Physics basis for the first ITER tungsten divertor

Analytical Solution of Heat Conduction in a Multi-Layer Orthotropic Cylinder Subject to Periodic and Asymmetric Heat Flux

Analytical considerations of slip flow and heat transfer through microfoams in mini/microchannels with asymmetric wall heat fluxes

KInetic code for Plasma Periphery (KIPP) was used to assess the importance of kinetic effects of parallel ion transport in the scrape-off layer (SOL) and divertor of JET high radiative H-mode inter-edge localised mode plasma conditions with strong nitrogen (N2) injection, leading to partial detachment at divertor targets. Plasma parameter profiles along the magnetic field from one of the EDGE2D-EIRENE simulation cases were used as an input for KIPP runs. The profiles were maintained by particle and power sources. This work is a continuation of the previous study carried out for electrons (Chankin et al 2018 Plasma Phys. Control. Fusion 60 115011).In this modelling KIPP calculated ion distribution functions and ion parallel power fluxes. In the main SOL kinetic effects lead to a reduction of heat (conductive power) fluxes compared to Braginskii fluxes by factors 3−4 (‘heat flux limiting’). In the divertor, on the contrary, a strong ‘heat flux enhancement’, by up to two orders of magnitude above Braginskii’s, was found. Similar to cases for electrons, high ion heat flux enhancement factors, in particular near targets, are attributed to a non-local transport of super-thermal ions originating from positions along field lines with the highest ion temperature, resulting in the appearance of bump-on-tail features on ion heat flux density profiles. Despite ion heat flux enhancement factors at the target being much higher than for electrons, total power fluxes, ion plus electron, were dominated by ion and electron convection and electron conduction, with ion conductive fluxes playing a secondary role. This must be attributed to lower ion (than electron) velocities (factor ∼ reduction), which are not compensated by kinetic effects of lower ion upstream collisionality.

The problem of heat conduction in a two-dimensional orthotropic cylinder subject to asymmetric and periodic heat flux distribution imposed on the outer wall was solved analytically. The dimensional analysis of the problem revealed that the heat conduction was a function of four nondimensional parameters: Biol number (Bi), the ratio of the cylinder outer radius to the inner radius (R2), nondimensional frequency (α), and orthotropicity factor (Kt). The results show that the insulation characteristics of a cylinder made from orthotropic material can be significantly better than that of a cylinder made from isotropic material subject to the same thermal conditions. The case of a graphite fiber epoxy was used to demonstrate the effectiveness of orthotropic materials under periodic and asymmetric thermal loading.

Modeling of divertor particle and heat loads during application of resonant magnetic perturbation fields for ELM control in ITER

ELM mitigation to avoid melting of the tungsten (W) divertor is one of the main factors affecting plasma fuelling and detachment control at full current for high Q operation in ITER. Here we derive the ITER operational space, where ELM mitigation to avoid melting of the W divertor monoblocks top surface is not required and appropriate control of W sources and radiation in the main plasma can be ensured through ELM control by pellet pacing. We apply the experimental scaling that relates the maximum ELM energy density deposited at the divertor with the pedestal parameters and this eliminates the uncertainty related with the ELM wetted area for energy deposition at the divertor and enables the definition of the ITER operating space through global plasma parameters. Our evaluation is thus based on this empirical scaling for ELM power loads together with the scaling for the pedestal pressure limit based on predictions from stability codes. In particular, our analysis has revealed that for the pedestal pressure predicted by the EPED1 + SOLPS scaling, ELM mitigation to avoid melting of the W divertor monoblocks top surface may not be required for 2.65 T H-modes with normalized pedestal densities (to the Greenwald limit) larger than 0.5 to a level of current of 6.5–7.5 MA, which depends on assumptions on the divertor power flux during ELMs and between ELMs that expand the range of experimental uncertainties. The pellet and gas fuelling requirements compatible with control of plasma detachment, core plasma tungsten accumulation and H-mode operation (including post-ELM W transient radiation) have been assessed by 1.5D transport simulations for a range of assumptions regarding W re-deposition at the divertor including the most conservative assumption of zero prompt re-deposition. With such conservative assumptions, the post-ELM W transient radiation imposes a very stringent limit on ELM energy losses and the associated minimum required ELM frequency. Depending on W transport assumptions during the ELM, a maximum ELM frequency is also identified above which core tungsten accumulation takes place.

