Tokamak Density Limit Research Articles

Characterizing the flow and turbulence structure near the last closed flux surface in L-mode plasmas of ASDEX Upgrade

Since high density operation is advantageous for building an efficient fusion reactor, understanding the density limit in tokamaks has been seen as one of the most important issues. This paper reports a series of measurements around the last-closed flux surface (LCFS) in L-mode plasmas by using a thermal helium beam diagnostic. Fluctuation analysis has been employed to characterize the poloidal flow and the turbulence structure. A reversal of the poloidal flow in the scrape-off layer and concomitant cooling of the outer divertor plasma are observed as the density is raised. While, in the confined region, the change in the density barely affects the poloidal flow, a higher density shifts the fluctuation power spectral densities toward lower frequencies and wave numbers. The eddy tilting of this region is consistent with what is expected from the magnetic shear effect. A radially coherent low frequency mode appears in the case of the highest density investigated in this study (n¯e/ne,GW = 0.51), and higher frequencies near the LCFS are modulated by this mode.

Greenwald density limit and power balance in tokamaks

The critical density limit in tokamaks is investigated. It is shown that the equality of the input power and power radiated by impurities corresponds to the Greenwald limit. In Ohmic tokamak plasmas the auxiliary heating may increase the density limit, as it has been shown in experiments. The radiated power threshold for plasmas with heavy impurities, observed in experiments, is derived. Radiation produced by heavy impurities is spread practically uniformly along the plasma radius in contrast to the radiation of light impurities. The effective heating power is decreased by radiation losses and, as a consequence, becomes lower than the threshold for the H-L transition. If the input power is close to the radiated one, the disruption occurs.

A predictive model for the tokamak density limit

The Greenwald density limit, found in all tokamak experiments, is reproduced for the first time using a phenomenologically correct model with parameters in the range of experiments. A simple model of equilibrium evolution and local power balance inside the island has been implemented to calculate the radiation-driven thermo-resistive tearing mode growth and explain the density limit. Strong destabilization of the tearing mode due to an imbalance of local Ohmic heating and radiative cooling in the island predicts the density limit within a few percent. The density limit is found to be a local edge limit and weakly dependent on impurity densities. Results are robust to a substantial variation in model parameters within the range of experiments.

Thermo-resistive disruptions and the tokamak density limit

The physical mechanism behind the tokamak density limit scaling is described in terms of a non-linear theory of tearing mode growth in cylindrical geometry coupled to a model for thermal transport in the island. Important new physics features of the model include: (1) island asymmetry due to finite island width in cylindrical geometry, (2) a model of radiation based on local coronal equilibrium including impurity radiation, (3) current perturbations due the perturbed resistivity, and (4) numerical solution of the cylindrical eigenfunctions and Δ′. The semi-analytic cylindrical model is then solved for a wide range of current profiles, magnetic field values, and plasma currents using reasonable assumptions for impurity densities and the Greenwald limit [M. Greenwald et al., Nucl. Fusion 28, 2199 (1988)] is reproduced. The limit is shown to be only weakly dependent on variations in the assumed parameters.

The tokamak density limit: A thermo-resistive disruption mechanism

The behavior of magnetic islands with 3D electron temperature and the corresponding 3D resistivity effects on growth are examined for islands with near-zero net heating in the island interior. We refer to the resulting class of non-linearities as thermo-resistive effects. In particular, the effects of varying impurity mix on the previously proposed local island onset threshold [Gates and Delgado-Aparicio, Phys. Rev. Lett. 108, 165004 (2012)] are examined and shown to be consistent with the well established experimental scalings for tokamaks at the density limit. A surprisingly simple semi-analytic theory is developed which imposes the effects of heating/cooling in the island interior as well as the effects of island geometry. For the class of current profiles considered, it is found that a new term that accounts for the thermal effects of island asymmetry is required in the modified Rutherford equation. The resultant model is shown to exhibit a robust onset of a rapidly growing tearing mode—consistent with the disruption mechanism observed at the density limit in tokamaks. A fully non-linear 3D cylindrical calculation is performed that simulates the effect of net island heating/cooling by raising/suppressing the temperature in the core of the island. In both the analytic theory and the numerical simulation, the sudden threshold for rapid growth is found to be due to an interaction between three distinct thermal non-linearities which affect the island resistivity, thereby modifying the growth dynamics.

