Confinement Scale Research Articles

Scaling of Electron and Ion Transport in the High-Power Spherical Torus NSTX

Dedicated $H$-mode parameter scans in the high-power National Spherical Torus Experiment have been used to establish the confinement scaling and underlying transport trends at low aspect ratio ($R/a\ensuremath{\simeq}1.3$). These scans indicate a strong dependence of the global and thermal energy confinement times on the toroidal field, ${B}_{T}^{0.9}$, while their dependence on plasma current is weaker, ${I}_{p}^{0.4}$. Local transport analysis indicates that the electrons control the ${B}_{T}$ scaling, whereas the ions control the ${I}_{p}$ scaling, with ${\ensuremath{\chi}}_{i}$ outside $r/a=0.5$ at the neoclassical level.

Confinement and Transport Research in Alcator C-Mod

Global and local transport experiments in ohmic, L-mode and H-mode regimes on the Alcator C-Mod tokamak are summarized. For ohmic plasmas, earlier results derived for energy confinement scaling in the Alcator (linear) regime have been confirmed, and the saturated confinement regime has been shown to be equivalent to that of L-mode. For auxiliary heated regimes, C-Mod provided a unique laboratory to test the standard scaling laws that had been previously derived. C-Mod’s L-mode performance matches the L-mode scaling laws quite well, but the confinement times in H-mode were about 50% above the existing H-mode scaling laws. This difference was significant and pointed up shortcomings in the range and conditioning of the existing database. H-mode studies emphasize quasi-steady regimes with good energy confinement, no impurity accumulation, and no large edge-localized modes. A new H-mode regime, where the pedestal is regulated by a continuous quasi-coherent mode, has been investigated extensively. The regime is most accessible at higher safety factor, triangularity, and collisionality and at low ion mass, suggesting that the mode is a form of resistive ballooning. Studies on C-Mod first showed the quantitative link between edge temperatures, core temperature gradients, and core confinement. This link unified L-mode and H-mode and established a strong connection between local and global transport. Further work on the role of critical gradient lengths and marginal stability lent quantitative support to the ion temperature gradient theories for ion transport and have helped elucidate nonlinear saturation mechanisms for the turbulence. Local transport studies demonstrated connections between transport channels, with energy, particle, and momentum transport varying across regimes in similar ways. Experiments carried out in collaboration with the DIII-D, ASDEX-U, and JET groups confirmed the dimensionless scaling approach over the widest available range in machine sizes. These studies suggest that plasma physics is the dominant influence on transport in the core and pedestal for standard L- and H-mode discharges. Dimensionless scaling experiments have shown a strong improvement in confinement with the normalized gyro size (1/ρ*). Confinement was found to be Bohm-like in L-mode and gyro-Bohm-like in H-mode. These experiments also showed a strong degradation in confinement with collisionality.

Energy Confinement Scaling Predictions for the Stabilized Tandem Mirror

The tandem mirror remains an attractive magnetic confinement geometry for fusion. The absence of toroidal curvature and relatively weak internal plasma parallel current gives the system strongly favorable stability and transport properties. Recent GAMMA-10 experiments demonstrate that sheared plasma rotation suppresses turbulent radial losses. Total energy confinement times calculated for the GAMMA-10 are found to be significantly larger than the corresponding empirical confinement times in toroidal devices. The tandem mirror appears to have a qualitatively different form of drift wave radial transport from that in toroidal devices.

Assessment of Transport in NCSX

We explore whether the energy confinement and planned heating in the National Compact Stellarator Experiment (NCSX) are sufficient to test magnetohydrodynamic (MHD) stability limits, and whether the configuration is sufficiently quasi-axisymmetric to reduce the neoclassical ripple transport to low levels, thereby allowing tokamak-like transport. A zero-dimensional model with fixed profile shapes is related to global energy confinement scalings for stellarators and tokamaks, neoclassical transport properties are assessed with the DKES, NEO, and NCLASS codes, and a power balance code is used to predict temperature profiles. Reaching the NCSX goal of <β> = 4% at low collisionality will require HISS-95 = 3, which is higher than the best achieved in present stellarators. However, this level of confinement is actually ~10% lower than that predicted by the ITER-97P tokamak L-mode scaling. By operating near the stellarator density limit, the required HISS-95 is reduced by 35%. The high degree of quasi-axisymmetry of the configuration and the self-consistent “ambipolar” electric field reduce the neoclassical ripple transport to a small fraction of the neoclassical axisymmetric transport. A combination of neoclassical and anomalous transport models produces pressure profile shapes that are within the range of those used to study the MHD stability of NCSX. We find that <β> = 4% plasmas are “neoclassically accessible” and are compatible with large levels of anomalous transport in the plasma periphery.

