Peaked Density Profiles Research Articles

Overview of ASDEX Upgrade results

The medium size divertor tokamak ASDEX Upgrade (major and minor radii 1.65 m and 0.5 m, respectively, magnetic-field strength 2.5 T) possesses flexible shaping and versatile heating and current drive systems. Recently the technical capabilities were extended by increasing the electron cyclotron resonance heating (ECRH) power, by installing 2 × 8 internal magnetic perturbation coils, and by improving the ion cyclotron range of frequency compatibility with the tungsten wall. With the perturbation coils, reliable suppression of large type-I edge localized modes (ELMs) could be demonstrated in a wide operational window, which opens up above a critical plasma pedestal density. The pellet fuelling efficiency was observed to increase which gives access to H-mode discharges with peaked density profiles at line densities clearly exceeding the empirical Greenwald limit. Owing to the increased ECRH power of 4 MW, H-mode discharges could be studied in regimes with dominant electron heating and low plasma rotation velocities, i.e. under conditions particularly relevant for ITER. The ion-pressure gradient and the neoclassical radial electric field emerge as key parameters for the transition. Using the total simultaneously available heating power of 23 MW, high performance discharges have been carried out where feed-back controlled radiative cooling in the core and the divertor allowed the divertor peak power loads to be maintained below 5 MW m−2. Under attached divertor conditions, a multi-device scaling expression for the power-decay length was obtained which is independent of major radius and decreases with magnetic field resulting in a decay length of 1 mm for ITER. At higher densities and under partially detached conditions, however, a broadening of the decay length is observed. In discharges with density ramps up to the density limit, the divertor plasma shows a complex behaviour with a localized high-density region in the inner divertor before the outer divertor detaches. Turbulent transport is studied in the core and the scrape-off layer (SOL). Discharges over a wide parameter range exhibit a close link between core momentum and density transport. Consistent with gyro-kinetic calculations, the density gradient at half plasma radius determines the momentum transport through residual stress and thus the central toroidal rotation. In the SOL a close comparison of probe data with a gyro-fluid code showed excellent agreement and points to the dominance of drift waves. Intermittent structures from ELMs and from turbulence are shown to have high ion temperatures even at large distances outside the separatrix.

Density limit experiments on FTU

One of the main problems in tokamak fusion devices concerns the capability to operate at a high plasma density, which is observed to be limited by the appearance of catastrophic events causing loss of plasma confinement. The commonly used empirical scaling law for the density limit is the Greenwald limit, predicting that the maximum achievable line-averaged density along a central chord depends only on the average plasma current density. However, the Greenwald density limit has been exceeded in tokamak experiments in the case of peaked density profiles, indicating that the edge density is the real parameter responsible for the density limit. Recently, it has been shown on the Frascati Tokamak Upgrade (FTU) that the Greenwald density limit is exceeded in gas-fuelled discharges with a high value of the edge safety factor. In order to understand this behaviour, dedicated density limit experiments were performed on FTU, in which the high density domain was explored in a wide range of values of plasma current (Ip = 500–900 kA) and toroidal magnetic field (BT = 4–8 T). These experiments confirm the edge nature of the density limit, as a Greenwald-like scaling holds for the maximum achievable line-averaged density along a peripheral chord passing at r/a ≃ 4/5. On the other hand, the maximum achievable line-averaged density along a central chord does not depend on the average plasma current density and essentially depends on the toroidal magnetic field only. This behaviour is explained in terms of density profile peaking in the high density domain, with a peaking factor at the disruption depending on the edge safety factor. The possibility that the MARFE (multifaced asymmetric radiation from the edge) phenomenon is the cause of the peaking has been considered, with the MARFE believed to form a channel for the penetration of the neutral particles into deeper layers of the plasma. Finally, the magnetohydrodynamic (MHD) analysis has shown that also the central line-averaged density at the onset of the MHD activity depends only on the toroidal magnetic field.

