Fokker-Planck Current-Drive Solvers
Fokker-Planck solvers evolve the plasma distribution under collisions and wave-driven diffusion to predict non-inductive current drive and heating.
Distortion of the distribution
Waves and beams push the plasma away from a Maxwellian, and the resulting distortion is what drives non-inductive current and determines absorption efficiency. A Fokker-Planck solver evolves the distribution function in velocity space under two competing processes: collisional relaxation toward Maxwellian, described by the Fokker-Planck collision operator, and quasilinear diffusion driven by the applied waves.
The steady-state balance between drive and collisions gives the distorted distribution, from which the driven current, the absorbed power, and the current-drive efficiency are computed.
Bounce averaging
In a tokamak, trapped and passing particles behave differently, so the relevant equation is often bounce-averaged over the orbit. This reduces the dimensionality and captures the trapped-particle effects that reduce current-drive efficiency near the edge.
Coupling to wave codes
The quasilinear diffusion coefficient comes from the wave fields, computed by ray-tracing or full-wave codes. Because absorption depends on the distribution and the distribution depends on absorption, the wave and Fokker-Planck solvers are iterated to a self-consistent solution.
Design relevance
For the Hyperion breeder, non-inductive current drive helps sustain the plasma current and shape the profile. Fokker-Planck modeling predicts how much current a given wave power drives and where, feeding the current-balance calculation in the equilibrium. These are simulation studies ahead of construction.
- Evolves the distribution in velocity space
- Balances collisions against wave-driven diffusion
- Predicts driven current and CD efficiency
- Iterated self-consistently with wave codes