JOREK simulations of the X-point radiator formation and its movement in ASDEX Upgrade

Future large-scale magnetic confinement fusion reactors require operational regimes that can avoid extreme heat fluxes onto the plasma-facing components. One promising regime is the X-point radiator (XPR), which relies on a highly radiative, cold and dense plasma volume forming above the X-point, and which can be accessed via impurity seeding. Experimentally, the height of the XPR can be controlled by adjusting the seeding rate and heating power. This contribution presents axisymmetric (2D) simulations of the XPR regime in ASDEX Upgrade using the nonlinear MHD code JOREK extended with a kinetic particle framework for the main species neutrals and nitrogen impurities. With the time-dependent simulations, the progression from attached divertors to a complete detachment with the XPR formation is shown, highlighting the effects of the neutrals and impurities separately. Amidst this progression, the formation and the loss of the high-field-side high-density are observed. After the XPR is well-formed at the height of 6.8 cm, the fuelling and seeding rates are adjusted so that the XPR remains stationary. From the stationary case, the seeding rate is then changed to see how the XPR location reacts. By increasing and decreasing the seeding rate, the XPR responds by moving upwards and downwards, respectively. These simulations show JOREK’s capability of simulating time-varying XPR, which will provide a baseline for the transition to 3D simulations, so the MHD activities and their interaction with the XPR can be studied.

💡 Research Summary

This paper presents a comprehensive study of the X‑point radiator (XPR) regime in the ASDEX Upgrade tokamak using the nonlinear magnetohydrodynamic (MHD) code JOREK extended with a kinetic particle framework for deuterium neutrals and nitrogen impurities. The authors aim to reproduce, in a fully time‑dependent manner, the formation, stabilization, and vertical movement of the XPR as observed experimentally when impurity seeding rates and heating power are varied.

The simulation is built on the experimental equilibrium of discharge #38773 at 3.65 s (0.8 MA plasma current, –1.8 T toroidal field, 10 MW heating, ~7.5 MW radiated power). Three sequential phases are defined. Phase 1 (0–4.4 ms) runs the baseline JOREK reduced‑MHD model (single‑temperature, toroidal field compression neglected) with ad‑hoc particle and heat diffusion profiles to match the initial plasma density and temperature. Phase 2 (4.4–13.5 ms) introduces kinetic deuterium neutrals and nitrogen impurity particles independently. The deuterium fuelling rate is ramped to 2 × 10²² e⁻/s (with an albedo of 100 % initially, then 98 % for recycling), followed by a simultaneous ramp of nitrogen seeding to the same rate. This phase captures the emergence of a high‑field‑side high‑density (HFSHD) region caused by strong recycling, the subsequent cooling of the inner target to ≈1 eV, and the onset of detachment. As nitrogen radiation intensifies, the inner divertor fully detaches, the electron temperature in the private flux region (PFR) drops below 1 eV, and a radiating mantle forms above the X‑point.

Phase 3 (13.5–50 ms) adjusts fuelling and seeding to keep the total (neutral + ionized) deuterium and nitrogen content constant (fuelling increased to 4.4 × 10²² e⁻/s, seeding reduced to 3.1 × 10²¹ e⁻/s). Under these conditions the XPR stabilizes at a height of 6.8 cm above the X‑point and remains quasi‑stationary for more than 30 ms, providing a reference “stationary case”.

The authors then explore XPR mobility by perturbing the nitrogen seeding rate while maintaining the total particle content. An increase in seeding pushes the radiation peak upward, moving the XPR higher; a decrease causes the opposite effect, lowering the XPR. This reproduces the experimentally observed controllability of XPR height via seeding.

A notable limitation is the omission of impurity‑background collisions (neo‑classical transport) in the presented runs. Consequently, impurity particles experience unrestricted E × B drift, leading to an artificial poloidal elongation of the XPR. Section 7 demonstrates that inclusion of a collision operator (Homma operator) suppresses this elongation, suggesting that future simulations should incorporate these effects for quantitative fidelity.

The study confirms that JOREK, equipped with a full‑f kinetic module, can capture the essential physics of XPR formation: HFSHD creation, sequential inner‑ and outer‑target detachment, radiation condensation, and the delicate balance between fuelling, seeding, and radiative cooling that determines XPR height. The authors propose extending this 2D framework to full 3D simulations to investigate interactions between XPR and edge‑localized MHD instabilities (e.g., type‑I ELMs), which are critical for reactor‑scale divertor heat‑flux management. Future work will also integrate additional physics such as molecular reactions, pumping, and self‑collisions of kinetic species to bring the model closer to experimental reality.