SOLPS-ITER simulations performed for Q DT = 10, P SOL = 100 MW burning plasmas on ITER extend the existing database to high values of separatrix averaged neon impurity concentration (⟨c Ne⟩ ≈ 6%) and divertor neutral pressure (⟨p div⟩ > 25 Pa) in order to determine the heat flux mitigation capability of these scenarios and whether strongly detached states are accessible. In the existing database of ITER simulations, the level of detachment was limited to cases where the integral ion flux to the outer target was greater than 80% of the value at rollover, with the impurity radiation localized near the target. With the possibility of narrow heat flux channels and increased deposited power due to tile shaping, it is important to explore operation at a higher degree of detachment. Two series of simulations were explored to extend the database of SOLPS simulations. By increasing the deuterium and neon puff rates proportionally, the peak divertor energy flux (q ⊥,max) is decreased from 5 to 3 MW m−2 while ⟨p div⟩ increased from 11 to 27 Pa. By increasing only the neon puff, q ⊥, max can be reduced to <1MW m−2 while ⟨p div⟩ is maintained at Pa. As the neon puff level is increased, the position of the impurity radiation peak is shifted towards the X-point. At the highest neon puff levels with steady-state solutions, the electron temperature is reduced below 1 eV across 50 cm of each divertor target. The new cases extend previously observed tight relationships in power and momentum loss factors to low electron temperature improving their utility for highly detached regimes.

Controlling the splitting divertor heat flux caused by resonant magnetic perturbations (RMPs) is a topic of concern for fusion devices. As a fundamental prerequisite, it is necessary to understand the characteristics of the heat flux distribution under the applied RMP field, which will be studied in this paper. The nonlinear phenomenon of strike point splitting was found to be strongly dependent on the plasma response under RMP. These splitting heat flux distributions are qualitatively explained by the simulated magnetic footprints. The RMP phase scanning experiment shows that scanning in a certain range of relative phase can maintain good ELM mitigation and simultaneously sweep the striations of heat flux on divertor target. Additionally, even in upper single null (USN) configurations, heat stripes are observed on the lower outer divertor (LO-div), attributed to RMP-induced additional magnetic connections to the LO-div, as confirmed by magnetic topology simulations. A dedicated investigation into the impact of the discrepancy between lower and upper separatrix radii mapped to the low field side mid-plane (〖dR〗_sep) reveals its significant influence on both ELM control and heat flux distribution. Within a certain range of 〖dR〗_sep, the heat flux distribution is improved while ELM suppression is maintained. These findings contribute to divertor heat flux understanding under RMP conditions in tokamak operations.

Theory of the ultimate heat transfer limit of cylindrical heat pipes

The evolution of the parameters of the plasma in the termination phase of high confinement H-modes at JET with carbon fibre composite plasma facing components (JET-C) has been analysed with a view to predict the dynamics of the plasma energy decrease for sudden terminations of the ITER QDT = 10 scenario caused by malfunction of additional heating systems. JET-C experiments show that the rate of decay of the plasma energy in the high performance H-mode termination phase is predominantly determined by the duration of the type III ELMy H-mode phase after the end of the type I ELMy H-mode regime. Longer type III ELMy H-mode phase durations lead to slower plasma energy decay rates. The duration of the type III ELMy H-mode phase is itself determined by the margin of the edge power flow (dominated by the rate of collapse of the plasma energy) over the H-mode threshold power in the termination phase, with larger margins leading to longer type III ELMy H-mode phase durations. For most of the JET-C discharges analysed the timescale for the plasma energy decrease in the termination of high energy confinement H-modes is comparable to the energy confinement time of the plasma in the high confinement phase rather than half of this value, which is to be expected for instantaneous H–L transitions. Modelling of the termination phase of ITER QDT = 10 H-modes (with transport assumptions in this phase validated against JET-C experiments) shows that similar to JET-C results the timescale for the decrease of the plasma energy is comparable and can even be longer than the energy confinement time of the burning phase, provided that ELM control can be maintained. This is due to the long sustainment of the type III ELMy H-mode by the substantial edge power flow compared to the H-mode threshold power during this phase. The large edge power flow in the termination phase of ITER high QDT plasmas is provided by the decrease of the plasma energy and the slow collapse of the alpha heating. Operational strategies in ITER to control the energy decay rate as well as the consequences of the lack of ELM control in the high QDT termination phase are presented.

