Engineering topics
Xu, X. Q.
Publications and source records attributed to Xu, X. Q..
Turbulence spreading effects on the ELM size and SOL width
BOUT++ turbulence simulations were performed to investigate the impact of turbulence spreading on the edge localized mode (ELM) size and divertor heat flux width (λ q ) broadening in small ELM regimes. Here, this study is motivated by EAST experiments. BOUT++ linear simulations of a pedestal radial electric field (E r ) scan show that the dominant toroidal number mode (n) shifts from high-n to low-n, with a narrow mode spectrum, and the maximum linear growth rate increases as the pedestal E r well deepens. The nonlinear simulations show that as the net E × B pedestal flow increases, the pressure fluctuation level and its inward penetration beyond the top of the pedestal both increase. This leads to a transition from small ELMs to large ELMs. Both inward and outward turbulence spreading are sensitive to the scrape-off-layer (SOL) plasma profiles. The inward turbulence spreading increases for the steep SOL profiles, leading to increasing pedestal energy loss in the small ELM regime. The SOL width (λ q ) is significantly broadened progressing from the ELM-free to small ELM regime, due to the onset of strong radial turbulent transport. The extent of the SOL width (λ q ) broadening depends strongly on outward turbulence spreading. The fluctuation energy intensity flux Γ ε at the separatrix can be enhanced by increasing either pedestal E r flow shear or local SOL pressure gradient. The λ q is broadened as the fluctuation energy intensity flux Γ ε at the last close flux surface (LCFS) increases. Local SOL E × B flow shear will restrain outward turbulence spreading and the associated heat flux width broadening. Operating in H-mode with small ELMs has the potential to solve two critical problems: reducing the ELM size and broadening the SOL width.
How fluctuation intensity flux drives SOL expansion
Abstract Predictions of heat load widths λ q based on particle orbits alone are very pessimistic. This paper shows that pedestal peeling-ballooning (P-B) magnetohydrodynamic (MHD) turbulence broadens the stable scrape-off layer (SOL) by the transport, or spreading, of fluctuation energy from the pedestal. λ q is seen to increase with Γ ε , the fluctuation energy density flux. We elucidate the fundamental physics of the spreading process. Γ ε increases with pressure fluctuation correlation length. P-B turbulence is seen to be especially effective at spreading, on account of its large effective mixing length. Spreading is shown to be a multiscale process, which is enhanced by the synergy of large and small-scale modes. Pressure fluctuation skewness correlates well with the spreading flux–with the zero crossing of skewness and Γ ε spatially coincident–suggesting the role of coherent fluctuation structures and the presence of intermittency in λ q broadening. λ q ∼ B p − 1 scaling persists for the broadened SOL. We show that the spreading flux increases for increasing pedestal pressure gradient ∇ P 0 and for decreasing pedestal collisionality υ ped ∗ . This trend is due to the dominance of peeling modes for large ∇ P 0 and low υ ped ∗ . Ultimately, we see that a state of weak MHD turbulence, as for small ELMs, is very attractive for heat load management. Our findings have transformative implications for future fusion reactor designs and call for experimental investigations to validate the observed trends.
Impact of pedestal density gradient and collisionality on ELM dynamics
BOUT++ turbulence simulations are conducted to capture the underlying physics of small ELM characteristics achieved by increasing separatrix density via controlling strike points from vertical to horizontal divertor plates for three EAST discharges. BOUT++ linear simulations show that the most unstable modes change from high-n ideal ballooning modes to intermediate-n peeling–ballooning modes and eventually to peeling–ballooning stable plasmas in the pedestal. Nonlinear simulations show that the fluctuation is saturated at a high level for the lowest separatrix density. The ELM size decreases with increasing separatrix density, until the fraction of this energy lost during the ELM crash becomes less than 1% of the pedestal stored energy, leading to small ELMs. Simulations indicate that small ELMs can be triggered either by the marginally peeling–ballooning instability near the peak pressure gradient position inside the pedestal or by a local instability in the pedestal foot with a larger separatrix density gradient. The pedestal collisionality scan for type-I ELMs with steep pedestal density gradient shows that both linear growth rate and ELM size decrease with increasing collisionality. On the contrary, the pedestal collisionality and pedestal density width scan with a weak pedestal density gradient indicate small ELMs can either be triggered by a high-n ballooning mode or by a low-n peeling mode in a low collisionality region 0.04–0.1. We report the simulations indicate the weaker the linear unstable modes near marginal stability with small linear growth rate, the lower nonlinearly saturated fluctuation intensity and the smaller turbulence spreading from the linear unstable zone to stable zone in the nonlinear saturation phase, leading to small ELMs.
