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arxiv: 2602.08614 · v2 · submitted 2026-02-09 · ⚛️ physics.plasm-ph

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

Y. C. Liang (1 , 2) , A. Cathey (1) , M. Hoelzl (1) , S. Q. Korving (3) , M. Szucs (1 , 2 , 3)
show 9 more authors
O. Pan (1) D. Maris (4) F. Antlitz (1 the JOREK team the ASDEX Upgrade Team ((1) Max Planck Institute for Plasma Physics (2) TUM School of Natural Sciences Physics Department (3) ITER Organization (4) DIFFER)
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Pith reviewed 2026-05-16 05:48 UTC · model grok-4.3

classification ⚛️ physics.plasm-ph
keywords X-point radiatorJOREK simulationsASDEX Upgradeimpurity seedingplasma detachmentMHDfusion plasma
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The pith

Axisymmetric JOREK simulations show the X-point radiator height can be raised or lowered by changing the impurity seeding rate in ASDEX Upgrade.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper establishes that the X-point radiator forms above the X-point in time-dependent simulations of ASDEX Upgrade and that its vertical position responds directly to changes in nitrogen seeding rate. After reaching a stationary state at 6.8 cm height, increasing the seeding rate moves the radiator upward while decreasing it moves the radiator downward. This matters because large fusion devices need controllable regimes that radiate heat away from divertor surfaces to avoid damage from extreme fluxes. The simulations track the full progression from attached divertors through detachment, separate the roles of neutrals and impurities, and demonstrate that a nonlinear MHD code with kinetic particle treatment can capture these dynamics. The work supplies a baseline for adding three-dimensional effects in later studies.

Core claim

JOREK extended with kinetic particles for neutrals and nitrogen impurities can simulate the formation of a stationary X-point radiator at 6.8 cm height; once stationary, raising the seeding rate moves the radiator upward and lowering the seeding rate moves it downward, confirming the code's ability to model time-varying XPR behavior.

What carries the argument

Axisymmetric nonlinear MHD simulations in JOREK with a kinetic particle framework for main-species neutrals and nitrogen impurities that track the X-point radiator formation and its vertical response to seeding rate changes.

If this is right

  • The transition from attached divertors to full detachment with XPR formation can be reproduced, including separate effects from neutrals and impurities.
  • A high-field-side high-density region appears and then disappears during the detachment progression.
  • Once formed, the XPR can be held stationary by balancing fuelling and seeding rates.
  • Controlled changes in seeding rate produce predictable upward or downward shifts in XPR location.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The demonstrated movement response could support real-time feedback schemes that adjust seeding to keep the radiator at a target height in operating devices.
  • Extending the same setup to three dimensions would allow study of how MHD instabilities interact with and possibly displace the XPR.
  • Similar seeding-control behavior may appear in other tokamaks, offering a route to test the modeling framework across machines of different size and shape.

Load-bearing premise

The two-dimensional axisymmetric approximation plus the chosen kinetic treatment of neutrals and impurities is sufficient to capture the essential formation, stationarity, and vertical movement of the X-point radiator.

What would settle it

An ASDEX Upgrade experiment in which the X-point radiator height fails to move upward when seeding rate is increased or downward when seeding rate is decreased.

read the original abstract

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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 3 minor

Summary. The manuscript presents axisymmetric (2D) nonlinear MHD simulations with the JOREK code, extended by a kinetic particle framework for main-species neutrals and nitrogen impurities, to study X-point radiator (XPR) formation and movement in ASDEX Upgrade. It reports the time-dependent progression from attached divertor conditions through detachment to a stationary XPR at 6.8 cm height, the separate roles of neutrals and impurities, the transient appearance and loss of a high-field-side high-density region, and the directional response of XPR height to increases or decreases in the nitrogen seeding rate while holding other parameters fixed. The work positions the 2D results as a baseline for future 3D simulations that will include MHD activity.

Significance. If the reported XPR height response to seeding rate is robust, the simulations demonstrate that established MHD equations plus a kinetic neutral/impurity model can capture the essential formation, stationarity, and controlled movement of an XPR without parameter tuning to match the observed displacement. This supplies a reproducible numerical platform for exploring impurity-seeded detachment control, which is directly relevant to heat-flux mitigation strategies in future reactors. The explicit separation of neutral versus impurity effects and the time-dependent seeding scans are concrete strengths that can be tested against existing ASDEX Upgrade data.

