic probe, motional Stark effect and electron cyclotron emission (ECE) data. Analysis of the data after the onset shows that the instability has an n=1 mode number and a growth time of about 400 μs. The electron temperature fluctuations obtained from ECE measurements indicate a localized interchange-like structure early in time, the resistive interchange criterion indicates marginal stability, and ideal mode analyses indicate robust stability with an ideal beta limit of about a factor of 2 higher than the βN value at the time of onset. Therefore this interchange-parity mode is not an ideal MHD mode. The marginal value of the resistive interchange criterion observed only in discharges with the instability, indicates that this is probably a resistive interchange mode. However, some observed characteristics of the instability may require models beyond the linear resistive interchange theory.

Simulation of neoclassical tearing modes in the DIII-D tokamak. II. Suppression by radially localized electron cyclotron current drive

The problem of neoclassical tearing mode (NTM) suppression by a radially localized toroidal current from electron cyclotron current drive (ECCD) is considered. Simulation of NTM stabilization by ECCD is performed with the Nonlinear Fully Toroidal Code (NFTC) [Phys. Plasmas 8, 3605 (2001)] for DIII-D discharges. The optimal parameters are determined for the radially localized ECCD current required to reduce the NTM instability. The time response and nonlinear evolution of the magnetic island width for ECCD and the required modulation phasing, the current drive location with respect to the rational surface, and the width of the spatial distribution are determined for both monotonic q-profile and negative central shear discharges.

First principles model of internal transport barriers in negative central shear discharges

At and around minima or maxima of the safety factor q, overlapping, and therefore toroidicity induced coupling of drift eigenmodes centred on neighbouring rational surfaces rl,m defined by q(rl,m) = m/l and rl,m±1 defined by q(rl,m±1) = (m±1)/l, is generally negligible; l and m (m±1) are the toroidal and (main) poloidal mode numbers, respectively. Under these conditions, a careful analysis shows that the growth rate of the ion temperature gradient (ITG) mode is proportional to the absolute value of the magnetic shear parameter; its radial width and frequency (in the E × B rotating frame) are larger in the axisymmetric torus than in the plasma slab or cylinder, especially at small values of kθ ai (kθ is the poloidal mode number and ai the characteristic ion Larmor radius). These results provide a straightforward theoretical interpretation of the origin of internal ion transport barriers (ITBs) in discharges with negative central shear if the ITG instability is indeed the main channel for ion energy transport. In agreement with recent experiments, the mechanism does not degrade for Te∼Ti, an important result for extrapolation to reactors. Once initiated, an ITB will locally increase the curvature of the ion temperature profile and, consequently, the gradients of the radial electric field and E × B rotation profiles (until neoclassical (or sub-neoclassical) transport comes into play). The damping associated with velocity shear yields an upper bound on the unstable mode number range, whereas Landau damping is expected to introduce a lower bound. In cases where toroidal effects are subdominant, the ratio of the damping rate associated with velocity shear to the growth rate associated with magnetic shear leads naturally to the Hamaguchi-Horton parameter (divided by the factor ηi-2/3 which characterizes the departure from the instability threshold (ηi is the ratio of the density and temperature length scales)) when introducing the most unfavourable mode number. Toroidal effects are always dominant for sufficiently weak magnetic shear or sufficiently large values of |LN|/R (where LN is the density gradient length), and therefore before steepening of the profiles has occurred near the zero magnetic shear layer; the counterpart of the Hamaguchi-Horton characteristic parameter appropriate to that case is also obtained, considering again the most unfavourable mode number.

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.

Predictive transport simulations of internal transport barriers using the Multi-Mode model

The formation of internal transport barriers observed in both Joint European Torus (JET) [P. H. Rebut, R. J. Bickerton, and B. E. Keen, Nucl. Fusion 25, 1011 (1985)] and Doublet III-D Tokamak (DIII-D) [J. L. Luxon and L. G. Davis, Fusion Technol. 8, 441 (1985)] are reproduced in predictive transport simulations. These simulations are carried out for two JET-optimized shear discharges and two DIII-D negative central shear discharges using the Multi-Mode model in the time-dependent 1-1/2-D BALDUR transport code [C. E. Singer et al., Comput. Phys. Commun. 49, 275 (1988)]. The Weiland model is used for drift modes in the Multi-Mode model in combination with either Hahm–Burrell or Hamaguchi–Horton flow shear stabilization mechanisms, where the radial electric field is inferred from the measured toroidal velocity profile and the poloidal velocity profile computed using neoclassical theory. The transport barriers are apparent in both the ion temperature and thermal diffusivity profiles of the simulations. The timing and location of the internal transport barriers in the simulations and experimental data for the DIII-D cases are in good agreement, though some differences remain for the JET discharges. The formations of internal transport barriers are interpreted as resulting from a combination of E×B flow shear and weak magnetic shear mechanisms.

