Approaching the radiating X-point in SOLPS-ITER modeling of ASDEX Upgrade H-mode discharges

Abstract

In the present paper the ASDEX Upgrade (AUG) experimental trend of reaching the radiating X-point with nitrogen seeding is reproduced by SOLPS-ITER code modeling. In these experiments the whole divertor region below the X-point is cooled down by the impurity radiation if the seeding rate is large enough, and the maximal radiation is registered from the X-point region, or even from the confinement zone above the X-point. It is demonstrated that for constant seeding rate SOLPS-ITER simulations of the intensively seeded AUG discharges result in that the confined plasma goes into the radiation collapse as a certain threshold in seeding rate is exceeded. This threshold value increases with increasing discharge power. No stable regimes with the electron temperature below 5 eV in the confinement zone even above the X-point are achieved in the modeling if the seeding rate is large enough, in contrast to the experiment. However, such a regime may be achieved if the fueling, seeding and pumping rates are changing in time. Since the SOLPS-ITER code can simulate only steady state, another modeling strategy is chosen. The fueling and seeding rates are artificially reduced by 3 orders of magnitude and the impurity content is set to satisfy the condition that the ratio of electrons contribution originating from fuel atoms to ones coming from impurity atoms is about unity. It is suggested that the radial width of the cooled region in the confinement zone is of the order of the scrape-off layer width λ q , since it is driven by the same physics leading the energy flux to go from mostly radial to mostly parallel. Under these conditions, the radiative spot above the X-point behaves as the energy sink similarly to the energy sink near the divertor in the conventional regime. In extreme regimes (with large seeding rate), the width of the cold region inside the separatrix may exceed λ q , and up to 90% of discharge power can be radiated from the confined region. An estimate of the poloidal length of the radiative spot is suggested as well. Flow patterns of neutrals, deuterium ions, impurities, electric current and heat flows are analyzed for the regimes with intensive X-point radiation. The formation of an electric potential peak above the X-point is observed in the simulations, and the corresponding E × B drift flux appears to give the largest contribution to the main ion and impurity fluxes. This E × B drift flux together with the large ionization source change the parallel velocity with respect to its neoclassical profile. Consequently, the radial E field deviates from the neoclassical one, which might improve the turbulence suppression.

Detached regime with highly radiating X‐point: Physics and modelling

“…Reproduced with permission. [24] All rights reserved much smaller than at the OMP. Thus the maximal height of the radiating mantle above the X-point of 15 cm corresponds only to 8 mm as measured at the OMP, and the whole perturbation thus lies outside the flux surface of 𝜌 pol = 0.99.…”

“…Reproduced with permission. [24] All rights reserved radiation (visible in the experiment) lies within this mantle in its LFS branch-Figure 5 illustrates the spatial location of such a maximum for different amount of nitrogen in the system (marked by N core boundary density and D boundary density). One can see that its location moves from the HFS SOL below the X-point towards the LFS part of the confined region above the X-point, and after reaching some maximal height, it moves down and simultaneously deeper into the core.…”

“…Stable solutions appear to be only achievable with prescribed N density at the core boundary and artificially reduced both fuelling and seeding rates, thus controlling the N ions–atoms content in the computational domain (see details in ref. [24]). This reflects the necessity for feedback controlling loop in experiment to stabilize the radiating spot above the X‐point.…”

“…As it is demonstrated in ref. [24], this drift vortex near the X‐point gives the major contribution to particle fluxes and their divergence on those flux surfaces, which are perturbed by the XPR. These fluxes are directed outside the separatrix, compensating the ion source due to neutral ionization, which, like the radiation, takes place mainly inside or near the radiating band.…”

“…This difficulty was overcome by Saint Petersburg team by prescribing the impurity density at the core boundary of SOLPS-ITER computational domain (i.e., affecting the particle content in the system rather than seeding rate)-most observed features of AUG experiment with XPR controlled by intensive nitrogen seeding were reproduced qualitatively in SOLPS-ITER simulations. [24] Recently a quantitative comparison of SOLPS-ITER modelling results to newly developed in AUG divertor Thomson scattering diagnostics data was reported for the XPR regime, however, yet without drifts. [25] However, it is unclear whether XPR regime is achievable in the reactor-scale machines, like ITER, CFETR, or DEMO.…”