Numerical studies of confinement scalings for the dynamo-free reversed-field pinch

In the reversed-field pinch (RFP), tearing modes associated with the dynamo are responsible for reduced energy- and particle confinement. In this study, it is observed that by implementing current profile control (CPC) in the RFP, a dynamo-free state can be achieved. The effect of CPC in the RFP is examined by the use of numerical simulations, and scaling laws are presented for confinement parameters. The model is nonlinear MHD in 3D including finite resistivity and pressure. A linear regression analysis is performed on simulation data from a series of computer runs for a set of initial parameter values. Scaling laws are determined for radial magnetic field, energy confinement time, poloidal beta and temperature. Confinement is improved substantially as compared with the conventional RFP—the temperature reaches reactor relevant levels by ohmic heating alone. It is observed that the configuration spontaneously develops into a quasi single helicity state. The CPC scheme is designed to eliminate the fluctuating electric dynamo field Ef = −⟨v × B⟩, using feedback of an externally imposed electric field. The focus of this study is on obtaining principal theoretical optimization of confinement in the RFP by implementing CPC and to formulate scaling laws for confinement parameters, thus investigating the reactor viability of the concept.

Peculiarities in the spectrum of the adjoint scalar kinetic operator in Yang-Mills theory

We study the spectrum of low-lying eigenmodes of the kinetic operator for scalar particles, in the color adjoint representation of Yang-Mills theory. The kinetic operator is the covariant Laplacian, plus a constant which serves to renormalize mass. In the pure gauge theory, our data indicates that the interval between the lowest eigenvalue and the mobility edge tends to infinity in the continuum limit. On these grounds, it is suggested that the perturbative expression for the scalar propagator may be misleading even at distance scales that are small compared to the confinement scale. We also measure the density of low-lying eigenmodes, and find a possible connection to multicritical matrix models of order $m=1$.

Gyrokinetic particle simulation of fusion plasmas: path to petascale computing

Gyrokinetic particle simulation of fusion plasmas for studying turbulent transport on state-of-theart computers has a long history of important scientific discoveries. The primary examples are: (i) the identification of ion temperature gradient (ITG) drift turbulence as the most plausible process responsible for the thermal transport observed in tokamak experiments; (ii) the reduction of such transport due to the presence of zonal flows; (iii) the confinement scaling trends associated with size of the plasma and also with the ionic isotope species. With the availability of terascale computers in recent years, we have also been able to carry out simulations with improved physics fidelity using experimentally relevant parameters. Computationally, we have demonstrated that our lead Particle-in- Cell (PIC) code, the Gyrokinetic Turbulence Code (GTC), is portable, efficient, and scalable on various MPP platforms. Convergence studies with unprecedented phase-space resolution have also been carried out. Since petascale resources are expected to be available in the near future, we have also engaged in developing better physics models and more efficient numerical algorithms to take advantage of this exciting opportunity. For the near term, we are interested in understanding some basic physics issues related to burning plasmas experiments in International Thermonuclear Experimental Reactor (ITER) - a multi-billion dollar device to be constructed over the next decade. Our long range goal is to carry out integrated simulations for ITER plasmas for a wide range of temporal and spatial scales, including high-frequency short-wavelength wave heating, low-frequency meso-scale transport, and low-frequency large scale magnetohydrodynamic (MHD) physics on these computers.

