Hollow Density Profiles Research Articles

Improvement of core heat transport in NBI plasmas of heliotron J using high-intensity gas puffing

Controlling the heat transport profile is important for high performance in magnetically confined fusion plasmas. In this study, improved electron heat transport was achieved in neutral beam injection plasmas by applying high-intensity gas puffing (HIGP) on a stellarator/heliotron device called Heliotron J. Compared with conventional gas puffing (GP) fueling discharge, a higher and more peaked electron temperature profile was obtained, and the core ion temperature was slightly higher but similarly shaped. Using similar parameters, the electron density profile for HIGP remained similar and differed from the hollow density profile observed in electron cyclotron heating-eIBT plasma. Transport analysis using the FIT3D and TR-snap codes showed a clear reduction in the effective electron heat transport coefficient in the plasma core region. However, more detailed experiments are required to understand the mechanisms underlying this improvement fully.

Light impurities: equilibrium, transport and density profiles in tokamak and stellarator plasmas

The density profiles of light impurities observed in recent decades in a relatively wide variety of experiments on tokamaks and stellarators are analyzed and modeled based on the concept of self-consistent equilibrium and transport of impurity charge states (Shurygin 2020 Nuclear Fusion 60 046001). The emphasis is on the formation of charge-radial equilibrium and its invariant properties affecting transport and density profile. The impurity invariant equilibrium arises due to random compatible charge-radial variations, linking the impurity motion into a general ergodic (Markovian) process governed by a matrix of final probabilities. More than 60 profiles of helium, boron and carbon with central accumulation, flat and hollow were accurately reproduced by invariant dimensionless transport functions. It is shown that the leading processes determining the formation of impurity invariant density profiles in stationary plasma are the processes of ionization-recombination, and not the transport of particles. Successive variations in the hollow density profiles of helium, boron, and carbon observed in experiments can be described as successive invariant profile changes in the recombination rate profiles. The invariant particle diffusive-convective profiles can be calculated directly from the impurity density profiles. A general empirical formula for equilibrium constant of light impurities was proposed.

Peaking and hollowness of low-Z impurity profiles: an interplay between ITG and TEM induced turbulent transport

The transport of low-Z impurities in fusion plasmas is dominated, in many regimes of interest, by ion temperature gradient (ITG) and trapped electron mode (TEM) turbulence. We use a statistical test-particle approach to analyze the effects of these drift instabilities on the transport coefficients. It is found that the convection of motion by the polarization drift drives an outward radial pinch via ITG and an inward pinch via TEM turbulence. Opposite radial pinches are driven by turbulent motion along magnetic field-lines. The interplay between these effects can explain the co-existence of peaked and hollow impurity density profiles observed in tokamak plasmas. The theoretical framework is validated through comparison with experimental data on the transport of Boron impurities.

Investigation of core impurity transport in DIII-D diverted negative triangularity plasmas

Tokamak operation at negative triangularity has been shown to offer high energy confinement without the typical disadvantages of edge pedestals (Marinoni et al 2021 Nucl. Fusion 61 116010). In this paper, we examine impurity transport in DIII-D diverted negative triangularity experiments. Analysis of charge exchange recombination spectroscopy reveals flat or hollow carbon density profiles in the core, and impurity confinement times consistently shorter than energy confinement times. Bayesian inferences of impurity transport coefficients based on laser blow-off injections and forward modeling via the Aurora package (Sciortino et al 2021 Plasma Phys. Control. Fusion 63 112001) show core cross-field diffusion to be higher in L-mode than in H-mode. Impurity profile shapes remain flat or hollow in all cases. Inferred radial profiles of diffusion and convection are compared to neoclassical, quasilinear gyrofluid, and nonlinear gyrokinetic simulations. Heat transport is observed to be better captured by reduced turbulence models with respect to particle transport. State-of-the-art gyrokinetic modeling compares favorably with measurements across multiple transport channels. Overall, these results suggest that diverted negative triangularity discharges may offer a path to a highly-radiative L-mode scenario with high core performance.

Impact of impurities on drift wave instabilities in reversed-field pinch plasmas.

