ITER hybrid equilibrium in JOREK on the EQDSK separatrix
Entry 65 left JOREK’s ITER hybrid equilibrium with safety factor q and plasma current I_p a few percent high towards the edge, and the cause not yet separated. Edge-stability results depend on edge q and current, so the owner set an acceptance tolerance on q over normalised flux ψ_N 0.1–0.95 and on I_p, to be met before any stability run (OQ-39; the values are in the table).
Cause and fix
The TORAX ITER hybrid EQDSK comes from a fixed-boundary CHEASE solve. Its R–Z grid contains no X-point: the poloidal-flux gradient has no zero inside it. JOREK’s EQDSK converter nevertheless traces a default ITER boundary contour outside the plasma, and most of that contour lay outside the EQDSK grid. The flux there was extrapolated, and JOREK built an X-point and a separatrix of its own. The plasma it solved for was therefore not the EQDSK’s plasma.
We replaced that contour with the EQDSK separatrix itself: 300 points on the boundary flux surface, a fixed-boundary JOREK equilibrium without an X-point, on a polar flux-aligned grid. Pressure and FF′ are unchanged from entry 65.
Result
| grid (radial × poloidal) | JOREK against the EQDSK | accepted |
|---|---|---|
| 40 × 64 | I_p −1.38%, largest q difference 1.1%: fails the current toleranceC-220 | no |
| 80 × 128 | I_p −0.93%, largest q difference 1.1%, q 4.668 against 4.668 at psi_N 0.95: passes the tolerance of q within 2% and I_p within 1%C-221 | yes |
| 160 × 256 | I_p −0.20%, largest q difference 1.1%: passesC-222 | yes |
q now matches the EQDSK across ψ_N 0.1–0.95 on every grid, more closely at the edge than in the core, so the edge mismatch of entry 65 came from the boundary. The largest q difference is the same on all three grids; only the current deficit shrinks with resolution. The check compares JOREK’s q and I_p, which JOREK computes from the boundary, pressure and FF′, with the EQDSK’s own q and I_p, which JOREK does not read. The comparison script is ours, and so is the input generator, so the check is not independent of the author. C-216 is superseded by C-221.
This boundary has a known limitation. A fixed boundary on the separatrix acts as an ideal conducting wall there, with no vacuum region outside the plasma. That stabilises peeling modes artificially. Every growth rate in the following entries carries this limitation.
The owner accepted the rest of OQ-39 as recommended: - JOREK’s model303 (reduced MHD with parallel flow and one temperature) with diamagnetic terms; - Spitzer resistivity and viscosity at Prandtl number 1; - one toroidal mode number per run, n = 1, 2, 3, 5, 8, 12, 16, 20; - a mode counts as unstable if its growth rate γ is positive with diamagnetic terms included; - γ is quoted only if halving the time step Δt and doubling the grid each leave it within a fixed tolerance (entry 69); - up to three one-node jobs.
The 80 × 128 grid is used for the scans and 160 × 256 for the grid check.
Where this stands: the equilibrium for case (a), the EQDSK as given, is accepted, and the first stability scan follows (entry 68).
Technical details → JOREK. Decision → OQ-39.
JOREK acknowledgement. JOREK is developed by the JOREK team and is open source under the GNU LGPL v3. Results here use JOREK at commit 01a52be3. Citations: M. Hoelzl et al., Nuclear Fusion 61, 065001 (2021); M. Hoelzl et al., Nuclear Fusion 66, 116006 (2026). For a list of JOREK team members, refer to the author list of M. Hoelzl, G.T.A. Huijsmans, F.J. Artola, E. Nardon, M. Becoulet, N. Schwarz, A. Cathey, S.J.P. Pamela et al., Nuclear Fusion 64, 112016 (2024).
Technical details → JOREK › iter equilibrium
Decisions → OQ-39