Observation of Impurity Accumulation After Hydrogen Multi-Pellet Injection in Large Helical Device

Impurity accumulation is studied for neutral beam-heated discharges after hydrogen multi-pellet injection in Large Helical Device (LHD). Iron density profiles are derived from radial profiles of EUV line emissions of FeXV-XXIV with the help of the collisional-radiative model. A peaked density profile of Fe23+ is simulated by using one-dimensional impurity transport code. The result indicates a large inward velocity of −6 m/s at the impurity accumulation phase. However, the discharge is not entirely affected by the impurity accumulation, since the concentration of iron impurity, estimated to be 3.3 × 10−5 to the electron density, is considerably small. On the other hand, a flat profile is observed for the carbon density of C6+, which is derived from the Zeff profile, indicating a small inward velocity of −1 m/s. These results suggest atomic number dependence in the impurity accumulation of LHD, which is similar to the tokamak result.

Dependence of the density limit on the toroidal magnetic field on FTU

The capability of predicting the density limit of a magnetically confined burning plasma is of crucial importance to establish the ultimate performance of a fusion power plant. The Greenwald density limit, commonly used as an empirical scaling law, predicts that the maximum achievable central line-averaged density is given by the relation , where is the average plasma current density and k is the plasma elongation. However, several experiments have pointed out that such a limit can be overcome in the presence of peaked density profiles. This paper proposes a new empirical scaling law for a limiter tokamak operating in the low-energy confinement mode (L-mode) concerning the case of peaked density profiles associated with the presence of multifaceted asymmetric radiation from the edges. This result is based on dedicated experiments performed on the Frascati Tokamak Upgrade (FTU) under extremely clean machine conditions (Zeff = 1.0–1.5), in which the high-density domain is explored in a wide range of values of plasma current (Ip = 500–900 kA) and toroidal magnetic field (BT = 4–8 T). It is found that the maximum achievable central line-averaged density essentially depends on the toroidal magnetic field only and does not depend on the average plasma current density: the behaviour is explained in terms of density profile peaking in the high-density domain. As a confirmation that the limit is an edge limit, it is also shown that a Greenwald-like scaling (i.e. depending on the current density) actually holds for the edge line-averaged density (at r/a ≃ 4/5).

Gas fueling effect on plasma profile in Heliotron J

The optimization of gas fueling scenarios has been studied to improve the plasma performance in Heliotron J. Gas fueling effects on the plasma profile are discussed by comparing two fueling methods, a short pulse H2-beam fueling with a supersonic molecular-beam injection (SMBI) technique and a high intensity gas-puff fueling (HIGP) with a conventional gas puff technique. The maximum plasma stored energy Wp after SMBI is about 20% higher than that after HIGP in this NBI-only sustained plasma experiment, where the line-averaged density is almost the same (∼3×1019m−3) for both cases. The electron and ion temperatures in the SMBI case are higher than those are in the HIGP case at the Wp-peak timing. A peaked density profile is observed after SMBI, while it is flat or slightly hollow for the case of HIGP. These observations point out the importance of SMBI fueling for plasma density control to obtain better plasma performance.

Self-consistent simulation study on magnetized inductively coupled plasma for 450 mm semiconductor wafer processing

The characteristics of weakly magnetized inductively coupled plasma (MICP) are investigated using a self-consistent simulation based on the drift–diffusion approximation with anisotropic transport coefficients. MICP is a plasma source utilizing the cavity mode of the low-frequency branch of the right-hand circularly polarized wave. The model system is 700mm in diameter and has a 250mm gap between the radio-frequency window and wafer holder. The model chamber size is chosen to verify the applicability of this type of plasma source to the 450mm wafer process. The effects of electron density distribution and external axial magnetic field on the propagation properties of the plasma wave, including the wavelength modulation and refraction toward the high-density region, are demonstrated. The restricted electron transport and thermal conductivity in the radial direction due to the magnetic field result in small temperature gradient along the field lines and off-axis peak density profile. The calculated impedance seen from the antenna terminal shows that MICP has a resistance component that is two to threefold higher than that of ICP. This property is practically important for large-size, low-pressure plasma sources because high resistance corresponds to high power-transfer efficiency and stable impedance matching characteristics. For the 0.665Pa argon plasma, MICP shows a radial density uniformity of 6% within 450mm diameter, which is much better than that of nonmagnetized ICP.

