Ion Thermal Diffusivity Research Articles

Scaling of heat transport with collisionality

The scaling of heat transport with collisionality (ν) in the banana regime has been measured in both L-mode (low confinement) and H-mode (high confinement) plasmas on the DIII-D tokamak [Fusion Technol. 8, 441 (1985)] with the other dimensionless parameters held fixed. Understanding the collisionality scaling of heat transport helps to distinguish between the different proposed mechanisms of turbulent transport and allows the origin of power degradation and density scaling of confinement to be determined. For L-mode plasmas on DIII-D, the scaling of the effective (or one-fluid) thermal diffusivity with collisionality is close to zero at all radii, χeff∝χBν−0.08±0.10, which is the expected scaling for the collisionless ion temperature gradient (ITG) and collisionless trapped electron modes. The ion and electron thermal diffusivities have the same collisionality scaling to within the experimental error. For H-mode plasmas, a stronger collisionality dependence of heat transport is observed, χeff∝χBν0.49±0.08 for a factor-of-8 scan in ν, which falls between the expected scalings of the collisionless ITG and collisionless trapped electron modes and that of the (edge) resistive ballooning mode. A portion of this H-mode collisionality scaling can be attributed to the ν dependence of neoclassical heat transport, especially in low collisionality regions of the plasma.

Tests of local transport theory and reduced wall impurity influx with highly radiative plasmas in the Tokamak Fusion Test Reactor

The electron temperature (Te) profile in neutral beam-heated supershot plasmas (Te0∼6–7 keV ion temperature Ti0∼15–20 keV, beam power Pb∼16 MW) was remarkably invariant when radiative losses were increased significantly through gas puffing of krypton and xenon in the Tokamak Fusion Test Reactor [McGuire et al., Phys. Plasmas 2, 2176 (1995)]. Trace impurity concentrations (nz/ne∼10−3) generated almost flat and centrally peaked radiation profiles, respectively, and increased the radiative losses to 45%–90% of the input power (from the normal ∼25%). Energy confinement was not degraded at radiated power fractions up to 80%. A 20%–30% increase in Ti, in spite of an increase in ion–electron power loss, implies a factor of ∼3 drop in the local ion thermal diffusivity. These experiments form the basis for a nearly ideal test of transport theory, since the change in the beam heating power profile is modest, while the distribution of power flow between (1) radiation and (2) conduction plus convection changes radically and is locally measurable. The decrease in Te was significantly less than predicted by two transport models and may provide important tests of more complete transport models. At input power levels of 30 MW, the increased radiation eliminated the catastrophic carbon influx (carbon “bloom”) and performance (energy confinement and neutron production) was improved significantly relative to that of matched shots without impurity gas puffing.

Ion cyclotron heating of JET DD and DT optimized shear plasmas

The unique roles played by ICRH in the preparation, formation and sustainment of internal transport barriers (ITBs) in high fusion performance JET optimized shear experiments using the Mark II poloidal divertor are discussed. Together with LHCD, low power ICRH is applied during the early ramp-up phase of the plasma current, `freezing in' a hollow or flat current density profile with q(0)>1. In combination with up to ∼20 MW of NBI, the ICRH power is stepped up to ∼6 MW during the main low confinement (L mode) heating phase. An ITB forms promptly after the power step, revealed by a region of reduced central energy transport and peaked profiles, with the ion thermal diffusivity falling to values close to the standard neoclassical level near the centre of both DD and DT plasmas. At the critical time of ITB formation, the plasma contains an energetic ICRF supported hydrogen minority ion population, contributing ∼50% to the total plasma pressure and heating mainly electrons. As both the NBI population and the thermal ion pressure develop, a substantial part of the ICRF power is damped resonantly on core ions (ω = 2 ωcD = 3ωcT), contributing to the ion heating. In NBI step-down experiments, high performance has been sustained by maintaining central ICRH; analysis shows the efficiency of central ICRH ion heating to be comparable to that of NBI. The highest DD fusion neutron rates (RNT = 5.6 × 1016 s-1) yet achieved in JET plasmas have been produced by combining a low magnetic shear core with a high confinement (H mode) edge. In DT, a fusion triple product niTiτE = (1.2 ± 0.2) × 1021 m-3 keV s was achieved with 7.2 MW of fusion power obtained in the L mode and with up to 8.2 MW of fusion power in the H mode phase.

