H-mode Tokamak Research Articles

Simulation of electron thermal transport in H-mode discharges

Electron thermal transport in DIII-D H-mode tokamak plasmas [J. L. Luxon, Nucl. Fusion 42, 614 (2002)] is investigated by comparing predictive simulation results for the evolution of electron temperature profiles with experimental data. The comparison includes the entire profile from the magnetic axis to the bottom of the pedestal. In the simulations, carried out using the automated system for transport analysis (ASTRA) integrated modeling code, different combinations of electron thermal transport models are considered. The combinations include models for electron temperature gradient (ETG) anomalous transport and trapped electron mode (TEM) anomalous transport, as well as a model for paleoclassical transport [J. D. Callen, Nucl. Fusion 45, 1120 (2005)]. It is found that the electromagnetic limit of the Horton ETG model [W. Horton et al., Phys. Fluids 31, 2971 (1988)] provides an important contribution near the magnetic axis, which is a region where the ETG mode in the GLF23 model [R. E. Waltz et al., Phys. Plasmas 4, 2482 (1997)] is below threshold. In simulations of DIII-D discharges, the observed shape of the H-mode edge pedestal is produced when transport associated with the TEM component of the GLF23 model is suppressed and transport given by the paleoclassical model is included. In a study involving 15 DIII-D H-mode discharges, it is found that with a particular combination of electron thermal transport models, the average rms deviation of the predicted electron temperature profile from the experimental profile is reduced to 9% and the offset to −4%.

On Greenwald density limit in H-mode

The experimental Greenwald density limit in tokamak H-mode is explained from the requirements that in the edge transport barrier the radial pressure gradient does not exceed the ballooning stability threshold and the plasma collisionality corresponds to the transition from the plateau regime of neoclassical transport to the Pfirsch–Schlüter one, where the edge temperature and plasma energy content decrease dramatically with increasing density.

Study of the spectral properties of ELM precursors by means of wavelets

The high confinement regime (H-mode) in tokamaks is accompanied by the occurrence of bursts of MHD activity at the plasma edge, so-called edge localized modes (ELMs), lasting less than 1 ms. These modes are often preceded by coherent oscillations in the magnetic field, the ELM precursors, whose mode numbers along the toroidal and the poloidal directions can be measured from the phase shift between Mirnov pickup coils. When the ELM precursors have a lifetime shorter than a few milliseconds, their toroidal mode number and their nonlinear evolution before the ELM crash cannot be studied reliably with standard techniques based on Fourier analysis, since averaging in time is implicit in the computation of the Fourier coefficients. This work demonstrates significant advantages in studying spectral features of the short-lived ELM precursors by using Morlet wavelets. It is shown that the wavelet analysis is suitable for the identification of the toroidal mode numbers of ELM precursors with the shortest lifetime, as well as for studying their nonlinear evolution with a time resolution comparable to the acquisition rate of the Mirnov coils.

Two dimensionally steep structure of the electric field in tokamak H-mode

The formation of a poloidal shock structure is predicted in H-mode transport barriers, which must be taken into account for transport analyses to clarify the rapid formation mechanism of the H-mode pedestal. The analyses are carried out with edge plasmas in tokamak H-modes, which are induced either spontaneously or by electrode biasing. Two-dimensional structures of the potential, density and flow velocity are calculated with the momentum conservation equation. The validity of one-dimensional L/H transition theory and the iterative process to obtain the two-dimensional structure are confirmed by our analysis. A steep electric field structure both in the radial and poloidal directions induces radial ion fluxes, which increase in the H-mode transport barrier. If the Boltzmann relation is violated, radial electron fluxes are induced. A transport model is constructed, including generation of particle fluxes associated with the two-dimensional structure and reduction of anomalous transport by the steep gradient of the radial electric field. A self-consistent evolution of the density profile is calculated in the L/H transition, which clarifies that the generation of particle fluxes accelerates the density pedestal formation.

Electron Bernstein wave heating of over-dense H-mode plasmas in the TCV tokamak via O-X-B double mode conversion

This paper reports on the first demonstration of electron Bernstein wave heating (EBWH) by double mode conversion from ordinary (O-) to Bernstein (B-) via the extraordinary (X-) mode in an over-dense tokamak plasma, using low field side launch, achieved in the TCV tokamak H-mode, making use of its naturally generated steep density gradient. This technique offers the possibility of overcoming the upper density limit of conventional EC microwave heating. The sensitive dependence of the O-X mode conversion on the microwave launching direction has been verified experimentally. Localized power deposition, consistent with theoretical predictions, has been observed at densities well above the conventional cut-off. Central heating has been achieved, at powers up to two megawatts. This demonstrates the potential of EBW in tokamak H-modes, the intended mode of operation for a reactor such as ITER.

