Confinement Mode Transition Research Articles

Investigation of the cause of the high-to-low mode confinement transition following multifaceted asymmetric radiation from edge formation in DIII-D

The common observation that the onset of a core MARFE (multifaceted asymmetric radiation from edge) is followed immediately by a H-L (high-to-low) confinement mode transition in DIII-D [J. Luxon, Nucl. Fusion 42, 614 (2002)] was investigated by comparing a theoretical prediction of the threshold nonradiative power across the separatrix needed to maintain H mode with an experimental determination of the nonradiative power flowing across the separatrix. It was found that in three shots with continuous gas fueling the increased neutral influx associated with the MARFE formation caused a sharp increase in the predicted threshold nonradiative power crossing the separatrix that was required for the plasma to remain in H mode to a value comparable to the experimental power crossing the separatrix.

Thermal instability analysis of different types of density limits in DIII-D gas fueled, high-mode discharges

High density, gas fueled, high confinement mode, DIII-D [Luxon, Anderson, Batty et al., Plasma Physics and Controlled Nuclear Fusion Research 1986 (International Atomic Energy Agency, Vienna, 1987), Vol. 1, p. 159] shots that were limited in density buildup by: (1) an H–L (high-to-low confinement mode) transition apparently triggered by a core X-point MARFE (multifaceted asymmetric radiation from edge), following the thermal instability sequence of detachment-divertor MARFE-core X-point MARFE; (2) a density limit apparently triggered by large scale core magnetohydrodynamic activity; and (3) an H–L transition apparently triggered by excessive radiated power from the plasma core are analyzed. The presence or absence of a MARFE was correctly predicted by thermal instability theory. A sharp edge temperature gradient was identified as an important factor inhibiting the usual detachment-MARFE sequence in DIII-D and thus leading to the achievement of higher density.

Characteristics of the first H-mode discharges in the national spherical torus experiment.

We report observations of the first low-to-high ( L-H) confinement mode transitions in the National Spherical Torus Experiment. The H-mode energy confinement time increased over reference discharges transiently by 100-200%, as high as approximately 100 ms. This confinement time is approximately 2 times higher than predicted by a multimachine scaling. Thus the confinement time of spherical tori has been extended to a record high value, leading to an eventual revision of confinement scalings. Finally, the power threshold for H-mode access is >10x higher than predicted by an international scaling from conventional aspect-ratio tokamaks, which could lead to new understanding of H-mode transition dynamics.

Comparative studies of the d W/d t effect in the net heating power for ignition analyses

We compare two cases with and without subtraction of d W/d t in the net heating power after the high confinement mode transition (H-transition) and study the effects of d W/d t on zero-dimensional ignition analyses in various ignition phases in a deuterium–tririum (D–T) tokamak reactor including International Thermonuclear Experimental Reactor (ITER). Subtraction of d W/d t from the net heating power after the H-transition as done in H-mode power threshold analyses results in a wrong control action in feedback control during the confinement factor increment and abnormal behaviors in operation phases such as fusion power ramp-up, steady state, and shutdown phases in a reactor. As subtraction of dW/dt in the L-mode phase is to describe the delay time effect of the heating power to the plasma edge, we conclude that d W/d t should not be subtracted from the net heating power after the H-transition in the zero-dimensional approach. This is because that the H-mode is determined by the net heating power to the plasma edge both before and after the H-transition, but not by the plasma conduction loss power out of the plasma edge.

Results from helical axis stellarators

Helical axis stellarators produce magnetic surfaces of high rotational transform and moderate shear solely by means of external currents, with the promise of high β. Several machines with quite different toroidal, helical, and “bumpy” Fourier components of magnetic field are now producing results, including high quality magnetic surfaces, confinement mode transitions, configuration studies, and confinement consistent with International Stellarator Scaling (ISS95) scaling up to Te∼2 keV. These devices permit concept evaluation over an unprecedented configuration space, and allow basic comparisons with those designed by established and alternative optimization strategies.