The drift wave in the presence of impurity ions was investigated numerically in reversed-field pinch plasmas, using the gyrokinetic integral eigenmode equation. By comparing the results of regular and hollow plasma density profiles, it was found that the ion temperature gradient mode for the hollow density profile case is much harder to excite. For the impurity effects, when the impurity density gradient is opposite to the electrons, namely when L_{ez} (L_{ez}=L_{ne}/L_{nz} with 1/L_{n} being the density gradient scale length, and the subscript "e" and "z" indicates electrons and impurity ions, respectively) is negative, the impurities can enhance the instability. On the contrary, when L_{ez} is positive, the instability is stabilized. Regarding the trapped electron mode (TEM), the growth rate for plasmas with a hollow density profile remains smaller than that of the standard density gradient. There exists a threshold in L_{ez}. When L_{ez} is less than this value, the impurities destabilize the TEMs, while when L_{ez} is greater than this value, the impurities stabilize the TEMs. In addition, the influence of the collisionality on the TEMs was also studied.

Identification of electrostatic microinstability maps in quasi-axisymmetric stellarator

Microinstabilities such as ion temperature gradient (ITG) mode and trapped electron mode (TEM) in quasi-axisymmetric (QA) stellarator are investigated by using gyrokinetic Vlasov simulations, where the QA configuration of Chinese first quasi-axisymmetric stellarator is utilized. Extensive parameter scans with respect to the density and temperature gradients for the zero beta cases identify the microinstability maps that indicate the transition boundary among ITG and TEM. It is found that, in particular for the modes with the ion-gyroradius scale, a relatively more stabilized regime appears along the transition boundary of ITG–TEM. Such a valley-like stability structure is not observed in the other cases with the sub-ion-gyroradius-scale. A stabilization effect attributed to the hollow density profile is also demonstrated.

Nonlinear decay of high-power microwaves into trapped modes in inhomogeneous plasma

We present novel experimental evidence of parametric decay instability of microwave beams in the plasma edge of the Wendelstein 7-X stellarator. We propose that the instability is sustained by trapping of only one daughter wave in the non-monotonic density profile measured with high spatial resolution within a stationary magnetic island. The power levels and spectral shapes of the detected microwave signal are reproduced by numerical modelling and a theoretical power threshold is predicted around 300 kW, comparable with observations. We predict a fraction of power drained by daughter waves around 4% in the experiments, potentially increasing above 50% for more hollow edge density profiles. Such absorption levels could significantly reduce the efficiency of the microwave heating and current-drive system in tokamaks and stellarators.

Analysis of anomalous transport based on radial fractional diffusion equation

Anomalous transport in magnetically confined plasmas is investigated by radial fractional transport equations. It is shown that for fractional transport models, hollow density profiles are formed and uphill transports can be observed regardless of whether the fractional diffusion coefficients (FDCs) are radially dependent or not. When a radially dependent FDC is imposed, compared with the case under it is observed that the position of the peak of the density profile is closer to the core. Further, it is found that when FDCs at the positions of source injections increase, the peak values of density profiles decrease. The non-local effect becomes significant as the order of fractional derivative and causes the uphill transport. However, as the fractional diffusion model returns to the standard model governed by Fick’s law.

The impact of inverted density gradients on density profiles measured by reflectometry: an experimental and numerical investigation at ASDEX Upgrade

The high-field side high-density (HFSHD) region at ASDEX Upgrade (AUG) is a well-documented phenomenon leading to a dense plasma in the inner divertor region that expands upwards to the midplane, resulting in poloidally asymmetric scrape-off layer density profiles. This work investigates, via simulation and experiment, whether the HFSHD at the midplane leads to hollow density profiles at the high-field side. Using the frequency-modulated continuous-wave O-mode reflectometer at AUG, experimental evidence has been found of reflection patterns compatible with a hollow density profile that are reproduced by 1D full-wave simulations. Furthermore, this work assesses the uncertainties in the density profile reconstruction as a consequence of the inverted gradient, showing that the presence of an HFSHD may lead to an overestimation of the density in the confined region.