20 years of research on the Alcator C-Mod tokamak

The object of this review is to summarize the achievements of research on the Alcator C-Mod tokamak [Hutchinson et al., Phys. Plasmas 1, 1511 (1994) and Marmar, Fusion Sci. Technol. 51, 261 (2007)] and to place that research in the context of the quest for practical fusion energy. C-Mod is a compact, high-field tokamak, whose unique design and operating parameters have produced a wealth of new and important results since it began operation in 1993, contributing data that extends tests of critical physical models into new parameter ranges and into new regimes. Using only high-power radio frequency (RF) waves for heating and current drive with innovative launching structures, C-Mod operates routinely at reactor level power densities and achieves plasma pressures higher than any other toroidal confinement device. C-Mod spearheaded the development of the vertical-target divertor and has always operated with high-Z metal plasma facing components—approaches subsequently adopted for ITER. C-Mod has made ground-breaking discoveries in divertor physics and plasma-material interactions at reactor-like power and particle fluxes and elucidated the critical role of cross-field transport in divertor operation, edge flows and the tokamak density limit. C-Mod developed the I-mode and the Enhanced Dα H-mode regimes, which have high performance without large edge localized modes and with pedestal transport self-regulated by short-wavelength electromagnetic waves. C-Mod has carried out pioneering studies of intrinsic rotation and demonstrated that self-generated flow shear can be strong enough in some cases to significantly modify transport. C-Mod made the first quantitative link between the pedestal temperature and the H-mode's performance, showing that the observed self-similar temperature profiles were consistent with critical-gradient-length theories and followed up with quantitative tests of nonlinear gyrokinetic models. RF research highlights include direct experimental observation of ion cyclotron range of frequency (ICRF) mode-conversion, ICRF flow drive, demonstration of lower-hybrid current drive at ITER-like densities and fields and, using a set of novel diagnostics, extensive validation of advanced RF codes. Disruption studies on C-Mod provided the first observation of non-axisymmetric halo currents and non-axisymmetric radiation in mitigated disruptions. A summary of important achievements and discoveries are included.

Stabiity of the Radiative Mode m = n = 0 and Density Limit in Tokamaks

AbstractThe problem of density limit and thermal disruption is one of the most important in ITER project. Different reasons for the disruption discuss now. At least 3% of disruptions are produced by the high level of impurity radiation from the edge [P.C. De Vries et al., Nucl. Fusion 51, 053018 (2011)]. Two reasons of the thermal disruption have been discussed earlier using simplified radiation model, the equilibrium loss [J.F. Drake, Phys. Fluids 30, 2429 (1987)], and radiation instability of the mode m = 0, n = 0 [M.Z. Tokar, Phys. Plasmas 7, 2432 (2000)]. Using the simplified model M.Z. Tokar founds two solutions. One of them is stable, the other is unstable. It is shown in the present paper that the unstable solution appears if the plasma density exceeds the critical value. The latter is found as a function of discharge parameters. It is shown also that the stable regime exists for realistic discharge parameters independently of plasma density. These regimes didn't investigated by M.Z. Tokar. Also, more adequate radiation models are discussed including charge‐exchange. It is shown that the impurity ‐ main plasma charge‐exchange decreases the critical density. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Physics of radiation-driven islands near the tokamak density limit