Measurement of local ion diffusion coefficients in the Tokamak Fusion Test Reactor

The perturbations in ion temperature, density and parallel velocity resulting from sawtooth disruptions in TFTR are measured with a novel diagnostic. The local ion thermal diffusivity, particle diffusivity and parallel momentum diffusivity are determined in a high power discharge at r/a = 0.64 by fitting the observed pulses to a simple model of the radial diffusive propagation of heat, particles and momentum caused by the crash. The incremental ion thermal diffusivity, χiinc, is found to be similar in amplitude to the ion and electron thermal diffusivities obtained from a steady state 1-D power balance analysis, and the particle and parallel momentum diffusivities are found to be an order of magnitude smaller than χiinc.

Electron and ion internal transport barriers in Tore Supra and JET

Formation of core regions in Tore Supra and JET tokamaks with reduced transport coefficients is reported. Characteristics of the enhanced confinement regions and the physics process involved in their formation and maintenance should be considered separately when the electron or ion components are predominantly heated. In Tore Supra and JET, central electron temperature transitions are observed by injecting lower hybrid waves at modest power levels during the current ramp-up phase of the discharges. Transport analyses stress the importance of the low magnetic shear in the core to explain the anomalous electron transport reduction. With high-power dominant ion heating schemes in JET (neutral beam injection and ion cyclotron resonance heating), internal transport barriers have been obtained in plasmas fuelled with a mixture of deuterium-tritium (D-T) ions leading to a successful production of fusion power (8.2 MW) in this regime. Similar additional power levels to those applied in pure deuterium (D-D) plasmas are required to establish internal transport barriers in D-T plasmas. In D-D and D-T plasmas, ion thermal diffusivities are reduced close to their neoclassical levels in the plasma core and electron thermal diffusivities decrease by one order of magnitude at midplasma radius. The combined role of magnetic shear and velocity shear can explain the formation and evolution of plasma core regions with low energy transport coefficients.

Improved Confinement and Neoclassical Effect.

Matrix Inversion (MI) method is developed in order to estimate the neoclassical ion thermal diffusivity, χNC, correctly. In the MI method, effects of impurity on χNC are treated self-consistently and no approximation on the friction and the viscosity matrix elements is carried out. The comparison of χNC value between the MI method and the Chang-Hinton’s (CH) formula shows that the CH formula over-estimates χNC value twice as large as that of MI method for typical JT-60U plasmas. The different dependence of χNC on the inverse aspect ratio, e, the effective charge number, Zeff, and the normalized ion collisionality, ν*i, between the MI method and the CH formula is presented. The radial electric field. Er, is estimated from the momentum and the heat momentum balance equations parallel to the magnetic field. Profiles of Er are compared between the two types of improved core confinement plasmas with internal transport barrier (ITB) in JT-60U, the “parabolic type ITB” and the “box type ITB”. In the box type ITB, the experimentally estimated thermal diffusivity. χexp, decreases in the core region. However, the Er shear is not so strong. In the box type ITB, a strong Er shear appears inside the ITB layer and the χexp value decreases drastically to the level of χNC. The E×B shearing rate becomes almost the same as the linear growth rate of the drift microinstability inside the ITB layer of the box type ITB.

Scaling of heat transport with beta in the DIII-D tokamak

Experiments in the DIII-D tokamak have measured the scaling of heat transport with beta (β) whileall other dimensionless parameters are held constant for both H mode and L mode plasmas.Experimental results from the beta scaling of heat transport help to differentiate betweenvarious proposed mechanisms of turbulent transport.For L mode plasmas, the beta scaling of heat transport over the range 0.26 ⩽ βN ⩽ 0.49 isclose to zero, with the thermal confinement time scaling asBτth ∝ β-0.05±0.10 andthe effective (or one fluid) thermal diffusivityscaling as χeff ∝ χBβ0.11±0.20.The beta scalings of the ion and electron thermal diffusivities are the same as the effective diffusivity to within the experimental errors. Higher values of beta are investigated in H mode plasmas, where a weak-to-moderate beta scaling of transport is observed over the range 0.8 ⩽ βN ⩽ 1.7, with the thermal confinement time scaling as Bτth ∝ β0.03±0.11 and the effective thermal diffusivity scaling as χeff ∝ χBβ-0.54±0.21.The ion channel isresponsible for the favourable beta scaling of H mode plasmas; theelectron channel has no measurable beta dependence.These beta scalings determined by dimensionless parameter scansare much weaker than the predicted beta scalings fromthe L mode and H mode confinement scaling expressions that are currently being used to predict the performance of ITER.