Internal transport barriers on Alcator C-Mod

The formation of internal transport barriers (ITBs) has been observed in the core region of Alcator C-Mod [I. H. Hutchinson et al., Phys. Plasmas 1, 1511 (1994)] under a variety of conditions. The improvement in core confinement following pellet injection (pellet enhanced performance or PEP mode) has been well documented on Alcator C-Mod in the past. Recently three new ITB phenomena have been observed which require no externally applied particle or momentum input. Short lived ITBs form spontaneously following the high confinement to low confinement mode transition and are characterized by a large increase in the global neutron production (enhanced neutron or EN modes). Experiments with ion cyclotron range of frequencies power injection to the plasma off-axis on the high field side results in the central density rising abruptly and becoming peaked. The ITB formed at this time lasts for ten energy confinement times. The central toroidal rotation velocity decreases and changes sign as the density rises. Similar spontaneous ITBs have been observed in ohmically heated H-mode plasmas. All of these ITB events have strongly peaked density profiles with a minimum in the density scale length occurring near r/a=0.5 and have improved confinement parameters in the core region of the plasma.

The role of thermal instabilities in limiting the density in DIII-D

The mechanisms which apparently govern the maximum achievable density in several DIII-D [Luxon, Anderson, Batty et al., Plasma Physics on Controlled Nuclear Fusion Research 1986 (IAEA, Vienna, 1987), Vol. 1, p. 159] shots in which different operating procedures were used in building up the density were investigated and compared with the predictions of thermal instability theory. Core MARFEs (multifaceted asymmetric radiation from the edge) followed by a H–L (high-to-low confinement mode) transition limit the density well below the Greenwald limit in continuous gas puffed lower single-null discharges with low triangularity. Similar continuous gas puff fueled discharges with higher triangularity or with pumping in the lower divertor achieve densities at or above the Greenwald value, apparently limited by confinement degradation, without the formation of core MARFEs. Pellet fueled discharges achieve densities up to twice the Greenwald value, limited by global radiative collapse. Thermal instability theory predictions of the limiting core MARFEs, confinement degradation or global radiative collapse are in good agreement with the experimental observations for the shots examined. Evidence for an important role of neutral particles in the plasma edge in core MARFE onset and in confinement degradation was identified.

Measurement of neutral density near the X point in the DIII-D tokamak

Theories predict that neutrals play a role in the low to high (L-H) confinement mode transition in tokamak plasmas via charge exchange damping and other effects. Previous estimates of neutral damping have been based on calculations of the edge neutral density. This work introduces a new method of measuring the neutral density near the X point, where simulations predict it to be a maximum. The technique employed uses Dα light from a TV camera reconstructed onto a poloidal plane, along with Thomson scattering measurements of the electron temperature and density. Measured neutral densities span the range 109-1013cm-3. Good agreement,considering the neutral density error bars, is found between the measurements and the 2-D simulations. This work represents the first step in verifying previous 2-D simulations and in corroborating previous conclusions that the neutral damping is large enough to play a role in the L-H transition process.

Versatile millimeter-wave interferometer with two frequencies in the divertor region of JT-60U

A millimeter-wave interferometer having a capability of concomitant electron temperature measurement, based on the electron cyclotron absorption (ECA) technique, has been developed for divertor diagnostics in JT-60U. Three lines of sight, which pass through the X point horizontally, the inboard divertor and the outboard divertor, are chosen. Two transmitter/receiver units with frequencies of 217 and 183 GHz are employed in order to eliminate the spurious vibration effect using a two color scheme. The two independent units are also arranged to enable two sight line measurements without the vibration compensation. Furthermore, these units allow us to apply the simultaneous ECA diagnostic. Due to the complexity of the transmission line inside the tokamak, the insertion loss is as large as 65 dB. However, the interferometer system can be operated with the signal-to-noise (S/N) ratio of about 20 dB due to the low equivalent input noise of −90 dB m. The measurements performed for several types of the JT-60U discharges indicate the feasibility of the system and the rapid reduction of the electron density near the X point at the high confinement mode transition is first demonstrated.

Safety Analyses for Transient Behavior of Plasma and In-vessel Components during Plasma Abnormal Events in Fusion Reactor

Safety analyses on plasma abnormal events have been performed using a hybrid code of a plasma dynamics model and a heat transfer model of in-vessel components. Several abnormal events, e.g., increase in fueling rate, were selected for the International Thermonuclear Experimental Reactor (ITER) and transient behavior of the plasma and the invessel components during the events was analyzed. The physics model for safety analysis was conservatively prepared. In most cases, the plasma is terminated by a disruption or it returns to the original operation point. When the energy confinement improves by a factor of 2.0 in the steady state, which is a hypothetical assumption under the present plasma data, the maximum fusion power reaches about 3.3 GW at about 3.6s and the plasma is terminated due to a disruption. However, the results obtained in this study show the confinement boundary of ITER can be kept almost intact during the abnormal plasma transients, as long as the cooling system works normally. Several parametric studies are needed to comprehend the overpower transient including structure behavior, since many uncertainties are connected to the filed of the plasma physics. And, future work will need to discuss the burn control scenario considering confinement mode transition, system specifications, experimental plans and safety regulations, etc. to confirm the safety related to the plasma anomaly.

