Sawtooth Oscillations and Reconnection
Periodic internal crashes that flatten the core when the central safety factor drops below one.
The sawtooth cycle
When the safety factor on axis falls below one, the internal m=1, n=1 kink becomes unstable and triggers a rapid reconnection event, the sawtooth crash. The core temperature rises slowly (ohmic and auxiliary heating peak the profile), then crashes suddenly as the reconnection flattens it, producing the characteristic sawtooth shape on central temperature traces.
Kadomtsev reconnection
Kadomtsev's model describes the crash as full magnetic reconnection: the q less than one region reconnects with surrounding flux, resetting q on axis to about one and mixing the core. The model predicts the crash time and the mixing radius, though real crashes are often faster than Kadomtsev predicts, motivating two-fluid and kinetic reconnection models.
Effects on the plasma
- Sawteeth flatten central temperature, density, and current, degrading peak performance
- They can be beneficial by flushing impurities and helium ash from the core
- They can seed neoclassical tearing modes at outer rational surfaces
Control
Because sawteeth can both help (ash removal) and harm (seeding tearing modes, limiting peak pressure), their period is often controlled deliberately using localized current drive or heating near the q=1 surface to tailor the crash frequency.
How it is modeled
Sawteeth are studied with nonlinear resistive and extended MHD simulation, which captures the internal kink growth and reconnection. The trigger is evaluated from the internal-kink stability of the equilibrium (via the Newcomb and energy-principle analysis) as the current profile evolves. Sawtooth behavior and control are part of scenario design for high-performance tokamaks, including the Hyperion breeder.