RFX-mod wall conditioning by lithium pellet injection

Plasma–wall interaction is one of the most important issues that present magnetic confinement devices have to face. In the RFX-mod reversed field pinch experiment plasma–wall interaction has become a hard point increasing plasma current up to the RFX-mod maximum design value of 2 MA, since in this case local power deposition can be as high as 10 MW m−2. Since the first wall of RFX-mod is entirely covered by graphite tiles different techniques have been tested to control hydrogen wall influx: He glow discharges cleaning, He discharges at high plasma currents, wall boronization and baking. With the best results obtained by boronization, at high plasma currents all such techniques improve the situation but do not allow a complete and stationary hydrogen influx reduction. Furthermore, in the presence of localized high power load the wall still responds providing very high influxes. In order to improve this situation wall conditioning by lithium has been tested. As a first lithization method to deposit a controllable amount of lithium on the wall, a room temperature pellet injector has been used (maximum pellet diameter of 1.8 mm and maximum length of 5 mm). Lithium coatings with a theoretical thickness of about 10 nm have been applied both to clean graphite tiles and over boronized ones. Lithization demonstrated to be effective in lowering hydrogen wall recycling to a value smaller than that of boronized graphite, with the effect lasting 20–30% more than in the boronized case. Compared with boronization, lithization slightly improves (by about 30%) particle confinement time and also clearly affects edge particle transport providing a lower edge density and more peaked density profiles. Lithization also reduces carbon content by about 10% over boronization but still no clear improvement has been observed in terms of energy confinement. Similar results have been obtained performing lithization over boronized graphite.

Core transport properties in JT-60U and JET identity plasmas

The paper compares the transport properties of a set of dimensionless identity experiments performed between JET and JT-60U in the advanced tokamak regime with internal transport barrier, ITB. These International Tokamak Physics Activity, ITPA, joint experiments were carried out with the same plasma shape, toroidal magnetic field ripple and dimensionless profiles as close as possible during the ITB triggering phase in terms of safety factor, normalized Larmor radius, normalized collision frequency, thermal beta, ratio of ion to electron temperatures. Similarities in the ITB triggering mechanisms and sustainment were observed when a good match was achieved of the most relevant normalized profiles except the toroidal Mach number. Similar thermal ion transport levels in the two devices have been measured in either monotonic or non-monotonic q-profiles. In contrast, differences between JET and JT-60U were observed on the electron thermal and particle confinement in reversed magnetic shear configurations. It was found that the larger shear reversal in the very centre (inside normalized radius of 0.2) of JT-60U plasmas allowed the sustainment of stronger electron density ITBs compared with JET. As a consequence of peaked density profile, the core bootstrap current density is more than five times higher in JT-60U compared with JET. Thanks to the bootstrap effect and the slightly broader neutral beam deposition, reversed magnetic shear configurations are self-sustained in JT-60U scenarios. Analyses of similarities and differences between the two devices address key questions on the validity of the usual assumptions made in ITER steady scenario modelling, e.g. a flat density profile in the core with thermal transport barrier? Such assumptions have consequences on the prediction of fusion performance, bootstrap current and on the sustainment of the scenario.

High-β plasma formation and observation of peaked density profile in RT-1

High-β ECH plasma is generated and stably sustained in a magnetospheric configuration, the Ring Trap 1 (RT-1) device, generated by a levitated dipole field magnet. Geomagnetic-field compensation and optimized operation have realized drastic improvements in plasma properties. The maximum local β value has reached 70% and the pressure profiles have a rather steep gradient near the superconducting magnet. Electrons of the high-β plasma typically consist of 70% hot (∼50 keV) and the rest of cold populations. Confinement time of the hot component plasma is 0.5 s with the optimized neutral gas pressure. By removing the coil support structure, the peaked density profile is observed in the strong field region.