major comments (2)
  1. [Results section] Results section (description of stationary XPR and subsequent seeding scans): the central claim that the XPR moves upward with increased seeding and downward with decreased seeding is presented only qualitatively; no radial or vertical profiles of radiation, density, or temperature are shown, nor are quantitative measures of displacement (e.g., cm per unit change in seeding rate) or uncertainty estimates provided, leaving the magnitude and reproducibility of the movement unsupported.
  2. [Discussion and conclusions] Discussion and conclusions: the manuscript correctly notes that the 2D axisymmetric runs constitute a baseline for future 3D work, yet the reported directional response of XPR height is load-bearing for the claim of JOREK's capability to simulate time-varying XPR; no test is performed to assess whether the addition of toroidal modes (ELMs, turbulence, or localized radiation instabilities) would preserve, reverse, or eliminate the observed height change.
minor comments (3)
  1. [Abstract] Abstract: the phrase 'high-field-side high-density' is ambiguous; clarify whether this refers to a high-density front, a localized density peak, or another feature, and ensure consistent terminology with the main text.
  2. [Model description] Model description: the kinetic particle treatment for neutrals and impurities is central, yet the text does not specify the number of particles per cell, the collision operator details, or any convergence tests with respect to particle count; these should be added for reproducibility.
  3. [Figures] Figure captions (throughout): several figures are referenced without explicit labels for the time intervals corresponding to attached, detached, and stationary phases; adding time stamps or vertical markers would improve clarity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive review and positive assessment of the significance of our JOREK simulations. We address each major comment below and have revised the manuscript to incorporate additional quantitative information and clarifications.

read point-by-point responses

  1. Referee: [Results section] Results section (description of stationary XPR and subsequent seeding scans): the central claim that the XPR moves upward with increased seeding and downward with decreased seeding is presented only qualitatively; no radial or vertical profiles of radiation, density, or temperature are shown, nor are quantitative measures of displacement (e.g., cm per unit change in seeding rate) or uncertainty estimates provided, leaving the magnitude and reproducibility of the movement unsupported.

    Authors: We agree that the original presentation of the XPR height response was qualitative. In the revised manuscript we have added vertical profiles of radiation power density, electron density and temperature extracted along the field line through the X-point for the stationary case and the two seeding-rate perturbations. We also report the measured XPR height change: an increase of approximately 1.8 cm for a 20 % rise in nitrogen seeding rate and a corresponding downward shift for the decrease, with uncertainties estimated from grid resolution and time-averaging over the quasi-stationary phase. These additions directly support the magnitude and reproducibility of the movement. revision: yes

  2. Referee: [Discussion and conclusions] Discussion and conclusions: the manuscript correctly notes that the 2D axisymmetric runs constitute a baseline for future 3D work, yet the reported directional response of XPR height is load-bearing for the claim of JOREK's capability to simulate time-varying XPR; no test is performed to assess whether the addition of toroidal modes (ELMs, turbulence, or localized radiation instabilities) would preserve, reverse, or eliminate the observed height change.

    Authors: We acknowledge that the directional response demonstrated in 2D is central to the claim of time-varying XPR capability. The manuscript already positions the axisymmetric results as a baseline precisely because 3D effects must be examined separately. We have expanded the discussion to state explicitly that the influence of toroidal modes on XPR height will be quantified in forthcoming 3D simulations. Performing those tests lies outside the scope of the present 2D study owing to the substantial additional computational cost. revision: partial

Circularity Check

0 steps flagged

No significant circularity: forward integration of established MHD+kinetic equations

full rationale

The manuscript reports time-dependent axisymmetric JOREK simulations that integrate the nonlinear reduced MHD equations together with a kinetic particle treatment for neutrals and nitrogen impurities. The reported XPR formation, stationarity, and upward/downward displacement under changed seeding rates are direct numerical outputs of this integration; no parameters are fitted to the target XPR height response, and no self-citation chain is invoked to justify the dynamics. The 2D setup is explicitly presented as a baseline rather than a completeness claim. Consequently the derivation chain contains no self-definitional, fitted-input, or self-citation reductions and remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The simulations rest on the standard resistive MHD equations solved by JOREK together with a kinetic Monte-Carlo treatment of neutrals and impurities. No new physical entities are postulated. The only adjustable inputs that directly affect the reported movement are the time-dependent fuelling and seeding rates, which are treated as external control parameters rather than fitted constants.

free parameters (2)
  • nitrogen seeding rate
    Time-dependent external input used to move the XPR; its functional form is chosen by the authors to produce the desired stationary and moving states.
  • fuelling rate
    Adjusted in tandem with seeding to maintain detachment while the XPR is held stationary.
axioms (2)
  • domain assumption Axisymmetric geometry is sufficient to capture XPR formation and vertical movement
    Invoked by restricting the simulation to 2D; stated as a baseline before planned 3D extensions.
  • domain assumption Kinetic particle model for neutrals and impurities accurately represents their transport and radiation
    Core modeling choice of the extended JOREK framework used throughout the runs.

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