Transport Solver Frameworks
Transport solvers evolve the flux-surface-averaged density, temperature, and current profiles by integrating conservation equations with fluxes supplied by physics models.
The transport problem
Once an equilibrium is known, the plasma profiles evolve on the slow transport timescale. A transport solver integrates one-dimensional (flux-surface-averaged) conservation equations for particle density, electron and ion energy, momentum, and poloidal flux. Each equation has the form of a diffusion-convection PDE with sources from heating and fueling and sinks from radiation and losses.
The transport coefficients, the diffusivity and pinch, are not fundamental constants. They come from turbulence and neoclassical models, ranging from analytic formulas to reduced quasilinear models to full gyrokinetic fluxes.
Stiff transport and the closure problem
Turbulent transport is stiff: fluxes rise steeply once a critical gradient is exceeded, pinning profiles near marginal stability. This makes the equations numerically challenging and demands implicit time integration. The choice of flux model is the dominant source of prediction uncertainty, more than the numerics.
Coupling to sources
Heating and current-drive deposition, computed by ray-tracing and Fokker-Planck modules, enter as source terms. Neutral fueling from neutral transport supplies the particle source. The solver therefore sits at the center of an integrated framework, calling many modules per timestep.
Design use
Transport solvers predict the profiles the Hyperion breeder would run at for a given heating and fueling recipe, in simulation. Because the machine is not built, these predictions carry explicit uncertainty and are cross-checked against multiple turbulence models rather than presented as guaranteed performance.
- Evolves 1D flux-averaged profiles
- Transport coefficients come from turbulence models
- Requires implicit solvers due to stiffness
- Central hub of integrated modeling