Formation of high-β plasma and stable confinement of toroidal electron plasma in Ring Trap 1

Formation of high-β electron cyclotron resonance heating plasma and stable confinement of pure electron plasma have been realized in the Ring Trap 1 device, a magnetospheric configuration generated by a levitated dipole field magnet. The effects of coil levitation resulted in drastic improvements of the confinement properties, and the maximum local β value has exceeded 70%. Hot electrons are major component of electron populations, and its particle confinement time is 0.5 s. Plasma has a peaked density profile in strong field region [H. Saitoh et al., 23rd IAEA Fusion Energy Conference EXC/9-4Rb (2010)]. In pure electron plasma experiment, inward particle diffusion is realized, and electrons are stably trapped for more than 300 s. When the plasma is in turbulent state during beam injection, plasma flow has a shear, which activates the diocotron (Kelvin–Helmholtz) instability. The canonical angular momentum of the particle is not conserved in this phase, realizing the radial diffusion of charged particles across closed magnetic surfaces. [Z. Yoshida et al., Phys Rev. Lett. 104, 235004 (2010); H. Saitoh et al., Phys. Plasmas 17, 112111 (2010).].

Recent Progress in Plasma Control Studies on the Improvement of Plasma Performance in Heliotron J

Recent progress in plasma control studies on the improvement of plasma performance in Heliotron J is reviewed. The supersonic molecular beam injection (SMBI) fueling is successfully applied to Heliotron J plasma. A supersonic H2-beam is effectively injected to increase fueling efficiency and generate a peaked density profile. Local fueling with a short-pulsed SMBI can increase the core plasma density and avoid the degradation arising from edge cooling. Second harmonic electron cyclotron current drive (ECCD) experiments were conducted by launching a focused Gaussian beam with a parallel refractive index of −0.05 ≤ N‖ ≤ 0.6. Results show that the electron cyclotron (EC) driven current is determined not only by N‖ but also by local magnetic field (B) structure where the EC power is deposited. Detailed analysis of the observed N‖ and B dependences is in progress with a ray-tracing simulation using the TRAVIS code. Fast ion velocity distribution was investigated using fast protons generated by ion cyclotron resonant frequency (ICRF) minority heating. For the standard configuration in Heliotron J, charge exchange neutral particle analysis (CX-NPA) measurements show higher effective temperature of fast minority protons in the on-axis resonance case compared to that in the HFS (high field side) off-axis resonance case. However, the increase in bulk ion temperature in the HFS resonance case is larger than that in the on-axis resonance.

Stationary density profiles in the Levitated Dipole Experiment: toward fusion without tritium fuel

The Levitated Dipole Experiment (LDX) is used to study high-temperature plasma confined by the magnetic field produced by a high-current superconducting ring. Multiple-frequency electron cyclotron resonance heating (ECRH) heats and sustains plasma discharges for long, quasi-steady periods, and conditions of high plasma beta are reached by adjusting the rate of neutral fueling. When the superconducting ring is levitated by attraction to a coil located above the vacuum chamber, cross-field transport becomes the main loss channel for plasma particles and energy. We find operation with a levitated dipole always leads to centrally peaked density profiles, even when the plasma ionization source occurs near the plasma edge. In recent experiments, we also observe the normalized gradient, or shape, of the density profile to be ‘stationary’ while the ECRH heating power and gas fueling rates are strongly modulated. Theoretically, stationary profiles result in an energy confinement time (of the thermal plasma) that greatly exceeds the particle confinement time. This condition, along with high-beta plasma stability, is a necessary condition for utilizing advanced fuels in a fusion power source.