Transport in JET deuterium plasmas with optimized shear

Plasmas with the highest deuterium fusion neutron rates yet achieved in JET have been produced by combining a hollow or flat central current profile with a high-confinement (H-mode) edge. In these discharges, lower hybrid current drive (LHCD) and ion cyclotron resonance heating (ICRH) preheating, applied early in the current ramp-up phase, `freezes in' a hollow or flat current density profile. When the combined neutral beam injection (NBI) and ICRH heating power is increased, a region of reduced transport and highly peaked profiles forms during the L-mode phase and persists into the later H-mode phase when the fusion reactivity reaches a maximum. Transport analysis shows the formation of a central region of good confinement (the internal transport barrier or ITB) which expands with radial velocity . The clearest signatures of this region are large gradients in the ion temperature and toroidal rotation profiles. Ion thermal diffusivities in the central region are of the order of the neoclassical value. The position and rate of expansion of the ITB radius correlates well with the calculated rational q = 2 surface. The confinement improvement can also be seen in electron density, and, to a lesser extent, in electron temperature. The ITB can persist in combination with the edge transport barrier characteristics of the H-mode.

Internal Transport Barriers in JET Deuterium-Tritium Plasmas

The observation of internal transport barriers (ITBs) in which ion thermal diffusivity is reduced to a neoclassical level has been made for the first time in tokamak plasmas fueled with deuterium and tritium ions using a broad current density profile. The heating and current profiles required to obtain an ITB are similar in D-T and D-D plasmas. Central ion temperatures of 40 keV and plasma pressure gradients of ${10}^{6}\mathrm{Pa}/\mathrm{m}$ were observed in a D-T plasma, leading to a fusion triple product ${n}_{i}{T}_{i}{\ensuremath{\tau}}_{E}{\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1.10}^{21}{\mathrm{m}}^{\ensuremath{-}3}\mathrm{keV}\mathrm{s}$ and 8.2 MW of fusion power. There is potential for further optimization as a step towards the development of efficient tokamak fusion reactors.

Energy transport during off-axis neutral beam heating in the DIII-D tokamak

Energy transport in discharges with off-axis neutral beam injection (NBI) has been compared with transport in similar discharges with on-axis NBI. A two fluid power balance analysis assuming purely diffusive transport indicates substantial improvements in the plasma centre in both the ion and the electron channels during off-axis NBI. The ion thermal diffusivity, χi, and the angular momentum diffusivity, χϕ, in the plasma centre improve by over 2 orders of magnitude, and χi decreases below the Chang-Hinton neoclassical level. A detailed error analysis of the energy transport has been carried out. The electron thermal diffusivity in the plasma centre improves by an order of magnitude during off-axis NBI. The predicted peak ion temperature, assuming the same ion diffusivity profile for off-axis NBI as with on-axis NBI, is nearly a factor of 2 lower than the measured ion temperature profile with off-axis NBI. In addition, assuming unchanged diffusivities, significant inward energy flow is required to explain the observed ion temperature profiles during off-axis NBI.

Testing the ρ* scaling of thermal transport models: Predicted and measured temperatures in the Tokamak Fusion Test Reactor dimensionless scaling experiments

Theoretical predictions of ion and electron thermal diffusivities are tested by comparing calculated and measured temperatures in low (L) mode plasmas from the Tokamak Fusion Test Reactor [D. J. Grove and D. M. Meade, Nucl. Fusion 25, 1167 (1985)] nondimensional scaling experiments. The DIII-D [J. L. Luxon and L. G. Davis, Fusion Technol. 8, 441 (1985)] L-mode ρ* scalings, the transport models of Rebut-Lallia-Watkins (RLW), Boucher’s modification of RLW, and the Institute for Fusion Studies-Princeton Plasma Physics Laboratory (IFS-PPPL) model for transport due to ion temperature gradient modes are tested. The predictions use the measured densities in order to include the effects of density profile shape variations on the transport models. The uncertainties in the measured and predicted temperatures are discussed. The predictions based on the DIII-D scalings are within the measurement uncertainties. All the theoretical models predict a more favorable ρ* dependence for the ion temperatures than is seen. Preliminary estimates indicate that sheared flow stabilization is important for some discharges, and that inclusion of its effects may bring the predictions of the IFS-PPPL model into agreement with the experiments.