Characteristics of grassy ELMs and their impact on the divertor heat flux width
We report BOUT++ turbulence simulations are conducted for a 60 s steady-state long pulse high β p EAST grassy ELM discharge. BOUT++ linear simulations show that the unstable mode spectrum covers a range of toroidal mode numbers from low-n (n = 10–15) peeling–ballooning modes (P–B) to high-n (n = 40–80) drift-Alfvén instabilities. Nonlinear simulations show that the ELM crash is triggered by low-n peeling modes and fluctuation is generated at the peak pressure gradient position and radially spread outward into the scrape-off-layer, even though the drift-Alfvén instabilities dominate the linear growth phase. However, drift-Alfvén turbulence delays the onset of the grassy ELM and enhances the energy loss with the fluctuation extending to pedestal top region. Simulations further show that if the peeling drive is removed, the fluctuation amplitude drops by an order of magnitude and the ELM crashes disappear. The divertor heat flux width is ~2 times larger than the estimates based on the HD model and the Eich's ITPA multi-tokamak scaling (or empirical Eich scaling) due to the strong radial turbulence transport.
Experimental and theoretical study of weakly coherent mode in I-mode edge plasmas in the EAST tokamak
The I-mode is a promising operation mode for fusion in the future, featuring high-temperature and low-density confinement, but the reason why the temperature and density are decoupled remains an important aspect to be explored. The experimental results from the experimental advanced superconducting tokamak (EAST) showed that the weakly coherent mode (WCM) is directly related to sustaining the I-mode and that the peak amplitude of the WCM is proportional to the temperature in the pedestal. Here, simulating the experimental data from EAST with the six-field model of BOUT++, we find a density perturbation close to the frequency of the WCM observed in the experiment. By testing all the physical terms in this model, we find that the density perturbation and particle transport are directly related to the drift Alfvén wave (DAW) mode. Additionally we use the SymPIC program (Xiao et al Plasma Sci. Technol. 20 110501; Phys. Plasmas 22 112504; Plasma Sci. Technol. 23 055102) to simulate the same experimental data and find that the frequency range of the WCM is close to both experimental and BOUT++ results. Therefore, the WCM of the I-mode can be considered to be driven by the DAW, which helps improve the transport of the I-mode.
A new discovery of edge localized modes suppression using ICRH
Here, the high-confinement mode (H-mode) is very important for the fusion performance of ITER and future fusion reactors. The H-mode pedestal is a region featuring strongly reduced turbulence and transport just inside the limiting flux surface with strong plasma gradients, which drive edge localized modes (ELMs) in tokamaks. The ELMs, however, are quasiperiodic relaxations of the pedestal, resulting in a series of hot plasma eruptions similar to magnetospheric substorms, solar and stellar flares, which could potentially damage the ITER divertor plates and first walls. To mitigate and suppress the ELMs in H-mode plasmas, the fusion community has tried to develop effective actuators over the past two decades. Two separate excellent inventions have been awarded to recognize their achievements. The 2018 APS excellence award in Plasma Physics Research was given to Drs. Todd E. Evans, Max E. Fenstermacher, and Richard Alan Moyer for their first experimental demonstration of the stabilization of ELMs in high-confinement diverted discharges by application of very small edge-resonant magnetic perturbations, which led to the adoption of suppression coils in the ITER design. The 2018 Fusion Technology Award from the IEEE’s Nuclear and Plasma Science Society (NPSS) was given to Dr. Larry Baylor for his work designing the fueling, pumping and disruption mitigation system for the US ITER Project and for the implementation of pellet ELM mitigation for ITER.