Self-consistent core-pedestal ITER scenario modeling

The purpose of these integrated ITER simulations is to identify dependencies that can impact the performance of ITER. The dependence of fusion power production, temperature and density pedestals, and core profiles on varying magnetic-q, edge density fueling strength, neoclassical transport, magnetic field strength, and alpha heating, are examined. It is noted that ion modes usually dominate the interior, while electron modes dominate the barrier. The electron mode without flow shear is substantially stronger. The q increase tends to cause more kinetic ballooning modes at the edge and the q decrease means that the peeling is getting worse, but the ballooning is getting better. The large edge q tends to provide hollow density while small edge q gives normal density profile. This is consistent with the observation that the density of particles is inversely proportional to the density of the plasma current. The rise in the source of the edge particle increases the density of the edge and the reaction rate close to the edge increases temperature fluxes, resulting in weak pedestal barriers. When neoclassical transport is turned off or the strength of B-field is increased, the pronounced edge barriers are identified. In addition, a distinct effect on the magnetohydrodynamic (MHD) modes is observed due to the increased B-field. The interesting aspect is that the barrier collapses about q = 2 as the stability of MHD has decreased to replace the barrier with a continuous slope but with roughly the same fusion power. This would actually be good for a reactor. The slope of the H-mode pedestal is found to be reduced due to the alpha heating. It is expected that the problem of edge-localized modes causing damage to the first wall will be eased. The effects of circular, elongated, and general geometry on plasma profiles are also compared and contrasted. The circular geometry has a hollow density profile and no edge or internal thermal transport barrier (ETB or ITB). However, both ETBs and ITBs can be found in the elongated geometry. In general geometry, there is a weaker ETB, comparable ITBs, but a higher edge particle transport barrier than in elongated geometry. Higher density near the edge, on the other hand, causes more wall erosion, so elongated geometry might be the best option.

Study on impurity hole plasmas by global neoclassical simulation

An impurity hole observed in the large helical device (LHD) is a hollow density profile of an impurity ion species formed in the core plasma where the negative (inward-pointing) ambipolar radial electric field (E r) exists. Although local neoclassical models have predicted that the sign of E r in impurity hole plasmas is negative for the entire minor radius, an experimental measurement of an impurity hole plasma has shown that the E r changes the sign from negative to positive along the minor radius. In the present work, we investigate neoclassical impurity transport in an impurity hole plasma using a global neoclassical simulation code FORTEC-3D. The variation of electrostatic potential on each flux surface (Φ1) is evaluated from the quasi-neutrality condition in multi-ion-species plasma by the global simulation. The ambipolar E r and neoclassical fluxes are determined in solving a global drift-kinetic equation including the effect of Φ1. By the global simulation, we show that an E r which changes the sign along the radius is obtained as a solution of the ambipolar condition and with such an E r, impurity carbon flux can be outwardly directed even where E r < 0 and the carbon density profile is hollow around the magnetic axis. Furthermore, it is found that the outward carbon flux is only a factor 2–3 from balancing the modeled inward turbulent flux. Our result indicates that we have moved one step closer to reproducing the impurity transport in impurity hole plasmas by kinetic simulation.

Impurity mode induced turbulent particle transport and its temperature screening effect

Turbulent transport of impurity ions with hollow density profiles (HDPs), which are widely observed in magnetically confined plasmas and desirable for fusion reactor, is self-consistently investigated. A full gyrokinetic description is employed for main and impurity ions. Instead of conventional ion temperature gradient (ITG, including impurity ITG) and trapped electron modes (TEMs), impurity modes (IMs), driven by impurity ion density gradient opposite to that of electrons, are considered. The impurity ion flux induced by IMs is shown to be approximately one order of magnitude higher than that induced by TEMs when both kinds of modes coexist. Main ITG and electron temperature gradient (ETG) are found to reduce influx of impurity ions significantly, resembling temperature screening effect of neoclassical transport of impurity ions. The simulation results such as peaking factor of the HDPs and the effects of main ITG are found in coincidence with the evidence observed in argon injection experiment on HL-2A tokamak. Thus, the IM turbulence is demonstrated to be a plausible mechanism for the transport of impurity ions with HDPs. A strong main ITG, ETG, and a low electron density gradient are expected to be beneficial for sustainment of HDPs of impurity ions and reduction of impurity accumulation in core plasma.

