Optimising tokamak divertor geometry without disturbing the core plasma

MAST Upgrade at UKAEA’s Culham Campus – the device whose geometry is used in the working examples bundled with FORGE

(Image courtesy of UKAEA)

Getting to an advanced divertor configuration in a free-boundary equilibrium is one of the more stubborn problems in tokamak modelling. Free-boundary solvers pushed to achieve both the desired core plasma and a well-formed divertor often deliver one at the expense of the other. FORGE, an open-source Python tool developed by Chris Marsden at Tokamak Energy, addresses this by separating the two problems entirely. Engineers provide an equilibrium with the core plasma they want; FORGE then reshapes the divertor magnetic geometry independently, without touching it.

How FORGE optimises divertor magnetic geometry

The tool takes a GEQDSK equilibrium file and a machine description of the poloidal field coil set as inputs. It decomposes the total poloidal magnetic flux into plasma and machine contributions, fixes the plasma contribution, and varies only the coil currents. Perturbations are generated within the null space of a constraint matrix that encodes the core topology, so every candidate current set leaves the X-point position, separatrix shape, and magnetic axis exactly intact. The equilibrium solver does not need to run again at any point in the process.

The optimiser uses simulated annealing, evaluating candidate coil current configurations against a configurable cost function. Increasing parallel connection length is a primary objective – longer field line paths between the upstream plasma and the divertor target give the plasma more distance to radiate energy, promoting detachment and reducing heat flux to the target surfaces. Strike-point placement and coil current regularisation are additional weighted objectives, with users able to tune the balance between them for their device and design priorities.

X-Point Target configurations and availability

FORGE also supports optimisation toward X-Point Target divertor configurations, in which a secondary X-point is formed within the divertor region. The cost function includes a dedicated component that rewards reduction of the poloidal field inside a user-defined target region, penalises secondary X-points that are magnetically disconnected from the separatrix, and registers a discrete reward when a secondary X-point is present. The tool is device-agnostic; the bundled examples use MAST-U geometry, but FORGE applies to any tokamak for which a GEQDSK equilibrium and PF coil description exist.

The tool is publicly available on GitHub under an LGPL-3.0 licence, covering use by both public research institutions and private companies. It ships with a GUI built using Panel and Bokeh, full documentation on ReadTheDocs, seven progressive example scripts on MAST-U, and a Discord server for community support. Sebastien Shaw contributed foundational work during a FOSTER summer placement in 2025, and Nathan Welch provided guidance on the simulated annealing approach. FORGE builds on routines from FreeGS (Ben Dudson et al.) under the same licence. For modelling teams working across device design and integrated scenario development, it represents a practical route to bringing advanced divertor configurations into workflows that have until now required repeated iteration between the equilibrium solver and the rest of the chain.

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