1D Core Transport Solvers
One-dimensional transport codes evolve plasma density, temperature, and current profiles along the minor radius using flux-surface-averaged conservation laws.
The transport ansatz
Because a tokamak plasma equilibrates rapidly along each flux surface, the slow evolution of density and temperature can be treated as one-dimensional: functions of a flux-surface label rho only. A 1D transport code evolves particle, energy, and current continuity equations averaged over flux surfaces, with the equilibrium providing the geometric metric coefficients.
The equations
For each species the code solves a diffusion-convection equation of the form d/dt (n) = (1/V') d/drho ( V' (D dn/drho - V n) ) + S, where D is a diffusivity, V a pinch velocity, and S the sources (fueling, ionization). Temperature follows an analogous energy equation with heat conductivity chi and heating/loss terms. The current profile evolves through a magnetic diffusion equation for the poloidal flux.
Transport coefficients
The diffusivities and conductivities are the physics that must be supplied. They can come from empirical scalings, from theory-based models, or from reduced models of turbulence. The transport solver itself is agnostic; its accuracy is set by the fidelity of the transport model plugged into it.
Inputs and outputs
- Inputs: equilibrium geometry, heating and fueling sources, boundary conditions at the plasma edge, and a transport model
- Outputs: time-evolving profiles of density, ion and electron temperature, rotation, and current; derived quantities such as fusion power and confinement time
Interpretive vs predictive modes
Run in interpretive mode, a transport code takes measured profiles and infers the transport coefficients that reproduce them. Run in predictive mode, it takes a transport model and predicts the profiles. Both modes are essential: interpretive analysis validates the models that predictive design work relies on.
For the Hyperion breeder, predictive 1D transport runs estimate the profiles and fusion output consistent with the design heating and confinement assumptions.