In previous work (Gates and Delgado-Aparicio 2012 Phys. Rev. Lett. 108 165004), the onset criterion for radiation-driven islands (Rebut et al 1985 Proc. 10th Int. Conf. on Plasma Physics and Controlled Nuclear Fusion Research 1984 (London, UK, 1984) vol 2 (Vienna: IAEA) p 197) in combination with a simple cylindrical model of tokamak current channel behaviour was shown to be consistent with the empirical scaling of the tokamak density limit (Greenwald et al 1988 Nucl. Fusion 28 2199). A number of the unexplained phenomena at the density limit are consistent with this novel physics mechanism. In this work, a more formal theoretical underpinning, consistent with cylindrical tearing mode theory, is developed for the onset criteria of these modes. The appropriate derivation of the radiation-driven addition to the modified Rutherford equation (MRE) is discussed. Additionally, the ordering of the terms in the MRE is examined in a regime near the density limit. It is hoped that, given the apparent success of this simple model in explaining the observed global scalings, it will lead to a more comprehensive analysis of the possibility that radiation-driven islands are the physics mechanism responsible for the density limit. In particular, with modern diagnostic capabilities detailed measurements of current densities, electron densities and impurity concentrations at rational surfaces should be possible, enabling verification of the concepts described above.

Origin of Tokamak Density Limit Scalings

The onset criterion for radiation driven islands [P. H. Rebut and M. Hugon, Plasma Physics and Controlled Nuclear Fusion Research 1984: Proc. 10th Int. Conf. London, 1984, (IAEA, Vienna, 1985), Vol. 2] in combination with a simple cylindrical model of tokamak current channel behavior is consistent with the empirical scaling of the tokamak density limit [M. Greenwald, Nucl. Fusion 28, 2199 (1988)]. Many other unexplained phenomena at the density limit are consistent with this novel physics mechanism.

Long-range correlations and edge transport bifurcation in fusion plasmas

Recently, a European transport project has been carried out among several fusion devices for studying the possible link between the mean radial electric field (Er), long-range correlation (LRC) and edge bifurcations in fusion plasmas. The main results reported in this paper include: (i) the discovery of low-frequency LRCs in potential fluctuations which are amplified during the development of edge mean Er using electrode biasing and during the spontaneous development of edge sheared flows in stellarators and tokamaks. Evidence of nonlocal energy transfer and the geodesic acoustic mode modulation on local turbulent transport have also been observed. The observed LRCs are consistent with the theory of zonal flows described by a ‘predator–prey’ model. The results point to a significant link between the LRC and transport bifurcation. (ii) Comparative studies in tokamaks, stellarators and reversed field pinches have revealed significant differences in the level of the LRC. Whereas the LRCs are clearly observed in tokamaks and stellarators, no clear signature of LRCs was seen in the RFX-mod reversed field pinch experiments. These results suggest the possible influence of magnetic perturbations on the LRC, in agreement with recent observations in the resonant magnetic perturbation experiments at the TEXTOR tokamak. (iii) The degree of the LRCs is strongly reduced on approaching the plasma density-limit in tokamaks and stellarators, suggesting the possible role of collisionality or/and the impact of mean Er × B flow shear on zonal flows.

Experimental studies of edge turbulence and confinement in Alcator C-Mod

The steep gradient edge region and scrape-off-layer (SOL) on the low-field-side of Alcator C-Mod [I. H. Hutchinson, R. Boivin, F. Bombarda et al., Phys. Plasmas 1, 1511 (1994)] tokamak plasmas are studied using gas-puff-imaging diagnostics. In L-mode plasmas, the region extending ∼2 cm inside the magnetic separatrix has fluctuations showing a broad, turbulent spectrum, propagating in the electron diamagnetic drift direction, whereas features in the open field line region propagate in the ion diamagnetic drift direction. This structure is robust against toroidal field strength, poloidal null-point geometry, plasma current, and plasma density. Global parameter dependence of spectral and spatial structure of the turbulence inside the separatrix is explored and characterized, and both the intensity and spectral distributions are found to depend strongly on the plasma density normalized to the tokamak density limit. In H-mode discharges the fluctuations at and inside the magnetic separatrix show fundamentally different trends compared to L-mode, with the electron diamagnetic direction propagating turbulence greatly reduced in ELM-free [F. Wagner et al., Proceedings of the Thirteenth Conference on Plasma Physics and Controlled Nuclear Fusion Research (IAEA, Vienna, 1982), Vol. I, p. 277], and completely dominated by the modelike structure of the quasicoherent mode in enhanced D-alpha regimes [A. E. Hubbard, R. L. Boivin, R. S. Granetz et al., Phys. Plasmas 8, 2033 (2001)], while the normalized SOL turbulence is largely unaffected.