Two-parameter modified rigid rotor radial equilibrium model for field-reversed configurations

A new equilibrium pressure profile is proposed that extends the rigid rotor (RR) model with a simple unified expression P = P(ψ; β s, α, σ) for both inside and outside the separatrix. A new method is described for solving the field-reversed configuration (FRC) one-dimensional (1D) equilibrium with only two parameters. The radial normalized FRC equilibrium profiles for pressure, magnetic field, and current density can be uniquely determined by the dimensionless parameters of and δ s ≡ L ps/R s. This modified rigid rotor (MRR) model has sufficient flexibility to accommodate narrow scrape-off layer (SOL) widths and hollow current density profiles, and can be used to fit experimental measurements. A database of 1D plasma equilibria in the (β s, δ s) space is provided for the convenience of real-time approximate FRC equilibrium reconstruction. The detailed one-dimensional (1D) characteristics of the equilibrium models are investigated analytically and numerically. The 1D results from the MRR models are also validated using two-dimensional (2D) Grad–Shafranov (G–S) equilibrium solutions.

Hollow current and reversed magnetic shear configurations in pellet injection discharges on Huanliuqi 2A tokamak

The tokamak with weak or negative magnetic shear and internal transport barrier (ITB) is considered to be the most promising approach to improving fusion performance. The hollow current density profile, as well as the reversed &lt;i&gt;q&lt;/i&gt; profile (negative magnetic shear), is one of the key conditions for improving core confinement in advanced tokamak schemes. In the Huanliuqi 2A (HL-2A) experiment, a hollow current distribution with a discharge duration of about 100 ms is successfully achieved by injecting the pellets in the Ohmic discharge. The discharge is characteristic of circular equilibrium configuration and three frozen pellets are injected continuously at three different time moments. As a result, the hollow current profiles are formed in the plasma with weak hollow electron temperature in the core region. At the same time, the hollow currents are combined with the reversed magnetic shear profiles. Because the power of Ohmic heating is not so high and there is no external auxiliary heating, we can see only a trend of the formation of weak internal transport barrier in the stable hollow current discharge stage. However, the electron thermal diffusivity decreases significantly after the pellets have been injected. The deep injection of frozen pellets improves the energy confinement. The enhancement of plasma performance is due to the peaked electron density profile in the center, caused by pellet injection and the negative magnetic shear in the plasma center. It is concluded that the electron density profile peaked highly in the core plasma, caused by pellet injection, is beneficial to the improvement of particle confinement and plays an important role in enhancing the energy confinement. In addition, it is also demonstrated that, in general, during a hollow current discharge, the poloidal beta &lt;inline-formula&gt;&lt;tex-math id="M2"&gt;\begin{document}$ {\beta }_{\mathrm{p}} $\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20210641_M2.jpg"/&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20210641_M2.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt; value and normalized beta &lt;inline-formula&gt;&lt;tex-math id="M3"&gt;\begin{document}$ {\beta }_{\mathrm{N}} $\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20210641_M3.jpg"/&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20210641_M3.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt; value are both obviously low although the reversed magnetic shear is conducive to stabilizing ballooning modes and weakening the drift instabilities. However, comparing with the hollow current profile, the plasma with peaked current profile is very beneficial to the improvement of beta limit. In order to improve the &lt;inline-formula&gt;&lt;tex-math id="M4"&gt;\begin{document}$ {\beta }_{\mathrm{N}} $\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20210641_M4.jpg"/&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20210641_M4.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt; limit, a conductive wall is necessary to be placed near the plasma boundary. The results of HL-2A pellet injection experiments present a possibility of obtaining high parameter discharge on a limiter tokamak.