Theory of plasma confinement in devices with pure toroidal field

Equilibrium, stability, and confinement in currentless toroidal device is studied in the terms of the flow-fluctuation cycle. In the initial seed equilibrium provided by the limiter, Rayleigh–Taylor (RT) fluctuations grow appreciably. These fluctuations are additional source of rotational transform in two ways. First, they directly drive a poloidal flow via Reynolds stress which improves the equilibrium. Second, the flow modifies the rms level profile in such a way that the ponderomotive force due to the fluctuations impedes the free fall. Detailed linear theory of Rayleigh–Taylor fluctuations with poloidal flow is presented and criteria for flow stabilization are identified. Using the exact eigenfunction of fluctuations, an exact ordinary differential equation for poloidal flow is derived and solved using an ansatz. Finally, the relevance of this analysis to the recently proposed low to high confinement mode transition theories is discussed.

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.

Safety Analyses for Transient Behavior of Plasma and In-vessel Components during Plasma Abnormal Events in Fusion Reactor.

Safety analyses on plasma abnormal events have been performed using a hybrid code of a plasma dynamics model and a heat transfer model of in-vessel components. Several abnormal events, e.g., increase in fueling rate, were selected for the International Thermonuclear Experimental Reactor (ITER) and transient behavior of the plasma and the invessel components during the events was analyzed. The physics model for safety analysis was conservatively prepared. In most cases, the plasma is terminated by a disruption or it returns to the original operation point. When the energy confinement improves by a factor of 2.0 in the steady state, which is a hypothetical assumption under the present plasma data, the maximum fusion power reaches about 3.3 GW at about 3.6s and the plasma is terminated due to a disruption. However, the results obtained in this study show the confinement boundary of ITER can be kept almost intact during the abnormal plasma transients, as long as the cooling system works normally. Several parametric studies are needed to comprehend the overpower transient including structure behavior, since many uncertainties are connected to the filed of the plasma physics. And, future work will need to discuss the burn control scenario considering confinement mode transition, system specifications, experimental plans and safety regulations, etc. to confirm the safety related to the plasma anomaly.

Wavelet bicoherence: A new turbulence analysis tool

A recently introduced tool for the analysis of turbulence, wavelet bicoherence [van Milligen, Hidalgo, and Sánchez, Phys. Rev. Lett. 16, 395 (1995)], is investigated. It is capable of detecting phase coupling—nonlinear interactions of the lowest (quadratic) order—with time resolution. To demonstrate its potential, it is applied to numerical models of chaos and turbulence and to real measurements. It detected the coupling interaction between two coupled van der Pol oscillators. When applied to a model of drift wave turbulence relevant to plasma physics, it detected a highly localized coherent structure. Analyzing reflectometry measurements made in fusion plasmas, it detected temporal intermittency and a strong increase in nonlinear phase coupling coinciding with the L/H (low-to-high confinement mode) transition.

The effect of an external torque on low to high confinement transitions

A number of experiments have attempted, with varying degrees of success, to influence the low to high confinement mode (L–H) transition through the application of an external flow shear forcing mechanism. In order to theoretically describe this type of experiment, an external torque is included in the phase transition model of Diamond et al. [Phys. Rev. Lett. 72, 2965 (1994)] for the L–H bifurcation. These equations exhibit a bifurcation between an L-mode fixed point and an H-mode fixed point with variation of a critical parameter, corresponding to the edge gradient, across a threshold value. With the addition of the external torque [from biased limiter, probe, or radio frequency (rf) wave], the character of the transition changes in a manner analogous to the addition of an external magnetic field to a ferromagnetic material. In addition to the change in the transition dynamics, there is a marked decrease in the threshold level. In this simple model, the decrease in threshold level is proportional to the applied torque to the two-thirds power, in approximate functional agreement with that seen by some experiments.

