Linear JOREK n-scan of the TORAX ITER hybrid state: three pedestal modes grow
The first case (b) job (entry 72) ended before most modes had grown far enough to measure. The second job continued every toroidal mode number n from its own last saved time slice, with unchanged inputs. The rule for fitting the growth rate γ was fixed before this job’s data were analysed: fit ½ ln E from 4 to 10 decades above the run’s minimum energy, require the two halves of the window and the magnetic and kinetic energies to give the same γ (the agreement test used for case (a)), and read the location from the flow perturbation.
What happened
All eight runs reached the time limit without a solver abort. Below n = 12 nothing grew measurably (the continuation job ran all eight n to its time limit (t ≈ 9470–9670) with no solver abort; n = 1, 2, 3, 5 and 8 show no measurable growth by t ≈ 9671 (under 6 decades above their minimum energy)C-243). The three highest n grew cleanly, all in the pedestal:
| n | γ√(μ₀ρ₀) and location |
|---|---|
| 12, 16, 20 | γ√(μ₀ρ₀) = 0.00218 (n = 12), 0.00192 (n = 16) and 0.00288 (n = 20), all with the flow perturbation peaked at ψ_N 0.925–0.975; fits over 2400–3400 points, half-window and magnetic/kinetic fits agreeing within 0.6%, and shifting the fit band by a decade changes γ by under 1e-4C-244 |
By the criterion the owner chose (γ > 0 with diamagnetic terms included), these three modes are unstable. They are weak: about 15 times slower than case (a)’s pedestal modes, and far below the EPED-like threshold on the ratio of γ to the ion diamagnetic frequency (γ/ωᵢ = 0.054 (n = 12), 0.036 (n = 16), 0.043 (n = 20), against the EPED-like threshold 0.25; ωᵢ is an estimate from the profiles, not a JOREK outputC-245). γ is not monotone in n.
One point on process. The window rule was fixed in the plan before any data from this job were read. While the job was still running, we looked once at interim output with the old case (a) rule. The code for the new rule was then written by a session that had not seen the data.
What is not yet checked
These growth rates are not converged. Decision 7 asks that halving the time step and doubling the grid each leave γ within the agreed tolerance. The time-step check is running now: each of the three modes restarts twice from the same saved slice, at Δt = 1 and Δt = 0.5. The slice is the first one inside its fit window. The same job also prepares the doubled grid’s axisymmetric state.
The grid check is the hard part. These modes take thousands of time units to rise from round-off, and JOREK in this version cannot start the fine grid from the coarse mode. A from-scratch check on the doubled grid would take many more jobs than remain (repeating the slow emergence (4 decades only by t ≈ 4700–6900) plus a fit window on 160 × 256 means about 7000–9000 steps per mode, about 60–190 h at an estimated 30–75 s per step, so 10–32 chained jobs for the three modes run togetherC-246). The recommendation to the owner (OQ-43) is to measure the grid sensitivity on case (a)’s faster pedestal modes instead, and to report case (b) as converged in time step only.
Technical details → JOREK. Decision → OQ-43.
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 › case b job2
Decisions → OQ-41 · OQ-43