Gyrokinetic simulation of isotope effects in tokamak plasmas

A three-dimensional (3-D) global gyrokinetic particle code in toroidal geometry has been used for investigating the transport properties of ion temperature gradient (ITG) drift instabilities in tokamak plasmas. Using the isotopes of hydrogen (H+), deuterium (D+) and tritium (T+), it is found that, under otherwise identical conditions, there exists a trend for favorable isotope scaling for the ion thermal diffusivity, i.e., χi decreases with mass. Such a trend, which exists both at the saturation of the instability and also at the fully nonlinear stage, can be understood from the resulting wave number and frequency spectra.

A New Self-Aligned Process for Fabrication of Microemitter Arrays Using Selective Etching of Silicon

Field electron emitter arrays (FEAs) have been fabricated by a novel self-aligned process. In this process the crystal-orientation dependent (anisotropic) and doping density dependent etching characteristics of single crystal Si are fully utilized. The emitter is formed by depositing a material in a mold prepared by anisotropic etching and thermal oxidation of Si. The gate is made of highly boron doped single-crystal Si, which acts as the etching mask for the mold formation. Gate/emitter spacing is determined by well-controlled ion implantation and thermal diffusion processes. FEAs with WSi2 emitters have been fabricated. The results demonstrate a small dispersion in gate/emitter spacing 3σ=0.19 µm where σ is the standard deviation. FEA operation at about 10 V is demonstrated.

Characteristics of and issues regarding combined H-modes

Owing to the recent progress of `profile controls' utilizing the freedom of profiles of plasma parameters, various types of combined (advanced) H-modes have been obtained; PEP H-mode, high- H-mode, high- H-mode, high- H-mode, reversed shear H-mode, CH-mode, VH-mode, etc. These combined H-modes with high potential for confinement and stability are characterized by improved transport in the core region in addition to the edge or deep inward penetration of the edge confinement pedestal. Such additional improvements seem to be related to flow shear, magnetic shear, safety factor, density profile or . The improved confinement region can propagate from the core to the edge or from the edge to the core, or appear almost simultaneously over the whole radius. However, there are some critical issues to be solved concerning reactor conditions, that is, under electron heating at high edge density with small impurity accumulation in the steady-state. Most of the NB heated combined H-modes have been obtained with ion heating, where ion thermal diffusivity and particle diffusivity can be reduced to the neoclassical level. However electron thermal diffusivity has so far not been clearly reduced except in the H-mode and in the VH-mode. Therefore, improvement of electron transport is one of the main issues. The second issue is that some improved modes are accompanied by strong density peaking which may result in large impurity accumulation. The third issue is the difficulty in achieving the improved modes at a high edge density with the high particle recycling essential for a dense and cold divertor. The fourth issue is the stability at high in the steady state. It is not certain that pressure and current profiles including the bootstrap current can be sustained stably. The requirement of ELMs for heat and particle exhaust is also an important issue in stability design as concerns the extent of the second regime access for the high-n ballooning mode.

Confinement and stability of DIII-D negative central shear discharges

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

Demonstration of high-performance negative central magnetic shear discharges in the DIII-D tokamak