Quasi-linear heat transport induced by ITG turbulence in the presence of impurities

The impurity effects on turbulent transport induced by ion temperature gradient (ITG) turbulence are numerically studied in tokamak plasmas, using a gyrokinetic quasi-linear model. The characteristics of the instability and heat fluxes in the presence of impurity ions are investigated for a broad parameter regime, including temperature and density gradients of main and impurity ions, concentration, charge and mass numbers of impurity ions, magnetic shear as well as wave vector spectrum. The heat fluxes are demonstrated to depend not only on the saturation amplitude of the instability but also on the phase shift between and . The peaking factor of temperature/density profile, defined as the ratio of major radius to gradient scale length when the total turbulent heat flux equals zero, is fitted with linear/quadratic functions. In addition, the contributions from diagonal and off-diagonal terms to heat fluxes are identified in detail, i.e. the main ion heat diffusion are proved to be dominated by off-diagonal (diagonal) terms for regions of weak (strong) ITG. In general, steep temperature gradients of main ions as well as hollow density profiles of impurity ions significantly enhance instability and heat fluxes. However, it is interesting to find that the effect of impurity ions with positive density gradient may transit from the enhancement to reduction of the quasi-linear heat flux of main ions in regions of steep ITG, corresponding to transport barriers (e.g. pedestal of H-mode and I-mode plasmas). Both strong and weak positive magnetic shear decrease heat transport.

Stability nature of ohmic discharges with hollow current profiles on the HL-2A tokamak

The equilibrium configurations with hollow current density profiles can effectively improve plasma confinement. The stability of the ohmic discharges with hollow current density profiles on the HL-2A tokamak was studied for various parameters, such as plasma poloidal beta βp, the axial and edge safety factors q0 and qs, as well as the minimum safety factor . The results suggest that the restriction to the parameters of discharges with hollow current density profiles is stricter than that of conventional discharges with peaked current density profiles. In the case of q profile with reverse shear, the instability of the configuration is significantly improved with higher βp. As a result, the configuration with a hollow toroidal current profile is stable for high βp operations. Only if q0, qs and satisfy the specific limitations, i.e. on HL-2A, only if both and hold, together with and , may the configurations with the reverse shears be stable for hollow-current-type Ohmic discharge. The results may give hints for the role of the discharges with hollow toroidal current densities in the coming advanced tokamak operations.

Global calculation of neoclassical impurity transport including the variation of electrostatic potential

Recently, the validity range of the approximations commonly used in neoclassical calculation has been reconsidered. One of the primary motivations behind this trend is observation of an impurity hole in LHD (Large Helical Device), i.e. the formation of an extremely hollow density profile of an impurity ion species, such as carbon $\text{C}^{6+}$ , in the plasma core region where a negative radial electric field ( $E_{r}$ ) is expected to exist. Recent studies have shown that the variation of electrostatic potential on the flux surface, $\unicode[STIX]{x1D6F7}_{1}$ , has significant impact on neoclassical impurity transport. Nevertheless, the effect of $\unicode[STIX]{x1D6F7}_{1}$ has been studied with radially local codes and the necessity of global calculation has been suggested. Thus, we have extended a global neoclassical code, FORTEC-3D, to simulate impurity transport in an impurity hole plasma including $\unicode[STIX]{x1D6F7}_{1}$ globally. Independently of the $\unicode[STIX]{x1D6F7}_{1}$ effect, an electron root of the ambipolar condition for the impurity hole plasma has been found by global simulation. Hence, we have considered two different cases, each with a positive (global) and a negative (local) solution of the ambipolar condition, respectively. Our result provides another support that $\unicode[STIX]{x1D6F7}_{1}$ has non-negligible impact on impurity transport. However, for the ion-root case, the radial $\text{C}^{6+}$ flux is driven further inwardly by $\unicode[STIX]{x1D6F7}_{1}$ . For the electron-root case, on the other hand, the radial particle $\text{C}^{6+}$ flux is outwardly enhanced by $\unicode[STIX]{x1D6F7}_{1}$ . These results indicate that how $\unicode[STIX]{x1D6F7}_{1}$ affects the radial particle transport crucially depends on the profile of the ambipolar- $E_{r}$ , which is found to be susceptible to $\unicode[STIX]{x1D6F7}_{1}$ itself and the global effects.