Edge-localized-mode simulation in CFETR steady-state scenario
We report the EPED1 model and self-consistent core-pedestal coupling in integrated modeling are used to design the pedestal structure of the China Fusion Engineering Testing Reactor (CFETR) steady-state scenario. The key parameters, such as β p and q 95 , are based on the grassy edge-localized-mode (ELM) experimental database. In this work, we use the BOUT++ six-field two-fluid code to simulate the onset of the ELM in the CFETR steady-state scenario. The ELM size is around 0.2% in nonlinear simulations, which is in the experimental range of the grassy ELM discharges, 0.1%–1% observed in multiple tokamak devices. Linear and nonlinear simulations show that the dominant high-n ballooning modes peak around n = 40. Compared to type-I ELM crashing dynamics, grassy ELM crashing has a smaller initial crash and is then followed by three phases of turbulence spreading, which are dominated by multi-modes, a high-n mode of n = 45 and low-n mode of n = 5, respectively. In contras to type-I ELM, the perturbation of the high-n mode has a narrow width around ψ = 0.95, and magnetic island formation and reconnection occur only beyond ψ = 0.95, leading to a small initial crash. Mode–mode interaction in the multi-mode coexistence stage stops the growth of individual modes and reduces the transport of particles and heat, and these are the two reasons why the ELM size is small. In–out asymmetry of transient heat flux with a ratio of E out /E in = 3.5 is found during grassy ELM crash. The rise and delay times of the heat flux match the calculation from the free-streaming model. To evaluate the erosion of the divertor target, the energy fluence at the outer divertor target is calculated, which is 0.029 MJ m -2 , 5.5 times smaller than the tungsten melting limit 0.16 MJ m -2 . The calculated energy fluency still follows the experimental scaling law from type-I ELM experiments. The fluctuation eddies in the toroidal direction show a filament structure at the outer mid-plane. Parallel heat flux patterns with a toroidal mode number n = 10 are found at the outer divertor with an amplitude of 680 MW m -2 .
Effects of radial transport on divertor power and particle flux widths under different operational regimes in EAST
Here, a study of the effects of radial transport on the outer divertor particle and power flux widths (λ js and λ q ) is carried out using plasmas under different operational regimes in the Experimental Advanced Superconducting Tokamak (EAST). In the EAST experiments, the λ js values measured during the grassy intra- and inter-ELM phases are similar, and the averaged value of λ js during grassy ELMy discharges is found to be smaller than that of the intra-ELM phase of type-I ELMy discharges but larger than that of the inter-ELM phase of type-I ELMy discharges. Simulations of scans of the radial particle and heat transport coefficients, D and χ e , performed using the BOUT++ transport code show that both λq and λjs increase with D and χe, especially when D or χ e is larger than a threshold value, indicating that background turbulence starts to matter in the determination of λ q and λ js when D or χ e surpasses the threshold value. A comparison between the simulation of the D scan and the experimental results shows that the different values of λ js obtained under different plasma operational regimes are probably due to the different intensities of background turbulence, which is beyond the scope of Goldston's heuristic drift-based model as reported by Goldston et al (2012 Nucl. Fusion 52 013009), since their model was derived by assuming that turbulent transport does not exceed a certain level. The ratio of λ js to λ q is greatly affected by the radial transport; however, simulations carried out using Scrape-off Layer Plasma Simulation (SOLPS) show that divertor geometry and plasma density have big influences on λ js , and thus could also affect the ratio of λ js to λ q .
Simulation of lithium transport using the BOUT++ framework
A numerical model that calculates the collisional interactions between the lithium atoms from a lithium pellet and the background plasmas has been upgraded. The ion density ($N_t$), electron temperature ($T_e$), ion temperature ($T_i$) and parallel ion velocity ($V_{∥, i}$) are used to characterize the background plasmas. The lithium atom density ($N^{a}_{Li}$) and parallel velocity ($V_{∥,a}$) of lithium atoms evolve with time. For each lithium ion, the density ($N_{Li^{n+}}$), temperature ($T_{Li^{n+}}$) and parallel velocity ($V_{∥, Li^{n+}}$) are self-consistently calculated. A C-mod lower single null equilibrium is used to generate the grid for the BOUT++ simulation. The lithium atoms can be fully ionized to $Li^{3+}$ in ~2 μs. The rapid radial and poloidal expansion of the lithium ions are found in the simulation. After the collision interaction process, the electron temperature rapidly decreases at the pellet location; then, it rapidly poloidally expands, and the temperature at the pellet location starts to recover. The electron pressure increases at the pellet location despite the decrease in electron temperature because of the extra electrons from the lithium ionization. The ion pressure profile decreases in the pellet location due to the decrease in ion temperature.