Energy confinement scaling in the low aspect ratio National Spherical Torus Experiment (NSTX)

Systematic and statistical studies have been conducted in order to develop an understanding of the parametric dependences of both the global and thermal energy confinement times at low aspect ratio in high power National Spherical Torus Experiment discharges. The global and thermal confinement times of both L- and H-mode discharges can exceed values given by H-mode scalings developed for conventional aspect ratio. Results of systematic scans in the H-mode indicate that the confinement times exhibit a nearly linear dependence on plasma current and a power degradation weaker than that observed at conventional aspect ratio. In addition, the dependence on the toroidal magnetic field is stronger than that seen in conventional aspect ratio tokamaks. This latter trend is also evident in statistical analyses of the available dataset. These statistical studies also indicate a weaker parametric dependence on plasma current than found in the systematic scans, due to correlations among the predictor variables. Regressions based on engineering variables, when transformed to dimensionless physics variables, indicate that the dependence of BτE on βt can range from being negative to null. Regressions based directly on the dimensionless physics variables are inexact because of large correlations among these variables. Scatter in the confinement data, at otherwise fixed operating parameters, is found to be due to variations in ELM activity, low frequency density fluctuations and plasma shaping.

Enhanced Energy Confinement and Performance in a Low-Recycling Tokamak

Extensive lithium wall coatings and liquid lithium plasma-limiting surfaces reduce recycling, with dramatic improvements in Ohmic plasma discharges in the Current Drive Experiment-Upgrade. Global energy confinement times increase by up to 6 times. These results exceed confinement scalings such as ITER98P(y,1) by 2-3 times, and represent the largest increase in energy confinement ever observed for an Ohmic tokamak plasma. Measurements of Dalpha emission indicate that global recycling coefficients decrease to approximately 0.3, the lowest documented for a magnetically confined hydrogen plasma.

The role of aspect ratio and beta in H-mode confinement scalings

The addition of high power, low aspect ratio data from the NSTX and MAST experiments has motivated a new investigation of the effect of aspect ratio on confinement scaling. Various statistical methods, including those that incorporate estimates of measurement error, have been applied to datasets constrained by the standard set of criteria in addition to the range of κ and Meff appropriate to ITER operation. Development of scalings using engineering parameters as predictor variables results in ε-scaling coefficients that range from 0.38 to 1.29; the transformation of these scalings to physics variables results in an unfavourable dependence of Bτ on β, but a favourable dependence on ε. Because the low aspect ratio devices operate at low BT and therefore high βT, a strong correlation exists between ε and β, and this makes scalings based on physics variables imprecise.

ITER plasma performance assessment on the basis of newly-proposed scalings

The ITER plasma performance is assessed on the basis of the newly-proposed confinement scalings, using 1.5D simulations with the ASTRA code. In the simulations, the transport coefficients are adjusted to satisfy HH ≡ τE/τE(scaling) = 1 for each scaling. It is shown that for plasma current I = 15 MA and plasma minor radius a = 2 m for each scaling there exists an operational window within the range of moderate densities n/nG = 0.65–0.85 where nG is the Greenwald density nG (1020 m−3) = I/π a2. The fusion power Pfus = 250–600 MW can be obtained with neutral beam injection of 33 MW and ion cyclotron central heating of 0–20 MW. The operational windows predicted by the three scalings are close to each other. The fusion multiplication factor Q can achieve values in the range of 10–20 even with a more conservative assumption on helium pumping that corresponds to the ratio of the effective helium confinement time to the energy confinement time . The impact of enhanced particle confinement and increased threshold power for L to H mode transition on the ITER operational space is studied.

Global energy confinement scaling predictions for the kinetically stabilized tandem mirror

Transport is studied for the kinetically stabilized tandem mirror, an attractive magnetic confinement device for achieving a steady-state burning plasma. For a magnetohydrodynamic stable system, three different radial transport models with Bohm, gyro-Bohm, and electron temperature gradient (ETG) scaling are derived. As a conservative estimate, numerical coefficients in the models are taken to be consistent with tokamak and stellarator databases. The plug mirrors create an ambipolar potential that controls end losses, whereas radial losses are driven by drift wave turbulence, which lowers the electron temperature through radially trapped particle modes and ETG transport losses. The radial transport equations are analyzed, taking into account the Pastukhov energy and particle end losses. For mirror ratio Rm=9 and a large density ratio between plug and central cell regions, there is a high axial ion confinement potential ϕi∕Ti⪢1, as demonstrated in the GAMMA-10 by Cho et al. [Nucl. Fusion 45, 1650 (2005)]. Profiles and total energy confinement times are calculated for a proof-of-principle experiment (length L=7m, central cell magnetic field B=0.28T, and radius a=1m) and for a test reactor facility (L=30m, B=3T, a=1.5m). For these parameter sets, radial loss dominates the end losses except in the low temperature periphery. In the limit of negligible radial losses, ideal ignition occurs at Ti=7.6keV from the two-body power end losses. The transport suppressing rotation rate is well below the sonic value and scales similarly to biased wall rotation rates in the Large Plasma Device experiments [Horton et al., Phys. Plasmas 12, 022303 (2005)]. Simulation results show that the positive dependence of electron radial transport with increasing electron temperature stabilizes the thermal instabilities giving steady state with Ti=30–60keV and Te=50–150keV with a fusion amplification Q of order 1.5 to 5.0.