Peaked density profiles and MHD activity on FTU in lithium dominated discharges

Density profiles become broader, as the line averaged density is increased. At higher density, change of the trend is associated with the appearance of the MARFE. Lithium coated wall extends the maximum density accessible at low current (well above the Greenwald density limit) and can produce profiles with very high density gradient. At higher current the effect on the density limit can be exceeded only if the magnetic field is raised too. A comparison of successive similar discharges before and after wall conditioning with lithium showed a reduction of the MHD activity.

Density Limits for the Core and Edge Plasmas Related to the Local Temperatures in LHD

Easy access to the high-density regime without fatal disruptive phenomena is one of the important characteristics of the Large Helical Device (LHD). The operational density is considerably higher than the Greenwald density limit for tokamak plasmas. The density limit in LHD is reached when the edge density at the last closed flux surface exceeds a value approximately equivalent to the Sudo density limit that increases with the square root of the heating power. Extremely high central density of >1 × 1021 m−3 is achievable with a peaked density profile, as long as the edge density is kept lower than the Sudo limit. Furthermore, the central heating power must be larger than the radiation loss in the core region to avoid the “cold-core” phenomenon. As for the plasma edge, complete detachment takes place when the edge density exceeds the limit. Then, reattachment/Serpens mode/radiative collapse will follow, depending on the recycling condition.

Particle Transport of LHD

Particle confinement processes are studied in detail on the Large Helical Device (LHD). Diffusion coefficients (D) and convection velocities (V) are estimated from density modulation experiments. The magnetic configuration and collisionality are widely scanned in order to investigate parameter dependences of D and V. To study the effect of the magnetic configuration, magnetic axis positions (Rax) are scanned from 3.5 to 3.9 m. This scan changes the magnetic ripples quite significantly, enabling the effects of neoclassical properties on measured values to be widely elucidated. Dependences of electron temperature (Te) and helically trapped normalized collisionality are examined using the heating power scan of neutral beam injection. It was found that generally larger (or smaller) contributions of neoclassical transport in the core region, where normalized position ρ < 0.7, resulted in more hollow (or peaked) density profiles. The larger neoclassical contribution was found to be situated at a more outwardly shifted Rax for the same Te and for higher Te or lower νh* at each Rax. However, it is to be noted that Rax = 3.5 m shows different characteristics from these trends, that is, a more peaked density profile at higher Te or lower νh*. The edge (ρ > 0.7) diffusion and convection are dominated by anomalous processes. Measured edge turbulence shows a possible linkage.

Momentum transport studies in JET H-mode discharges with an enhanced toroidal field ripple

In this study, enhancement of the toroidal field (TF) ripple has been used as a tool in order to reveal the impact of the momentum pinch on the rotation profiles in H-mode JET discharges. The analysis showed that flatter rotation profiles were obtained in discharges with a high TF ripple, attributed to a smaller inward momentum convection. An average inward momentum pinch of approximately Vp ≈ 3.4 m s−1 and a normalized pinch value of RVp/χ ≈ 6.6 could explain the observation. The data show that the momentum at the edge affects the peaking of the rotation and momentum density profiles. Under the assumption that the heat and momentum diffusivities are equal, an estimate of the levels of the momentum pinch in all discharges in the JET rotation database was made. For H-mode discharge these ranged from 0.3 m s−1 < Vp < 17 m s−1, with 2 < RVp/χ < 10. A larger momentum pinch was found in discharges with a smaller density profile gradient length, i.e. a more peaked density profile.

The role of ion and electron electrostatic turbulence in characterizing stationary particle transport in the core of tokamak plasmas

A general feature of particle transport in the core of tokamak plasmas is that when core particle sources are small, a stationary peaked density profile is provided by a balance of outward diffusion and inward convection, driven by either neoclassical or turbulent mechanisms. The turbulent contribution to the off-diagonal elements of the transport matrix is very sensitive to the type of dominant instability of the background turbulence. We present here a detailed quasi-linear gyrokinetic analysis of stationary turbulent particle transport by means of analytical and numerical calculations to show how the actual parametric dependence of the stationary normalized density gradient can strongly vary between an ion temperature gradient (ITG) dominated turbulence and a trapped electron mode dominated turbulence regime. It is also shown how the maximal achievable normalized density gradient is reached when the turbulence regime is in a mixed state. This result is interpreted as the interplay of different physical mechanisms arising from (linear) wave–particle resonances. The results presented here are addressed to interpret some of the still unresolved issues in interpreting known experimental results.

