Dieter Boeyaert, Kelly A. Garcia, Heinke Frerichs, Michael J. Gerard

Exhaust studies for non-resonant divertors in HSX

This work was funded by the U.S. Department of Energy under grant numbers DE-FG02-93ER54222 and DESC0014210

Main content summarized in following papers:

• D Boeyaert et al 2025 Nucl. Mater. Energy 42 101874
• K A Garcia et al 2025 Plasma Phys. Control. Fusion 67 035011
• H Frerichs et al 2025 Plasma Phys. Control. Fusion 67 045012

March 18, 2025 1/17

Requirements for a divertor

• Mandatory requirements for a divertor
• Power exhaust – max. heat flux of ~ 10 MWm^-2
• Particle exhaust – high subdivertor pressure to facilitate pumping
• Impurity control – enrich He and impurities in divertor to avoid core contamination and facilitate pumping
• Minimal net erosion – avoid T_d > 5 eV (for W)
• Divertor configurations in stellarators:
• Island divertor (W7-X)
• Helical divertor (LHD)
• Non-resonant divertor (HSX, CTH)

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[H. Frerichs et al., PPCF 2025]

[M. Kobayashi et al.., NME 2016]

[K. A. Garcia et al.., PPCF 2025]

March 18, 2025 2/17

Requirements for a divertor

• Mandatory requirements for a divertor
• Power exhaust – max. heat flux of ~ 10 MWm^-2
• Particle exhaust – high subdivertor pressure to facilitate pumping
• Impurity control – enrich He and impurities in divertor to avoid core contamination and facilitate pumping
• Minimal net erosion – avoid T_d > 5 eV (for W)
• Divertor configurations in stellarators:
• Island divertor (W7-X)
• Helical divertor (LHD)
• Non-resonant divertor (HSX, CTH)

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[H. Frerichs et al., PPCF 2025]

[M. Kobayashi et al.., NME 2016]

[K. A. Garcia et al.., PPCF 2025]

March 18, 2025 3/17

Available tools to study magnetic field and exhaust

• FLARE: Field Line Analysis and Reconstruction [H. Frerichs, NF 2024]
• Tracing field lines 🡺 used to determine magnetic topologies
• Making field-aligned grids for EMC3-EIRENE
• Fast, low fidelity model for heat deposition
• EMC3-EIRENE: Edge Monte Carlo 3D [Y. Feng, CPP 2014]
• Plasma edge code solving Braginskii equations (plasma) and Boltzmann equation (neutrals)
• FLF Lyapunov calculator
• Field line tracer (not as advanced as FLARE)
• Used to calculate Lyapunov exponents

March 18, 2025 4/17

Outline of the talk

• Justify choice of magnetic configuration to study NRD behavior in HSX
• Power exhaust analysis using low fidelity tools: FLARE
• Particle and radiation analysis using high fidelity tools: EMC3-EIRENE

March 18, 2025 5/17

Radial penetration depth

[K. A. Garcia et al.., PPCF 2025]

[H. Frerichs et al., PoP 2015]

March 18, 2025 6/17

[K. A. Garcia et al.., PPCF 2025]

March 18, 2025 7/17

Selection of configurations

[K. A. Garcia et al.., PPCF 2025]

March 18, 2025 8/17

Magnetic properties of “QHS” and “large island” configurations

QHS

Large island

March 18, 2025 9/17

Analysis of exhaust: fast, low fidelity model (FLARE)

• Development of unstructured quadrilateral mesh generator with adaptive refinement
• Motivation: highly shaped configurations like HSX
• Structured, field aligned mesh only possible in small toroidal region
• EMC3-EIRENE grid required from 3-5 toroidal blocks
• Increased demand of computational resources
• Developed in FLARE, can potentially be used in �EMC3 – EIRENE
• Gives alternative to EMC3-Lite in FLARE

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[H. Frerichs et al.., PPCF 2025]

March 18, 2025 10/17

Analysis of exhaust: fast, low fidelity model (FLARE)

• Applying unstructured mesh generator to HSX (QHS)
• Inner flux tubes span entire half period
• Outside LCFS more layers required

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[H. Frerichs et al.., PPCF 2025]

March 18, 2025 11/17

Analysis of exhaust: fast, low fidelity model (FLARE)

• Simulation result and comparison with “classical” field line tracing
• Good agreement between “classical”�and new field line tracing
• Heat loads on target can be quickly �estimated with FLARE�(outcome similar to EMC3-Lite)

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[H. Frerichs et al.., PPCF 2025]

Toroidal angle [deg]

Toroidal angle [deg]

Poloidal angle [deg]

Poloidal angle [deg]

Poloidal angle [deg]

Poloidal angle [deg]

Heat load/P_SOL [m^-2]

Strike point density[m^-2]

Profiles at 𝜑 = 17^∘

March 18, 2025 12/17

Analysis of exhaust: slow, high fidelity model �(EMC3-EIRENE) 🡺 neutral exhaust

• Baffles placed in regions with low connection lengths
• 2 baffle structures tested:

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[D. Boeyaert et al.., NME 2025]

March 18, 2025 13/17

Analysis of exhaust: slow, high fidelity model �(EMC3-EIRENE) 🡺 neutral exhaust

• Compression ratio determines exhaust efficiency�upstream neutral pressure similar 🡺 compare downstream pressures
• Baffles placed in regions with low connection lengths
• 2 baffle structures tested:
• Baffle 1 increases neutral�pressure in NRD
• Baffle 2 seems not�beneficial

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[D. Boeyaert et al.., NME 2025]

March 18, 2025 14/17

Analysis of exhaust: slow, high fidelity model �(EMC3-EIRENE) 🡺 neutral exhaust

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• At ϕ = 3°: P_n,d decreases for baffle 2
• Baffle 2 interacts with strikeline
• Location of baffles limits strikeline resiliency

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[D. Boeyaert et al.., NME 2025]

March 18, 2025 15/17

Analysis of exhaust: slow, high fidelity model �(EMC3-EIRENE) 🡺 power exhaust

• Preliminary analysis of power exhaust
• Same density (n_e =2e19 m^-3) and power (P=500 kW) imposed on inner grid boundary
• Same carbon sputtering coefficient at PWI (4%)
• Similar anomalous transport (D=0.25 m²s^-1, 𝛘_e/I = 0.75m²s^-1) for all simulations
• Power deposition shows more radiated power in island-like divertor than in non-resonant divertor for low density simulation

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Similar to [A. Bader et al. NF 2013]

March 18, 2025 16/17

Conclusion and future plans

• Metric developed to determine importance islands in the edge of HSX
• Fast model for heat flux calculation and unstructured mesh generator implemented in FLARE
• Initial possibility of baffles in NRDs performed with EMC3-EIRENE
• Further analysis of neutral behavior and comparison with earlier experimental work planned
• Analysis of P_targets and P_rad in NRDs in progress�🡪 Evaluate performance NRD towards power exhaust in� comparison with island divertor

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March 18, 2025 17/17

Backup slides

March 18, 2025 18/17

Comparison FLARE vs. EMC3-Lite

• Grid:
• Unstructured grid generation in FLARE faster than structured grid generation for EMC3-EIRENE: no outer plasma boundary to be determined, grid boundary determined by vessel wall 🡪 grid generation within minutes
• EMC3-Lite: structured grid with less requirements on flux conservation
• Speed:
• Fieldline reconstruction 2-3 times faster than �numerical integration
• Exact speed depending on number of particles
• Slower than EMC3-Lite due to unstructured grid
• Result (tested for W7-X):
• Very similar results with FLARE and EMC3-Lite

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March 18, 2025 19/17