Reliable operation of discharges with negative central magnetic shear has led to significant increases in plasma performance and reactivity in both low confinement, L-mode, and high confinement, H-mode, regimes in the DIII-D tokamak [Plasma Physics and Controlled Nuclear Fusion Research 1986 (International Atomic Energy Agency, Vienna, 1987), Vol. 1, p. 159]. Using neutral beam injection early in the initial current ramp, a large range of negative shear discharges have been produced with durations lasting up to 3.2 s. The total noninductive current (beam plus bootstrap) ranges from 50% to 80% in these discharges. In the region of shear reversal, significant peaking of the toroidal rotation [fφ(0)∼30–60 kHz] and ion temperature [Ti(0)∼15–22 keV] profiles are observed. In high-power discharges with an L-mode edge, peaked density profiles are also observed. Confinement enhancement factors up to H≡τE/τITER-89P∼2.5 with an L-mode edge, and H∼3.3 in an edge localized mode (ELM)-free H mode, are obtained. Transport analysis shows both ion thermal diffusivity and particle diffusivity to be near or below standard neoclassical values in the core. Large pressure peaking in the L mode leads to high disruptivity with βN≡βT/(I/aB)≤2.3, while broader pressure profiles in the H mode gives low disruptivity with βN≤4.2.

Action at distance and Bohm scaling of turbulence in tokamaks

Recent transport experiments in tokamaks have suggested the concept of ‘‘action at distance’’ in which the local turbulence depends on gradients at a distance larger than the correlation length. Furthermore, the scaling of the ion thermal diffusivity is not always consistent with local gyro-Bohm-like transport but rather scales worse than Bohm-like. This work is an attempt to reconcile these observations with simplified numerical simulations of toroidal ion temperature gradient (ITG) mode turbulence using a fast two-dimensional (2-D) inhomogeneous full radius turbulence code. It is found that action at a distance is possible, but only at weak damping rates, since the propagation range is given simply by the curvature drift group velocity divided by the average damping rate. The correlation lengths always scale linearly with the gyroradius. It is found that Bohm scaling or worse is possible when the gradients are close to the ITG threshold and the radial modes keep the turbulence level small enough to avoid destroying the slow to form global eigenmodes. In contrast to local ITG ballooning modes, the global eigenmode growth rates decrease with increasing gyroradius from the effect of larger diamagnetic rotational shear. This behavior results in an increase of the correlation time with increasing gyroradius, when the gradients are close to the thresholds. Thus, at sufficiently large relative gyroradius, the breaking of gyro-Bohm scaling can result from increased stability not mixing length.

Improved Confinement with Reversed Magnetic Shear in TFTR

A new tokamak confinement regime has been observed on the Tokamak Fusion Test Reactor (TFTR) where particle and ion thermal diffusivities drop precipitously by a factor of \ensuremath{\sim}40 to the neoclassical level for the particles and to much less than the neoclassical value for the ions in the region with reversed shear. This enhanced reversed shear confinement mode allows the central electron density to rise from 0.45 \ifmmode\times\else\texttimes\fi{} ${10}^{20}$ ${\mathrm{m}}^{\ensuremath{-}3}$ to \ensuremath{\sim}1.2 \ifmmode\times\else\texttimes\fi{} ${10}^{20}$ ${\mathrm{m}}^{\ensuremath{-}3}$ with ${T}_{i}\ensuremath{\sim}24$ keV and ${T}_{e}\ensuremath{\sim}8$ keV. This regime holds promise for significantly improved tokamak performance.

Nondimensional Transport Study of JT-60U Plasmas

Nondimensional local transport analysis of JT-60U plasmas has been carried out for NBI heated L-mode phase. Plasmas with the same poloidal cross section and almost the same profiles of nondimensional parameters such as ν * , β th , q , T e / T i except for ρ * are compared. The ρ * dependence of the one fluid thermal diffusivity, χ eff , the electron thermal diffusivity, χ e , and the ion thermal diffusivity, χ i , has been examined. The property of χ eff is between the weak gyroBohm type diffusion and the Bohm type diffusion in the region a /3≤ r ≤2 a /3, which is consistent with the results of the global confinement study done before. We have also found that χ e is weak gyroBohm type diffusion while χ i tends to be Bohm like diffusion.

Extension of a Bohm model for L-mode electron heat transport to ion heat transport and to the ohmic regime

The results of simulations of several JET L-mode and ohmic discharges performed with a Bohm-like expression for both ion and electron thermal diffusivities are presented. Comparisons with experimental ion and electron temperature profiles of auxiliary heated discharges show that xi i has to be at least twice larger than xi e to simulate the L-mode regime even for shots with dominant electron heating. Simulations of ohmic discharges with currents ranging from 1 to 7 MA show that the Bohm-like model for the L-mode is preferable to a neoalcator-like expression of the electron thermal diffusivities.