Evidence for electromagnetic fluid drift turbulence controlling the edge plasma state in the Alcator C-Mod tokamak

Plasma profiles across the separatrix and scrape-off layer (SOL) in Alcator C-Mod are examined for a range of plasma densities, currents and magnetic fields in Ohmic L-mode discharges and for a subset of conditions in Ohmic H-mode discharges. In all plasmas, electron pressure gradient scale lengths () exhibit a minimum value just outside the separatrix (i.e. in the near SOL), forming the base of a weak (strong) pedestal in L-mode (H-mode) plasmas. Over a wide range of conditions in Ohmic L-mode discharges, at this location are found to track with a monotonic function of electron collision frequency, when this quantity is normalized according to the framework of electromagnetic fluid drift turbulence (EMFDT) theory. Moreover, at fixed values of normalized collisionality parameter (characterized as the ‘diamagnetic parameter’, αd), electron pressure gradients in the near SOL increase with plasma current squared, holding the MHD ballooning parameter, αMHD, unchanged. Thus, the state of the near SOL is restricted to a narrow region within this two-parameter phase-space. An implication is that cross-field heat and particle transport are strong functions of these parameters. Indeed, as αd is decreased below ∼0.3, cross-field heat convection increases sharply and competes with parallel heat conduction along open field lines, making high plasma density regions of αMHD–αd space energetically inaccessible. These observations are consistent with the idea that the operational space of the edge plasma, including boundaries associated with the tokamak density limit, is controlled by EMFDT.

Transitions of turbulence in plasma density limits

A series of BOUT [X. Q. Xu et al., Phys. Plasmas 7, 1951 (2000)] simulations is conducted to investigate the physical processes which limit the density in tokamak plasmas. Simulations of turbulence in tokamak boundary plasmas are presented which show that turbulent fluctuation levels and transport increase with collisionality. At high edge density, the perpendicular turbulent transport dominates the parallel classical transport, leading to substantially reduced contact with divertor plates and the destruction of the edge shear layer, and the region of high transport then extends inside the last closed flux surface. As the density increases these simulations show resistive X-point mode→resistive ballooning modes. The simulations also show that it is easier to reach the density limit as the density increases while holding pressure constant than holding temperature constant. A set of 2D transport simulations with increasingly large radial outboard transport, as indicated by BOUT for increasing density, shows that such transport can lead to an X-point multifaced asymmetric radiation from the edge when impurity radiation is included, which is a common symptom of density-limit related disruptions. BOUT further demonstrates that the local transport scaling with the current is similar to the global low-confinement-mode (L-mode) transport model (τE∝Ip) (by fixing q profiles). This current scaling appears on a plot of discharge current versus density as abruptly large radial transport once the Greenwald density is approached or exceeded. All of these results indicate that rapid edge cooling due to large radial transport is a key for the physics of the tokamak density limit.

On the density limit in tokamaks

A model for an ultimate density limit in tokamaks is presented. The model is based on considerations of radiative power balance and ideal ballooning stability limits at the plasma edge. Predictions for MAST are made and a comparison with experimental data on MAST is presented and discussed.

Consequences of core and edge similarity for experiments

The role of similarity parameters for core and edge phenomena in tokamaks, and the possibility to use sets of matching discharges on different devices under identical dimensionless parameters are discussed. Such experiments, carried out so far have show that the Kadomtsev set of dimensionless parameters is well suited to describe global confinement, and also the L-to-H transition phenomenon, at least in the intermediate density regime. The comparison of the existing empirical data base for the observed density limit in tokamaks with the prediction of similarity laws suggest a role of finite-β effects in the explanation of this phenomenon. Finally we discuss the possibility to simulate the interference between confinement scaling laws and operating boundaries in similarity experiments.

