Nonlinear MHD Codes
Nonlinear MHD codes evolve large-amplitude instabilities in time, following islands, sawteeth, ELMs, and disruptions past the linear regime.
Past the linear limit
Linear stability codes tell you whether a mode grows and how fast, but not what happens once it reaches finite amplitude. Nonlinear MHD codes integrate the full MHD equations in time, following instabilities into saturation, island formation, and the violent relaxations that limit performance: sawtooth crashes, edge-localized modes (ELMs), and disruptions.
These are initial-value simulations rather than eigenvalue problems. They start from an equilibrium with a seed perturbation and march the coupled field, momentum, and pressure equations forward, resolving both the fast Alfven and slow resistive timescales, which makes them numerically demanding.
Extended physics
Purely resistive MHD is often insufficient. Realistic nonlinear simulation adds two-fluid effects, parallel thermal conduction along field lines that is many orders of magnitude faster than perpendicular, and sometimes kinetic corrections, the domain of extended MHD and kinetic-MHD models.
Numerical methods
Codes use finite elements, finite differences, or spectral methods, almost always with implicit or semi-implicit time stepping to step over the fastest waves. The enormous anisotropy between parallel and perpendicular conduction demands field-aligned discretization or high-order elements to avoid numerical pollution.
Design relevance
For the Hyperion breeder, nonlinear MHD estimates the amplitude and consequences of instabilities that survive linear design margins, for example how large a tearing island grows and how a sawtooth redistributes the core. These simulations inform control and mitigation design ahead of construction.
- Initial-value, time-domain simulation
- Follows islands, sawteeth, ELMs, disruptions
- Often needs two-fluid and extended physics
- Implicit stepping over fast waves