Energy and particle balance on the ITER benchmark
A transport simulation should conserve energy and particles: heating that goes in must either stay in the plasma or leave through the edge, and the same holds for particles. Milestone M1 asks us to show this for the benchmark we are reproducing, the ITER hybrid scenario run in TORAX, the open-source transport code we build on (see the Primer).
Method
TORAX divides the plasma radius into thin shells and, at each time step, solves one equation per shell: the change in stored energy equals heat flowing in, minus heat flowing out, plus local heating. Summed over all shells, the fluxes between neighbouring shells cancel, leaving one balance for the whole plasma: change in stored energy equals heating minus the flux through the edge. We computed this balance after every step from TORAX’s own coefficients and checked that it closes. We did not write our own physics for this, because a second implementation of TORAX’s equations would test our implementation, not TORAX’s.
We computed one term independently: the heat flux through the edge, from the temperature gradient at the boundary. It matches the balance’s edge term to 10-10C-039.
Results
With the solver settings the benchmark uses, the balance closes: energy to better than 10-6C-035 per step and particles to better than 10-10C-036. The shorter flat-top benchmark uses a cheaper solver setting that stops iterating early, and there about about 0.8%C-037 of each step’s energy is unaccounted for. The residual decreases with more iterations, so it comes from the early stop, not from the equations.
The largest term is on the source side. TORAX holds the temperature at the top of the edge region (the “pedestal”) at a prescribed value by adding a large artificial source there, which adds or removes whatever power is needed. In the 80-second ramp-up, most of the heating power goes into this source:
| where the heating power goes (ramp-up, every step after the first) | share of heating |
|---|---|
| removed by the pedestal source | 87–98%C-038 |
| conducted out through the edge | 1.5–10%C-041 |
| stored in the plasma | the small remainder |
Most of the heat that reaches the pedestal is removed by this numerical source, not transported across the edge. TORAX reports the power crossing the edge as heating minus the change in stored energy, which includes the pedestal source without listing it separately. This is how a prescribed pedestal works in TORAX, not a bug. It does mean that the “power crossing the edge” from this run, used for example to compare against the threshold for high-confinement mode, is not power that the transport model carried across the edge.
Where this stands: M1 in progress. Conservation now has tests on the benchmark; the tolerance for M1’s acceptance goes to the owner with the benchmark tolerance (OQ-5).
Technical details → Backends: energy and particle balance
Technical details → Backends › balance
Decisions → OQ-5