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

This paper presents 2D JOREK simulations of the X-point radiator (XPR) in ASDEX Upgrade, demonstrating the code's ability to model the formation, movement, and stability of the XPR in response to varying fueling and seeding rates.

The Gist

The "Plasma Heat Shield" Experiment: A Simple Guide

Imagine you are trying to run a high-powered furnace that is so hot it could melt the very walls of the building it’s in. This is the challenge scientists face with nuclear fusion. To create clean energy, we use a "plasma"—a super-hot, electrified gas—trapped inside a donut-shaped machine called a tokamak. The problem? This plasma is so energetic that it wants to blast the machine's walls with intense heat, which would destroy them.

This paper describes a high-tech way to create a "heat shield" inside the machine to protect it.

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1. The Concept: The X-Point Radiator (The "Mist Shield")

Think of the plasma like a high-pressure fire hose spraying water at a wall. If you spray it directly, the wall gets soaked and damaged.

Instead of letting the "water" (the heat) hit the wall directly, scientists try to create a "mist" right in front of the target. In a fusion machine, they do this by injecting a specific gas (like Nitrogen) near a specific spot called the X-point.

This gas creates a "cloud" of cold, dense plasma called an X-point Radiator (XPR). When the intense heat from the core hits this cloud, the energy doesn't hit the wall; instead, it gets "used up" by the gas, turning the heat into light (radiation) that spreads out harmlessly. It’s like using a thick fog to absorb the heat of a laser beam before it hits a sensor.

2. The Simulation: The "Digital Twin"

Since we can't just keep melting real machines to see what happens, scientists used a supercomputer program called JOREK.

Think of JOREK as a incredibly advanced flight simulator, but for plasma. Instead of simulating a plane, it simulates the movement of every "particle" of gas and heat. The researchers used this simulator to see how this "mist shield" forms, how it moves, and—most importantly—how it breaks.

3. The Three Scenarios: Moving the Shield

The researchers tested three different "weather patterns" for this plasma shield:

Scenario A: The Perfect Balance (The "Steady Mist")

They found they could reach a "sweet spot" where the shield stays perfectly still at a certain height. It’s like finding the perfect setting on a humidifier so the mist stays exactly where you want it to protect your skin.

Scenario B: Too Much Gas (The "Flood/MARFE")

What happens if you pump in too much nitrogen? The shield grows too large and moves too high. It becomes unstable and turns into something called a MARFE.

• Analogy: Imagine your mist shield becomes so thick and heavy that it turns into a giant, cold puddle that starts sliding down the wall toward the floor. This "puddle" is unstable and can cause the whole machine to "glitch" or shut down (a disruption).

Scenario C: Not Enough Gas (The "Evaporation")

What if you turn the gas off? The shield begins to shrink and move downward.

• Analogy: It’s like a cloud evaporating on a sunny day. As the "mist" disappears, the "fire hose" of heat from the core suddenly has a clear path to hit the machine's walls directly. The shield is lost, and the machine is in danger of overheating.

4. Why does this matter?

If we want to build a real fusion power plant that runs 24/7, we need to know exactly how to control this "mist shield." We need to know how to turn the gas up or down to move the shield up or down, ensuring the walls stay cool while the center stays hot enough to create energy.

In short: This paper proves that our "digital simulator" is powerful enough to predict how to manage these plasma shields, paving the way for building real, safe, and long-lasting fusion power plants.

Technical Summary

Technical Summary: JOREK Simulations of the X-point Radiator Formation and Movement in ASDEX Upgrade

1. Problem Statement

In future large-scale magnetic confinement fusion reactors (like ITER), managing power exhaust is critical to prevent damage to plasma-facing components. Two major challenges exist: managing quasi-stationary heat loads and mitigating transient heat bursts from Magnetohydrodynamic (MHD) instabilities like Edge Localized Modes (ELMs).

The X-point Radiator (XPR) is a promising operational regime where impurity seeding creates a highly radiative, cold, and dense plasma volume above the X-point. This distributes heat over a broader area and can lead to divertor detachment and ELM suppression. However, the underlying physical processes governing the movement of the XPR (upward/downward) and its transition into an unstable MARFE (Multifaceted Asymmetric Radiation From the Edge) are not fully understood.

2. Methodology

The study employs the JOREK nonlinear MHD code, extended with a fluid-kinetic hybrid framework. The simulation setup is based on experimental data from the ASDEX Upgrade (AUG) tokamak (discharge #38773).

• Hybrid Model:
  • Fluid (Reduced MHD): Used for the background deuterium plasma, accounting for $E \times B$, grad-B, and diamagnetic drifts.
  • Kinetic (Full-f Particle-in-Cell): Used for deuterium neutrals and nitrogen impurities, modeled via a Monte-Carlo particle tracker.
• Atomic Physics: The model includes ionization, charge exchange, volumetric recombination, and effective line/continuum radiation (sourced from the OpenADAS database).
• Simulation Phases:
  1. Phase 1: Base MHD model to establish initial plasma profiles.
  2. Phase 2: Introduction of kinetic neutrals (fuelling) and impurities (seeding) to trigger XPR formation.
  3. Phase 3: Adjustment of rates to achieve a quasi-stationary XPR.
• Comparative Scenarios: The researchers branched from the stationary case to simulate an increased seeding rate (leading to a MARFE) and a reduced seeding rate (leading to XPR loss).

3. Key Contributions

• Dynamic Modeling of XPR: Successfully simulated the time-dependent formation, stabilization, movement, and loss of the XPR.
• Mechanism Identification: Provided a detailed breakdown of the interplay between ionization fronts, recombination, and impurity radiation that dictates XPR height.
• Hybrid Validation: Demonstrated that the JOREK kinetic extension can accurately capture the transition from attached divertors to complete detachment and XPR formation.
• Collision Effects: Demonstrated that including impurity-background collisions (neoclassical transport) is necessary to prevent unphysical poloidal elongation of the XPR.

4. Results

• Stationary XPR Characteristics: In the reference case, the XPR height was $\sim 6.8$ cm. The XPR core is characterized by high electron density ($\sim 3 \times 10^{20} \text{ m}^{-3}$) and low temperature ($1\text{--}2$ eV). A "radiating mantle" exists above the core, where impurity radiation reduces the temperature to the point where neutrals can penetrate and fuel the ionization front.
• The MARFE Transition (Upward Movement): Increasing the nitrogen seeding rate causes the XPR to move upward. As impurity density increases, the radiation peak shifts higher, cooling the ionization front and allowing neutrals to penetrate deeper into the core. Eventually, the radiating mantle overlaps with the ionization front, causing a drastic temperature drop ($< 1$ eV) and high recombination, signaling a transition to an unstable MARFE.
• The Retreating Case (Downward Movement/Loss): Reducing the seeding rate causes the XPR to move downward. As impurity radiation weakens, the temperature in the mantle rises, increasing the ionization rate of neutrals. This depletes the neutral density in the core, causing the XPR to shrink and eventually disappear, leaving the radiating mantle in the Scrape-Off Layer (SOL).
• Transport Dynamics: The simulation identified an electrostatic potential hill above the XPR, which creates an $E \times B$ drift that transports impurities and plasma toward the inner midplane (HFS).

5. Significance

This work provides a crucial 2D baseline for understanding XPR dynamics. By successfully modeling the movement and stability of the XPR, the study paves the way for 3D simulations. These future 3D models will be essential to study the complex interaction between XPR physics and 3D MHD activities, such as ELMs, which is vital for the design and operation of future fusion power plants.