Particle pinch and collisionality in gyrokinetic simulations of tokamak plasma turbulence

The generic problem of how, in a turbulent plasma, the experimentally relevant conditions of a particle flux very close to the null are achieved, despite the presence of strong heat fluxes, is addressed. Nonlinear gyrokinetic simulations of plasma turbulence in tokamaks reveal a complex dependence of the particle flux as a function of the turbulent spatial scale and of the velocity space as collisionality is increased. At experimental values of collisionality, the particle flux is found close to the null, in agreement with the experiment, due to the balance between inward and outward contributions at small and large scales, respectively. These simulations provide full theoretical support to the prediction of a peaked density profile in a future nuclear fusion reactor.

Extrapolation of ASDEX Upgrade H-mode discharges to ITER

In this paper we discuss a procedure to evaluate the fusion performance of ASDEX Upgrade discharges scaled up to ITER. The kinetic profile shape is taken from the measured profiles. Multiplication factors are used to obtain a fixed Greenwald fraction and an ITER normalized thermal pressure as in the corresponding ASDEX Upgrade discharge. The toroidal field and the plasma geometry are taken from the ITER-FEAT design (scenario 2), whereas q95 is taken from the experiment. The confinement time is inferred assuming that the measured H-factor with respect to several existing scaling laws also holds for ITER. While retaining the information contained in the multi-machine databases underlying the different scaling laws, this approach adds profile effects and confinement improvement with respect to the ITER baseline, thus including recent experimental evidence such as the prediction of peaked density profiles in ITER. Under this set of assumptions, of course not unique, we estimate the ITER performance on the basis of a wide database of ASDEX Upgrade H-mode discharges, in terms of fusion power, fusion gain and triple product. According to the three scalings considered, there is a finite probability of reaching ignition, while more than half of the discharges require less auxiliary power than the one foreseen for ITER. For all the scaling laws, high values of the thermal βN up to 2.4 are accessible. A sensitivity study gives an estimate of the accuracy of the extrapolation. The impact of different levels of tungsten concentration on the fusion performance is also studied in this paper. This scaling method is used to verify some common 0D figures of merit of ITER's fusion performance.

Long-pulse hybrid scenario development in JT-60U

The performance and sustained duration of long-pulse discharges for the ‘ITER hybrid scenario’ have been improved in JT-60U. The modification of power supply systems for three perpendicular neutral beam (NB) injections provides a long period of central NB heating up to 30 s, which is important for keeping the internal transport barrier (ITB). The peaked density profile in the core plasma can be maintained even when the density at the pedestal increased in the latter phase of the discharge due to the increase in the divertor recycling. Then, the peaked pressure profile attributed to the ITB can be kept constant through the discharge with the peaked power deposition profile. In these long-pulse discharges, MHD activity with toroidal mode number n = 1 is observed even when neoclassical tearing modes (NTMs) are suppressed. When the amplitude of the mode in the peripheral region becomes large, the pedestal pressure is degraded. The mode amplitude is sensitive to the toroidal magnetic field (or edge safety factor) and heating power. After the adjustment of the toroidal magnetic field so as to reduce the mode amplitude, a high normalized beta (βN) of 2.6 and a high thermal confinement enhancement factor (HH98(y,2) > 1) are sustained for 25 s (∼14τR, where τR is the current diffusion time) under the ITER relevant small toroidal rotation condition. The peaked pressure profile in low safety factor plasma (safety factor at 95% flux surface q95 ∼ 3.2) is stable against NTMs up to βN ∼ 3. A high βNHH98(y,2) of 2.6 gives a high G-factor () of 0.25 and a peaked pressure profile gives a large bootstrap current fraction (fBS > 0.43).