Investigation of physical processes limiting plasma density in high confinement mode discharges on DIII-D

A series of experiments was conducted on the DIII-D tokamak [J. L. Luxon and L. G. Davis, Fusion Technol. 8, 441 (1985)] to investigate the physical processes which limit density in high confinement mode (H-mode) discharges. The typical H-mode to low confinement mode (L-mode) transition limit at high density near the empirical Greenwald density limit [M. Greenwald et al., Nucl. Fusion 28, 2199 (1988)] was avoided by divertor pumping, which reduced divertor neutral pressure and prevented formation of a high density, intense radiation zone (MARFE) near the X-point. It was determined that the density decay time after pellet injection was independent of density relative to the Greenwald limit and increased nonlinearly with the plasma current. Magnetohydrodynamic (MHD) activity in pellet-fueled plasmas was observed at all power levels, and often caused unacceptable confinement degradation, except when the neutral beam injected (NBI) power was ⩽3 MW. Formation of MARFEs on closed field lines was avoided with low safety factor (q) operation but was observed at high q, qualitatively consistent with theory. By using pellet fueling and optimizing discharge parameters to avoid each of these limits, an operational space was accessed in which density ∼1.5×Greenwald limit was achieved for 600 ms, and good H-mode confinement was maintained for 300 ms of the density flat-top. More significantly, the density was successfully increased to the limit where a central radiative collapse was observed, the most fundamental density limit in tokamaks.

Transport Simulations of a Density Limit in Radiation-Dominated Tokamak Discharges II

The procedures developed previously to simulate the radiatively induced tokamak density limit are used to examine in more detail the scaling of the density limit. It is found that the maximum allowable density increases with auxiliary power and decreases with impurity concentration. However, it is demonstrated that there is little dependence of the density limit on plasma elongation. These trends are consistent with experimental results. Our previous work used coronal equilibrium impurities; the primary result of that paper was that the maximum density increases with current when peaked profiles are assumed. Here, this behavior is shown to occur with a coronal nonequilibrium impurity as well. 26 refs., 4 figs.

Cold bubble formation during tokamak density limit disruptions

Tokamak density limit disruptions are studied by tomographically analysing soft X-ray emission data using a modified circular harmonic reconstruction technique. Both minor and major disruptions are associated with the presence of dominant m=1/n and m=2/n=1 soft X-ray emissivity perturbations leading to the penetration of a cold bubble-like plasma volume to the centre. The role of mode coupling between the various emission components is examined and the observed behaviour is compared with the results of recent theoretical models

Disruptive tokamak density limit as scrape-off layer/divertor phenomenon

A model based on analysis of the scrape-off layer and divertor region is proposed for the disruptive density limit in divertor tokamaks. A critical edge density is derived from the power balance in front of the divertor plates. A crucial element of the model is the description of recycling. The model is extensively validated against ASDEX results. Significant differences observed in ASDEX before and after hardening are described by the model as being a consequence of the modified divertor design. In both regimes the absolute value as well as the scaling of the critical density in terms of q, Bt and Pin are reproduced.

A new look at density limits in tokamaks

While the results of early work on the density limit in tokamaks from the ORMAK and DITE groups have been useful over the years, results from recent experiments and the requirements for extrapolation to future experiments have prompted a new look at this subject. There are many physical processes which limit the attainable densities in tokamak plasmas. These processes include: (1) radiation from low Z impurities, convection, charge exchange and other losses at the plasma edge; (2) radiation from low or high Z impurities in the plasma core; (3) deterioration of particle confinement in the plasma core; and (4) inadequate fuelling, often exacerbated by strong pumping by walls, limiters or divertors. Depending upon the circumstances, any of these processes may dominate and determine a density limit. In general, these mechanisms do not show the same dependence on plasma parameters. The multiplicity of processes leading to density limits with a variety of scaling has led to some confusion when comparing density limits for different machines. The authors attempt to sort out the various limits and to extend the scaling law for one of them to include the important effects of plasma shaping, i.e. n̄;e = kJ̄, where ne is the line average electron density (1020 m−3), κ is the plasma elongation and J̄(MA·m−2) is the average plasma current density, defined as the total current divided by the plasma cross-sectional area. In a sense, this is the most important density limit since, together with the q-limit, it yields the maximum operating density for a tokamak plasma. It is shown that this limit may be caused by a dramatic deterioration in core particle confinement occurring as the density limit boundary is approached. This mechanism can help explain the disruptions and Marfes that are associated with the density limit.