Response of internal transport barriers to central electron heating and current drive on ASDEX Upgrade

Internal transport barriers with the central electron temperature as large as the central ion temperature both in excess of 10 keV have been achieved in the Axi-symmetric divertor experiment (ASDEX Upgrade) [H. Vernickel et al., J. Nucl. Mater. 128, 71 (1984)]. By applying central electron cyclotron heating and current drive to negative central shear discharges, established by neutral beam heating in the current ramp, the core electron temperatures could be raised by more than a factor of 2. Despite the fivefold increase of the central electron heat flux, the ion and electron energy and also angular momentum transport did not deteriorate. For neutral beam injection alone and also with additional central electron cyclotron counter-current drive, a double tearing mode and the associated detrimental effect on the plasma confinement is destabilized only transiently, when the minimum of the safety factor (qmin) passes through 2. For co-current drive, however, the confinement does not recover after qmin has dropped below 2, as the (2,1) mode persists due to the influence of the current profile modification in the very plasma center.

Comparison of internal transport barriers in JT-60U and DIII-D NCS discharges

Negative central shear discharges in JT-60U revealed an internal transport barrier (ITB) which is located at larger minor radii than those in other devices and is accompanied by a clear reduction in . In order to investigate this origin of the unique and favourable feature for future reactors, the discharge parameters were compared with those in DIII-D, where ITB was at smaller minor radii and less reduction in was observed. Strong negative magnetic shear was found to be related to the reduction in . The thin skin depth in JT-60U originating from high , together with the continuous decrease in , was effective in moving the ITB location to larger minor radii and in sustaining the strong negative shear.

A gyro-Landau-fluid transport model

A physically comprehensive and theoretically based transport model tuned to three-dimensional (3-D) ballooning mode gyrokinetic instabilities and gyrofluid nonlinear turbulence simulations is formulated with global and local magnetic shear stabilization and E×B rotational shear stabilization. Taking no fit coefficients from experiment, the model is tested against a large transport profile database with good agreement. This model is capable of describing enhanced core confinement transport barriers in negative central shear discharges based on rotational shear stabilization. The model is used to make ignition projections from relative gyroradius scaling discharges.

Enhanced performance discharges in the DIII-D tokamak with lithium wall conditioning

Lithium wall conditioning has been used in a recent campaign evaluating high performance negative central shear (NCS) discharges. During this campaign, the highest values of stored energy (4.4 MJ), neutron rate (2.4 × 10 16/ s), and nT i τ (7 × 10 20 m −3 keV s) achieved to date in DIII-D were obtained. High performance NCS discharges were achieved prior to beginning lithium conditioning, but it is clear that shot reproducibility and performance were improved by lithium conditioning. Central and edge oxygen concentrations were reduced after lithium conditioning. Lithium conditioning, consisting of up to four pellets injected at the end of the preceding discharge, allowed the duration of the usual inter-shot helium glow discharge to be reduced and reproducible high auxiliary power discharges, P NBI ≤ 22 MW, were obtained with plasma currents up to 2.4 MA.

Electron temperature fluctuation measurements and techniques in the DIII-D tokamak

Several techniques for determining the level and characteristics of electron temperature fluctuations via measurements and analysis of electron cyclotron emission (ECE) have recently been proposed and demonstrated [S. Sattler and H. J. Hartfuss, Plasma Phys. Cont. Fus. 35, 1285 (1993) and G. Cima et al., Phys. Plasmas (1994)]. A technique relying on the correlation of ECE in orthogonal frequency bins but lying within the line broadening of the local emission spectrum is being pursued at DIII-D. Special concerns include the effect of large rotation in the discharges due to neutral beam injection and extremely low fluctuation levels in enhanced confinement regimes such as negative central shear discharges. An antenna design optimized for fluctuation studies is also being developed.

Confinement and stability of DIII-D negative central shear discharges

Negative central magnetic shear (NCS) discharges with and up to 80% of the current non-inductively driven are reproducibly produced in the DIII-D tokamak. Strong peaking of , plasma rotation and, in some cases, are observed inside the NCS region. Transport analysis shows that the core ion thermal diffusivity is substantially reduced and near the neoclassical value after the formation of the internal transport barrier. The negative central shear is necessary but not sufficient for the formation of this transport barrier. The power required for the formation appears to increase with the toroidal magnetic field. The high performance phase of H-mode NCS discharges often ends with an ELM-like collapse initiated from the edge whereas the L-mode discharges which have a more peaked pressure profile tend to end with a more global n = 1 MHD event.