Effects of temperature gradient driven turbulence and core MHD instability on particle transport in HL-2A L-mode plasmas

Experiments in L-mode plasmas in the HL-2A tokamak show that the electron and trace Al impurity transport is related to the normalized electron temperature gradient with opposite trends. Increasing in the confinement zone (0.25 ⩽ ρ⩽ 0.5, ρ is the normalized minor radius) tends to pump out electrons but accumulate impurity, leading to slightly hollow electron density profiles meanwhile with an overall stronger inward convection of injected impurity. Moreover, after the injection of Al impurity by laser blow-off (LBO), the impurity density profiles remain deeply hollow due to the combined effect of the impurity expulsion by core magneto-hydrodynamic (MHD) activity in the plasma centre and the inward impurity convection driven by turbulence in the outer confinement region. Gyrokinetic simulation results reveal that the local change of affects the relative strength of the trapped electron mode (TEM) and the ion temperature gradient (ITG) mode, eventually determining the electron particle transport in a way consistent with the experimental observations. Comparison of simulations with and without collisionallity shows that the plasma collisionality can significantly reduce the growth rate of the TEM and the associated outward particle flux.

Impacts of sawtooth crashes on tokamak plasmas in DEMOs

Self-consistent simulations of sawtooth oscillations on four DEMO (demonstration fusion power plant) designs, proposed by European, Indian, Chinese, and Korean teams, are carried out using the Porcelli sawtooth triggering model and the modified version of the Kadomtsev magnetic reconnection model coupled with the BALDUR integrated code. The simulation results suggest that all sawtooth crashes are triggered by the driving force for the internal kink instability overcoming the fast ion stabilization found in all DEMOs. Conversely, different expansions of the pre-crash helical flux are found, causing different mixing radii on each design. The mixing radius of the European DEMO is found to be the largest, resulting in the largest reduction of the core plasma temperature after the sawtooth crash. It is also observed that for all DEMOs except the Chinese DEMO, regular sawtooth crashes lead to an increase in the core plasma density and radiative power density in different levels, which are due to the steepness of the pre-crash hollow density profile. Furthermore, while helium is found to be outwardly transported by sawtooth crashes for all DEMOs, the sawteeth yield a penetration of the seeded impurities, remarkably found in the European design. Interestingly, based on the European design, a decrease in the atomic mass of the plasma fuels and seeded impurities are found to yield greater flatness of the pre-crash density profile and thus a smaller impact of sawtooth oscillations on central density. Additionally, the sawteeth degrade the plasma performance in the Chinese DEMO, but demonstrate positive impacts on the performance in the European, Indian, and Korean DEMOs, which results from the increase of the central ion density caused by the sawteeth. Furthermore, variation in neutral beam injection power exhibits both positive and negative correlations of sawtooth oscillation impacts on central ion density. The sensitivity of the mixing region of DEMOs is also investigated for scans where the main plasma parameters are varied.

On the heating mechanism of electron cyclotron resonance thruster immerged in a non-uniform magnetic field

To study the heating mechanism of electron cyclotron resonance thruster (ECRT) immersed in a non-uniform magnetic field, experiments and simulations are performed based on an electron cyclotron resonance plasma source at ASIPP. It is found that the first harmonic of electron cyclotron resonance is essential for plasma ignition at high magnetic field (0.0875 T), while the plasma can sustain without the first and second harmonics of electron cyclotron resonance at low magnetic field (till 0.0170 T). Evidence of radial hollow density profile indicates that upper hybrid resonance, which has strong edge heating effect, is the heating mechanism of low-field ECRT. The heating mode transition from electron cyclotron resonance to upper hybrid resonance is also revealed. Interestingly, the evolutions of electron temperature and electron density with input power experience a ‘delayed’ jump, which may be correlated with the different power levels required for cyclotron and ionization. Moreover, when the field strength decreased, the variation of electron density behaves in an opposite trend with that of electron temperature, implying a possible competition of power deposition between them. The present work is of great interest for understanding the plasma discharge in ECRT especially immersed in a non-uniform magnetic field, and designing efficient ECRT using low magnetic field for economic space applications.