Adjoint trapping: a new phenomenon at strong 't Hooft coupling

Adding matter of mass m, in the fundamental representation of SU(N), to N=4 supersymmetric Yang-Mills theory, we study ``generalized quarkonium'' containing a (s)quark, an anti(s)quark, and J massless (or very light) adjoint particles. At large 't Hooft coupling $\lambda$ >> 1, the states of spin <= 1 are surprisingly light (Kruczenski et al., hep-th/0304032) and small (hep-th/0312071) with a J-independent size of order $\sqrt{\lambda}/m$. This ``trapping'' of adjoint matter in a region small compared with its Compton wavelength and compared to any confinement scale in the theory is an unfamiliar phenomenon, as it does not occur at small $\lambda$. We explore adjoint trapping further by considering the limit of large J. In particular, for J >> $\sqrt{\lambda}$ >> 1, we expect the trapping phenomenon to become unstable. Using Wilson loop methods, we show that a sharp transition, in which the generalized quarkonium states become unbound (for massless adjoints) occurs at $J \simeq 0.22 \sqrt{\lambda}$. If the adjoint scalars of N=4 are massive and the theory is confining (as, for instance, in N=1* theories) then the transition becomes a cross-over, across which the size of the states changes rapidly from ~$\sqrt{\lambda}/m$ to something of order the confinement scale ~ $\Lambda^{-1}$.

Global confinement scaling for high-density plasmas in the Large Helical Device

Density and power scan experiments have been carried out at various magnetic field strengths on the Large Helical Device (LHD), to investigate the temperature and magnetic field dependences of the thermal diffusivity. In the moderate density regime, the thermal diffusivity shows gyro-Bohm-like parameter dependences. In the high-density and low-temperature regime, on the other hand, the thermal diffusivity increases with the square root of the local electron temperature and decreases with a 1.2 power of the magnetic field strength. The turning point temperature where the weak temperature dependence changes to the gyro-Bohm type is also found to increase with a 0.8 power of the magnetic field strength. Based on the experimental results, dimensionally correct scalings for the energy confinement time, τE, and the plasma stored energy for the high-density LHD plasmas have been derived. Compared with the gyro-Bohm model (τE ∝ (n/P)3/5, where n and P denote the density and the heating power, respectively) and the international stellarator scaling 1995 (τE ∝ n0.51P−0.59), our scaling has a weaker positive dependence on the density together with the mitigated power degradation as τE ∝ (n/P)1/3, owing to the weak temperature dependence of the thermal diffusivity.

Counterexamples to the correlated stability conjecture

We demonstrate explicit counter-examples to the Correlated Stability Conjecture (CSC), which claims that the horizon of a black brane is unstable precisely if that horizon has a thermodynamic instability, meaning that its matrix of susceptibilities has a negative eigenvalue. These examples involve phase transitions near the horizon. Ways to restrict or revise the CSC are suggested. One of our examples shows that N=1* gauge theory has a second order chiral symmetry breaking phase transition at a temperature well above the confinement scale.

Rho-Star Scaling and Physically Realistic Gyrokinetic Simulations of Transport in DIII-D

This paper briefly reviews the DIII-D experiments to determine rho-star (ρ*) confinement scaling to reactors, the theory of broken gyro-Bohm scaling from local rotational shear stabilization and various nonlocal effects, and how the gyrokinetic code GYRO is being used for physically realistic simulations to understand Bohm scaling in L-modes.