The kinetic code for plasma periphery (KIPP) was used to assess the importance of the kinetic effects of parallel electron transport in the scrape-off layer (SOL) and divertor of JET high radiative H-mode inter-ELM plasma conditions with the ITER-like wall and strong nitrogen (N2) injection. Plasma parameter profiles along a magnetic field from one of the EDGE2D-EIRENE simulation cases were used as an input for KIPP runs. Profiles were maintained by particle and power sources. KIPP generated electron distribution functions, fe, parallel power fluxes, electron–ion thermoforces, Debye sheath potential drops and electron sheath transmission factors at divertor targets. For heat fluxes in the main SOL, KIPP results showed deviations from classical (e.g. Braginskii) fluxes by factors typically of ∼1.5, sometimes up to 2, with the flux limiting for more upstream positions and flux enhancement near entrances to the divertor. In the divertor, at the same time, for radial positions closer to the separatrix, very large heat flux enhancement factors of up to ten or even higher, indicative of a strong nonlocal heat transport, were found at the outer target, with heat power flux density exhibiting bump-on-tail features at high energies. Under such extreme conditions, however, contributions of conductive power fluxes to total power fluxes were strongly reduced, with convective power fluxes becoming comparable, or sometimes exceeding, conductive power fluxes. Electron–ion thermoforce, on the other hand, which is known to be determined mostly by thermal and subthermal electrons, was found to be in good agreement with Braginskii formulas, including the Zeff dependence. Overall, KIPP results indicate, at least for the plasma conditions used in this modelling, a sizable, but not dominant, effect of kinetics on parallel electron transport.

Experimental implementation of a real-time power flux estimator for the ITER first wall on the TCV tokamak

In the previous papers, a method is proposed to obtain microscopic definitions for internal forces of continua such as stress, higher-order stresses and heat flux. In the present paper, the relationship between higher-order stress power and heat flux is discussed, expressing the 1st law of thermodynamics with microscopic quantities in mesodomain. Then an energy equation is obtained by dividing the kinematical quantity of an atom into macroscopic and thermal motion. It is clarified that heat flux in the energy equation is equivalent to higher-order stress power since heat flux is regarded as the amount of each order power due to higher-order stresses. When higher-order stress power is separated from heat flux in the energy equation considering this equivalence, the value of heat flux decreases. These expressions of heat flux and higher-order stress are useful to obtain macroscopic quantities from numerical solutions calculated by the molecular dynamics.

Comprehensive analysis on the effect of asymmetric heat fluxes on microchannel slip flow and heat transfer via a lattice Boltzmann method

An analytical study is performed on steady, laminar, and fully developed forced convection heat transfer in a parallel plate channel with asymmetric uniform heat flux boundary conditions. The channel is filled with a saturated porous medium, and the lower and upper walls are subjected to different uniform heat fluxes. The dimensionless form of the Darcy–Brinkman momentum equation is solved to determine the dimensionless velocity profile, while the dimensionless energy equation is solved to obtain temperature profile for a hydrodynamically and thermally fully developed flow in the channel. Nusselt numbers for the lower and upper walls and an overall Nusselt number are defined. Analytical expressions for determination of the Nusselt numbers and critical heat flux ratio, at which singularities are observed for individual Nusselt numbers, are obtained. Based on the values of critical heat flux ratio and Darcy number, a diagram is provided to determine the direction of heat transfer between the lower or upper walls while the fluid is flowing in the channel.