Equilibrium-to-Transport Mapping
Mapping converts a two-dimensional equilibrium into the flux-surface geometry and metric coefficients that one-dimensional transport solvers require.
Bridging two representations
An equilibrium code produces a two-dimensional flux map psi(R,Z). A transport solver works in one dimension, evolving profiles as functions of a flux-surface label. Equilibrium-to-transport mapping is the bridge: it computes the flux-surface averages, volumes, areas, and geometric metric coefficients that convert the 2D equilibrium into the 1D quantities the transport equations need.
This step is unglamorous but essential. Errors in the geometric factors, the flux-surface volume derivative or the surface-averaged gradient metrics, translate directly into errors in the transport prediction.
Flux-surface averaging
Many transport quantities are surface averages of 2D fields. The mapping traces each flux surface, integrates along it, and produces averages such as the surface area, enclosed volume, and the metric factors that appear in the divergence of the transport fluxes. Accurate contour tracing on the equilibrium grid is the core numerical task.
Consistency in the loop
Because transport changes the pressure and current, which change the equilibrium, the mapping is redone each time the equilibrium is updated in the integrated loop. Keeping the mapping consistent with the current equilibrium is part of what makes the coupled solution self-consistent.
Design relevance
For the Hyperion breeder, whose shaping is strong, accurate mapping ensures the 1D transport predictions faithfully reflect the true 2D geometry rather than a distorted approximation. This underpins the credibility of simulated profiles and power ahead of construction.
- Converts 2D equilibrium to 1D transport geometry
- Computes flux-surface averages and metrics
- Contour tracing is the core numerical step
- Redone whenever the equilibrium updates