On the correlation between density profile and particle flux in H-mode tokamak plasmas and the implication for ITER

Density peaking in tokamak ELMy H-mode plasmas is studied using data from the Joint European Torus (JET). It is shown that the electron density gradient and electron particle flux at mid-radius are correlated when these two quantities are normalized to their heat-power-balance counterparts. Therefore, the density profiles cannot be considered canonical and particle sources should be taken into account when extrapolating the density profiles to the ITER next-step device. The relation between density and temperature gradients at mid-radius is predicted in the range of (∇ne/ne)/(∇Te/Te) ∼ 0.15–0.35 for plasmas with safety factor and collisionality similar to ITER standard discharge.

Scaling of power threshold for edge transport barrier formation in CHS with density, magnetic field and magnetic configuration

An improved confinement state by the formation of an edge transport barrier can be obtained in the compact helical system. A power threshold exists, as is the case for the H-mode in tokamaks. The threshold scales as . These dependences are similar to those in tokamaks. The threshold also depends on magnetic configuration parameters such as the position of the magnetic axis. The absolute value of the threshold is 1–3 times larger than the tokamak H-mode power scaling.

The dimensionless scaling of ELMy H-mode confinement

This article describes the use of dimensionless analysis in the study of energy confinement in ELMy H-mode tokamak plasmas, with a focus on the use of dedicated dimensionless parameter experiments. This work has involved a strong collaboration between many machines and countries. The experiments have demonstrated that such analysis is indeed valid, and have given important information on the scaling of the characteristic turbulent length, the separation of electrostatic and electromagnetic transport regimes, and the effects of collisionality on plasma transport. They have also provided a method for scaling existing experiments to next step machines, such as ITER, and have suggested the possibility of enhanced performance at high normalised pressure. To cite this article: D.C. McDonald, C. R. Physique 7 (2006).

Origin of the various beta dependences of ELMy H-mode confinement properties**This paper was submitted as part of the special issue on the 10th Technical Meeting on H-mode Physics and Transport Barriers. To view the special issue go to stacks.iop.org/PPCF/48/i=5A.

Dependence of the energy confinement in ELMy H-mode tokamak on the beta has been investigated for a long time, but a common conclusion has not been obtained so far. Recent non-dimensional transport experiments in JT-60U demonstrated clearly the beta degradation. A database for JT-60U ELMy H-mode confinement was assembled. Analysis of this database is carried out, and the strong beta degradation consistent with the above experiments is confirmed. Two subsets of ASDEX Upgrade and JET data in the ITPA H-mode confinement database are analysed to find the origin of the various beta dependences. The shaping of the plasma cross section, as well as the fuelling condition, affects the confinement performance. The beta dependence is not identical for different devices and conditions. The shaping effect, as well as the fuelling effect, is a possible candidate for causing the variation of beta dependence.

Accessibility to a two-dimensionally steep structure of the electric field in tokamak H-mode

In the edge transport barrier of H-mode plasmas, a large poloidal flow exists and the electrostatic potential and density can have steep gradients both in the radial and poloidal directions. The accessibility to a two-dimensionally steep structure is demonstrated by solving the model equation including the poloidal structure, combined with the equation giving the time evolution of the radial electric field. The analysis is carried out with the parameter set of the electrode biasing experiment and shows the existence of the convective particle flux arising from poloidal inhomogeneity. This study provides an essential explanation for improving the transport analyses in H-modes by taking account of the two-dimensional effect in toroidal plasmas.

Simulations of pedestal formation and ELM cycles

Improved models are developed for integrated simulations of pedestal formation and edge localized mode (ELM) cycles at the edge of H-mode tokamak plasmas. The H-mode pedestal is formed in the simulations when flow shear and magnetic shear reduce the transport driven by drift modes at the edge of the plasma (Pankin A Y et al 2005 Plasma Phys. Control. Fusion 47 483). A large part of the flow shear is produced by the diamagnetic drift and the poloidal velocity, which is computed using a neoclassical model. Ion thermal transport is reduced to near the neoclassical level while electron thermal transport is reduced to the electron temperature gradient mode transport. A relatively large current density is driven in the pedestal by the bootstrap current. If the heating power is large enough, the pedestal growth is limited by ELM crashes, which are triggered by ideal MHD instabilities. Integrated simulations using these improved models are validated by comparing the simulation results with data for plasma profiles during the pedestal formation and with data for the ELM crash frequency. Simulations using the validated model are carried out for 31 Inernational Profile Database DIII-D and JET discharges.