Beyond paradigm: Turbulence, transport, and the origin of the radial electric field in low to high confinement mode transitions in the DIII-D tokamak

The paradigm of shear suppression of turbulence as the mechanism for the low to high confinement mode (L to H) transition is examined by quantitative comparison of the predictions of the paradigm with experimental results from the DIII-D tokamak [Plasma Physics and Controlled Fusion Research (International Atomic Energy Agency, Vienna, 1986), p. 159]. The L to H transition trigger is V×B rotation, not the main ion pressure gradient. The radial electric field Er shear increases before the fluctuation suppression, consistent with increasing Er shear as the cause of the turbulence suppression. The spatial dependence of the turbulence reduction is consistent with shear suppression for negative Er shear. For positive Er shear, the turbulence suppression is consistent with the effect of Er curvature for modes for which an Er well is destabilizing. Finally, the transport barrier depends on the phase angle between the density and potential fluctuations inside the Er well, an effect not included in existing L to H transition models.

L-H confinement mode dynamics in three-dimensional state space

A dynamical model for the low-high (L-H) confinement mode transitions consisting of three ordinary differential equations (3-ODE model) for the essential state variables is proposed. The model is derived from the energy balance equations for the resistive pressure-gradient-driven turbulence and describes temporal evolutions of three characteristic variables (u, k, f), the potential energy contained in the pressure gradient, the turbulent kinetic energy and the shear flow energy. The energy input to the peripheral plasma region is included as an external control parameter in the model. The model equations have stationary solutions corresponding to the L- and H-modes. The L to H and H to L transitions are obtained by varying the energy input parameter. The type of L-H transition, whether like a first- or second-order transition, is shown to be determined by the sheer flow damping. At a higher level of the energy input parameter the H-mode stationary solution becomes unstable and bifurcates to a limit cycle which shows periodic oscillations characteristic of the H-localized mode (ELM) confinement state.

Turbulent edge transport in the Princeton Beta Experiment-Modified high confinement mode

The first probe measurements of edge turbulence and transport in a neutral beam induced high confinement mode (H-mode) are reported. A strong negative radial electric field is directly observed in H-mode. A transient suppression of normalized ion saturation and floating potential fluctuation levels occurs at the low confinement mode to high confinement mode (L–H) transition, followed by a recovery to near low mode (L-mode) levels. The average poloidal wave number and the poloidal wave-number spectral width are decreased, and the correlation between fluctuating density and potential is reduced. A large-amplitude coherent oscillation, localized to the strong radial electric field region, is observed in H-mode but does not cause transport. In H-mode the effective turbulent diffusion coefficient is reduced by an order of magnitude inside the last closed flux surface and in the scrape-off layer. The results are compared with a heuristic model of turbulence suppression by velocity-shear stabilization.

Shear flow generation by Reynolds stress and suppression of resistive g modes

Suppression of resistive g-mode turbulence by background shear flow generated from a small external flow source and amplified by the fluctuation-induced Reynolds stress is demonstrated and analyzed. The model leads to a paradigm for the low-to-high (L–H) confinement mode transition. To demonstrate the L–H transition model, single-helicity nonlinear fluid simulations using the vorticity equation for the electrostatic potential, the pressure fluctuation equation, and the background poloidal flow equation are used in the sheared slab configuration. The relative efficiency of the external flow and the Reynolds stress for producing shear flow depends on the poloidal flow damping parameter ν, which is given by neoclassical theory. For large ν, the external flow is a dominant contribution to the total background poloidal shear flow and its strength predicted by the neoclassical theory is not enough to suppress the turbulence significantly. In contrast, for small ν, it is shown that the fluctuations drive a Reynolds stress that becomes large and suddenly, at some critical point in time, shear flow much larger than the external flow is generated and leads to an abrupt, order unity reduction of the turbulent transport just like that of the L–H transition in tokamak experiments. It is also found that, even in the case of no external flow, the shear flow generation due to the Reynolds stress occurs through the nonlinear interaction of the resistive g modes and reduces the transport. To supplement the numerical solutions, the Landau equation for the mode amplitude of the resistive g mode is derived, taking into account the fluctuation-induced shear flow and the opposite action of the Reynolds stress in the resistive g turbulence compared with the classical shear flow Kelvin–Helmholtz (KH) driven turbulence is analyzed.