Hybrid Scenario Development in DIII-D

Experiments in the DIII-D tokamak have demonstrated the ability to sustain ELMing H-mode discharges with high beta and good confinement quality under stationary conditions. These experiments have shown the ability to sustain normalized fusion performance (in terms of βNH89P /q952) at or above that projected for Qfus = 10 operation in the International Thermonuclear Experimental Reactor (ITER) design over a wide range in operating parameters. In the best cases, operation is maintained at the free boundary, n = 1 stability limit. Confinement is found to be better than standard H-mode confinement scalings over a wide range in operation space, and experimentally measured transport is consistent with predictions from the GLF23 transport code. Projections using the standard ITER H-mode scaling laws based on these discharges indicate that Qfus = 5 can be maintained for >5400 s in ITER at q95 = 4.5 while Qfus = 40 can be obtained for ~2400 s at q95 = 3.2. These projected performance levels further validate the ITER design and suggest that long-pulse, high neutron fluence operation as well as very high fusion gain operation may be possible in next-generation tokamaks.

Development, physics basis and performance projections for hybrid scenario operation in ITER on DIII-D

A potential new standard in stationary tokamak performance is emerging from experiments on DIII-D. These experiments have demonstrated the ability to operate near the free boundary, n = 1 stability limit with good confinement quality under stationary conditions. The normalized fusion performance is at or above that projected for Qfus = 10 operation in the International Thermonuclear Experimental Reactor (ITER) design over a wide operating range in both edge safety factor (2.8–4.7) and plasma density (35–70% of the Greenwald density). Projections to ITER based on this data are uniformly positive and indicate that a wide range of operating options may be available on ITER, including the possibility of sustained ignition. Recent experiments have demonstrated the importance of a small m = 3, n = 2 neoclassical tearing mode in avoiding sawteeth and the effect of edge localized modes on tearing mode stability at an edge safety factor near 3. Transport studies using the GLF23 turbulence transport code suggest that E × B shear stabilization is important in reproducing the measured profiles in the simulation. Yet, even in cases in which the toroidal rotation is moderate, confinement quality is robustly better than the standard H-mode confinement scalings.

Effects of Confinement on the Thermodynamics of a Collapsing Heteropolymer: An Off-Lattice Wang−Landau Monte Carlo Simulation Study

We present an analysis of the thermodynamics of the coil-to-globule transition of a bead−spring heteropolymer in selective solvent conditions in confined geometries. We have used the continuous-space version of the Wang−Landau Monte Carlo simulation algorithm. Generally, decreasing volume of confinement stabilizes the compact state, reflected directly by an increase in the transition temperature, in agreement with previous theoretical pictures. We propose a new scaling relationship for the shift in the transition temperature in which the changes in latent heat and latent entropies upon confinement scale with the confining geometry size with slightly different scaling exponents. The model agrees with the simulation data well and slightly outperforms simpler scaling models used in the past. Details of the algorithm, including novel trial moves, are presented and discussed. In particular, we find it useful to use so-called “partial molecular dynamics” trial moves.

Threshold for sheared flow and turbulence development in the TJ-II stellarator**This paper was first presented at the EPS04 conference.

The influence of plasma density and edge gradients on the development of perpendicular sheared flow has been investigated in the plasma edge region of the TJ-II stellarator. The development of the naturally occurring velocity shear layer requires a minimum plasma density. Experimental findings have shown that there is a coupling between the onset of sheared flow development and an increase in the level of plasma edge turbulence; once sheared flow is fully developed the level of fluctuations and turbulent transport slightly decreases whereas edge gradients and plasma density increases. Electron density profiles show a broadening evolution as density increases above the critical value where sheared flow is developed, while the temperature profile remains similar, reflecting the strong impact of plasma density in the global confinement scaling. Furthermore, the shearing rate of the spontaneous sheared flow turns out to be close to the one needed to trigger a transition to improved confinement regimes. Density ramp experiments show, within the experimental uncertainty, no evidence of hysteresis during the spontaneous shear development. Power modulation, in the proximity of the critical plasma density, allows the characterization of plasma potential and electric field relaxation during the transition. The present results have a direct impact on the understanding of the physics mechanisms underlying the generation of critical sheared flow, pointing to the important role of turbulent driven flow.