Bounce-Averaged Fokker-Planck Solvers
Bounce averaging reduces the Fokker-Planck equation by averaging over fast orbital bounce motion, isolating the slow evolution of the distribution.
Separating fast and slow
A trapped particle bounces between magnetic mirror points many times before collisions or waves change its energy. This separation of timescales lets the bounce-averaged Fokker-Planck approach average the kinetic equation over one bounce orbit, removing the fast bounce coordinate and leaving an equation for the slowly evolving distribution in energy and pitch angle on each flux surface.
The reduction cuts dimensionality and cost while retaining the essential neoclassical distinction between trapped and passing particles, which is decisive for current-drive efficiency.
Trapped-particle effects
Trapped particles carry no net toroidal current and their fraction rises toward the edge and at low aspect ratio. Bounce averaging captures how trapping reduces the current a wave can drive and how the boundary in velocity space between trapped and passing populations shapes the driven-current profile.
Quasilinear operator
The wave drive enters as a bounce-averaged quasilinear diffusion operator built from the local wave fields sampled along the orbit. This ties the solver to ray-tracing or full-wave field solutions, with the two iterated to consistency.
Design relevance
For the low-aspect-ratio Hyperion breeder, where the trapped fraction is large, bounce-averaged Fokker-Planck modeling is the appropriate way to estimate current-drive efficiency honestly rather than overstating it with a passing-only picture. All results are simulation-stage before construction.
- Averages over fast bounce motion
- Reduces dimensionality of the kinetic equation
- Retains trapped-passing neoclassical physics
- Important at low aspect ratio