Theory-based model for the pedestal, edge stability and ELMs in tokamaks

An improved model for triggering edge localized mode (ELM) crashes is developed for use within integrated modelling simulations of the pedestal and ELM cycles at the edge of H-mode tokamak plasmas. The new model is developed by using the BALOO, DCON and ELITE ideal MHD stability codes to derive parametric expressions for the ELM triggering threshold. The whole toroidal mode number spectrum is studied with these codes. The DCON code applies to low mode numbers, while the BALOO code applies to only high mode numbers and the ELITE code applies to intermediate and high mode numbers. The variables used in the parametric stability expressions are the normalized pressure gradient and the parallel current density, which drive ballooning and peeling modes. Two equilibria motivated by DIII-D geometry with different plasma triangularities are studied. It is found that the stable region in the high triangularity discharge covers a much larger region of parameter space than the corresponding stability region in the low triangularity discharge. The new ELM trigger model is used together with a previously developed model for pedestal formation and ELM crashes in the ASTRA integrated modelling code to follow the time evolution of the temperature profiles during ELM cycles. The ELM frequencies obtained in the simulations of low and high triangularity discharges are observed to increase with increasing heating power. There is a transition from second stability to first ballooning mode stability as the heating power is increased in the high triangularity simulations. The results from the ideal MHD stability codes are compared with results from the resistive MHD stability code NIMROD.

Study of Edge Transport Barrier Formation on CHS Plasma

An edge transport barrier (ETB) similar to the tokamak H-mode has been observed for beam-heated plasma with two co-injected Neutral Beam Injectors (NBIs) in CHS. The Hα emission showed a clear spontaneous drop followed by an increase of line-averaged electron density at the L-H transition. Stored energy increased by ˜ 40% with H-factor improvement up to ˜ 30% compared to the international stellarator scaling (ISS04v03). A rapid density increase in the edge region to two-times level of the L-mode was observed to accompany a ˜ 15% increase in the density gradient. An ETB was formed when the plasma density exceeded the lower density limit by ˜ 1.5 × 1013 cm-3 and the total NBI power exceeds the threshold level (Pdeposit / ne ˜ 200 × 10-13 kW/cm-3 at BT = 0.95 T, Rax = 92.1 cm, where Pdeposit is the deposited NBI power, ne is electron density, BT is troidal magnetic field strength and Rax is location of magnetic axis). The power threshold increased with the magnetic field strength, as in tokamak scaling, and depends on the magnetic field configuration of the helical plasma.

Multi-Dimensional Structure of the Electric Field in Tokamak H-Mode

In tokamak H-mode, a large poloidal flow exists in an edge transport barrier, and the electrostatic potential and density profiles can be steep both in the radial and poloidal direction. Two-dimensional structures of the potential, density and flow velocity near the edge of a tokamak plasma are investigated. The model includes the nonlinearity in bulk-ion viscosity and turbulence-driven shear viscosity. For the case with a strong radial electric field (H-mode), a two-dimensional structure in a transport barrier is obtained, giving a poloidal shock with a solitary radial electric field profile. The poloidal electric field induces convective transport in the radial direction, and poloidal asymmetry makes the flux-surface-averaged particle flux direct inward with a pinch velocity on the order of 1 [m/s]. A large poloidal flow with radial shear enhances the inward pinch velocity. The abrupt increase of this inward ion and electron flux at the onset of L-to-H-mode transition explains the rapid establishment of the density pedestal at the transition.

Structure of the edge density pedestal in tokamaks

A “first-principles” model for the structure of the edge density pedestal in tokamaks between or in the absence of edge localized magnetohydrodynamic instabilities is derived from ion momentum and particle conservation and from the transport theory of recycling neutral atoms. A calculation for (high) H-mode tokamak discharge parameters indicates that the equations have a self-consistent solution which has an edge pedestal in the ion density profile and sharp negative spikes in the poloidal velocity and radial electric field profiles in the edge pedestal, features characteristic of H-mode edge profiles. These sharp negative spikes in radial electric field and poloidal rotation produce a peak in the inward ion pinch velocity in the sharp gradient (pedestal) region which produces an edge particle transport barrier. The calculated magnitude of the density at the top of the pedestal and the density gradient scale length and radial electric field in the pedestal region are comparable to measured values.