The role of edge plasma parameters in H-mode density limit on the JET-ILW
A study of a dataset of JET H-mode plasma with the Be/W ITER-like wall (JET-ILW) shows that reaching the edge MHD ballooning limit leads to confinement degradation. However, unlike JET plasmas with a carbon wall (JET-C), the JET-ILW plasmas stay in a marginal dithering phase for a relatively long period, associated with a higher (≈20%) H-mode density limit (HDL) than JET-C equivalents. This suggests that ITER could be operated in H-mode with higher density than the scaling based on carbon wall devices, but likely with a dithering phase plasma with lower confinement. A new, reliable estimator for JET E r, min has been derived by combining HRTS measurements of pedestal gradient and edge-SOL decay lengths. JET radial E r ETB wells are observed in the range of -15 to -60 kV m -1 in high performance H-modes, consistent with previous CXRS results in ASDEX Upgrade. The results imply that a higher positive E × B shear in the near SOL plays a role in sustaining a marginal phase in JET-ILW which leads to a higher HDL than that in JET-C. The results of the JET-ILW dataset show agreement with the Goldston finite collisionality HD model for SOL broadening at high collisionality. A hypothesis for the dithering H-mode phase is proposed: as n e,SOL increases, ν *,SOL increases, SOL broadens, E r shear decreases, triggers L-mode; n e drops, ν *,SOL decreases, SOL becomes narrower, and E r shear increases, triggering H-mode, resulting in a cycle of H–L–H- oscillations. For burning plasma devices, such as ITER, operating just below the MHD limit for the dithering phase could be a promising regime for maximising core density, and fusion performance while minimising plasma-material interaction. The oscillatory signal during the dithering phase could be used as a precursor of undesirable plasma performance for control purposes.
Simulations of divertor heat flux width using transport code with cross-field drifts under the BOUT++ framework
The fluid transport code [trans-electric field (Er) module] under the BOUT++ framework has been used to simulatedivertor heat flux width and boundary Er with all drifts and the sheath potential in the scrape-off layer. The calculated steady state radial Er in the pedestal region has been compared with that of experimental measurements from the Alcator C-Mod tokamak. The magnitude and shape of Er are similar to those of the experimental data. In order to understand the relative role of cross-field drifts vs turbulent transport in setting the heat flux width, four C-Mod enhanced Dα H-mode discharges with a lower single null divertor configuration should be simulated. BOUT++ transport simulations with cross-field drifts included yield similar heat flux width λq to that of experimental measurements (within a factor of 2) from both the probe and the surface thermocouple diagnostics and show a similar trend with plasma current to that of the Eich experimental scaling. The simulations show that both drifts and turbulent transport compete to determine the heat flux width. The magnetic drifts play a dominant role in setting the divertor heat-flux width, while the E × B drift decreases the heat flux width by 10%–25%, leading to improved agreement with the experiment relative to Goldston’s model. A turbulence diffusivity scan (χ) identifies two distinct regimes: a drift dominant regime when χ is small and a turbulence dominant regime when χ is large. The Goldston heuristic drift model yields a lower limit of the width λq.
Impact of plasma density/collisionality on divertor heat flux width
Both ASDEX-Upgrade (AUG) data and the generalized HD (GHD) model showed that the scrape-off width broadens as the density/collisionality increases [1, 2]. A series of BOUT++ transport simulations are performed to study the physics of the scaling characteristics of the divertor heat flux width vs density/collisionality via a plasma density scan with either fixed pressure profile or fixed temperature profile inside separatrix. Additionally, the simulations show that even in the drift dominated regime, the divertor heat flux width can be broadened due to the transition of the SOL residence time from the parallel particle flow time to the enhanced parallel conduction time as the collisionality/density increases as posited in the GHD model. In addition, the heat flux width is found to be proportional to the square root of ion mass for low collisionality while it has a weakly dependence on ion mass for high collisionality. Furthermore, our simulations show that as the density increases, the radial electric field (E r ) well shallows, which potentially weakens E r × B flow shear stabilization of turbulence at high density.