JET and the Physics Basis of ITER

JET has made unique contributions to the physics basis of ITER by virtue of its ITER-like geometry, large plasma size and D-T capability. The paper discusses recent JET results and their implications for ITER in the areas of standard ELMy H-mode, D-T operation and advanced tokamak modes. In ELMy H-mode the separation of plasma energy into core and pedestal contributions shows that core confinement scales like gyroBohm transport. High triangularity has a beneficial effect on confinement and leads to an integrated plasma performance exceeding the ITER Q = 10 reference case. A revised type I ELM scaling predicts acceptable ELM energy losses for ITER, while progress in physics understanding of NTMs shows how to control them in ITER. The D-T experiments of 1997 have validated ICRF scenarios for heating ITER/a reactor and identified ion minority schemes (e.g. (3He)DT) with strong ion heating. They also show that the slowing down of alpha particles is classical so that the self-heating by fusion alphas should cause no unexpected problems. With the Pellet Enhanced Performance mode of 1988, JET has produced the first advanced tokamak mode, with peaked pressure profiles sustained by reversed magnetic shear and strongly reduced transport. More recently, LHCD has provided easy tuning of reversed shear and reliable access to ITBs. Improved physics understanding shows that rational q-surfaces play a key role in the formation and development of ITBs. The demonstration of real time feedback control of plasma current and pressure profiles opens the path towards fully controlled steady-state tokamak plasmas.

Impact of heat deposition profile on global confinement of NBI heated plasmas in the LHD**Original title in FEC2002, Lyon: response of temperature and density profiles to heat deposition profile and its impact on global scaling in LHD.

Energy confinement and heat transport of net-current-free NBI heated plasmas in the large helical device (LHD) are discussed with emphasis on density and power deposition profile dependences. Although the apparent density dependence of the energy confinement time has been demonstrated in a wide parameter range in LHD, the loss of this dependence has been observed in the high density regime under specific conditions. Broad heat deposition due to off-axis alignment and shallow penetration of neutral beams degrades the global energy confinement while the local heat transport maintains a clear temperature dependence, lying between Bohm and gyro-Bohm characteristics. The central heat deposition tends towards an intrinsic density dependence like τE∝(n̄e/P)0.6 from the state where density dependence is lost. The broadening of the temperature profile due to the broad heat deposition profile contrasts with the invariant property that has been observed widely as profile resilience or stiffness in tokamak experiments. The confinement improvement as a result of the inward shift of the magnetic axis is obvious in the core region, which emphasizes the improvement of transport because of the geometry being unfavourable for the central heating of NBI in this configuration. The edge pressure, clearly, does not depend on the magnetic axis position. Unlike a tokamak H-mode, the edge pressure is determined by transport and can be increased by increasing the heating power.

Recent results from the Large Helical Device

The most important finding in the Large Helical Device (LHD) experiments so far is that an inward-shifted configuration exhibits good plasma performance with a scaling similar to that of ELMy H-mode tokamaks. The inward-shifted configuration has been predicted to have unfavourable magnetohydrodynamic (MHD) properties, even though it has significantly better particle-orbit properties. However, no serious confinement degradation due to the MHD activities was observed, resolving favourably the potential conflict between stability and confinement. Neoclassical transport loss can be suppressed even in a low-collisionality regime, and in this way the inward-shifted configuration was shown to make the LHD plasma properties favourable. Then, it is very important to realize more improved plasma performance and higher temperature plasmas for extending the plasma-parameter regime in order to obtain data that can be extrapolated to a reactor. In the fifth campaign in 2001–2002, an increase in the heating power achieved an electron temperature Te of over 10 keV and an ion temperature Ti of 5 keV. A Te profile, which is characteristic of internal transport barriers, was also observed when the electron cyclotron resonance heating power was highly focused on the centre of the plasma sustained by neutral beam injection.

Models for the pedestal temperature at the edge of H-mode tokamak plasmas

Predictive models are developed for the temperature at the top at the edge of type 1 ELMy (edge localized mode) H-mode (high-confinement mode) plasmas. Theory-motivated models are used for the pedestal width and pressure gradient, while the pedestal density is obtained from experimental data in this study. The pedestal pressure gradient is assumed to be limited by the ballooning mode instability and is expressed in terms of the magnetic shear and geometrical factors. The effect of the bootstrap current, which reduces the magnetic shear in the steep pressure gradient region at the edge of the H-mode plasma, is included in the determination of the magnetic shear. Approaches for calculating the magnetic shear, combined with proposed models for the pedestal width, are used to determine the pedestal temperature. The computed pedestal temperatures are compared with more than 500 measured pedestal temperatures for type 1 ELMy H-mode discharges in four tokamaks. Some of the uncertainties in these results are discussed, and directions for future work to improve edge pedestal scalings are described.

Characterization of edge pressure in the Large Helical Device

The energy confinement time of net current-free plasmas in the Large Helical Device (LHD) is comparable to ELMy H-mode with q = 4.5 on the scale of IPB98(y,2). Broad temperature with high edge pressure, which is of robust nature in LHD, recalls the pedestal structure in tokamak H-mode. Basic parameter dependence is, however, weak gyro-Bohm in both edge and core regions. This suggests that one physical model could explain the observed profile. The edge temperature is proportional to the square root of heating power and inversely proportional to the square root of edge density. This means that edge pressure and its gradient are not limited and can be increased by heating power.