Sawtooth and Internal Mode Modeling
Sawtooth models describe the periodic core reconnection that flattens central profiles, a recurring instability that codes must predict and, ideally, control.
The sawtooth cycle
In the plasma core, where the safety factor drops below one, a repeating instability builds up and then suddenly reconnects, flattening the central temperature and density before the profiles rebuild. Diagnostics see the central temperature rise slowly and drop sharply, tracing a sawtooth pattern that names the phenomenon.
The internal kink
The sawtooth crash is triggered by an internal kink mode at the surface where the safety factor equals one. Modeling the trigger requires resistive and often two-fluid physics, since the reconnection that drives the crash depends on non-ideal effects. Predicting the crash time and the extent of the flattening is the modeling goal.
Why it matters
- Sawteeth flatten the core, capping central pressure and fusion rate
- Crashes can seed larger instabilities such as neoclassical tearing modes
- They also help flush impurities and helium ash from the core
- Their timing interacts with heating and current-drive deposition
Control
Sawteeth can be paced or suppressed by placing localized current drive or heating near the safety-factor-equals-one surface, changing the local magnetic shear. Models coupling the internal-kink trigger to current-drive deposition predict how to lengthen or shorten the cycle, which is used to avoid seeding worse modes.
Modeling approaches
Reduced models predict crash timing from a stability criterion at the one-surface, while nonlinear extended-MHD codes simulate the full reconnection. The reduced models are used inside transport simulations to represent the periodic flattening without resolving each crash in detail.
Sawtooth behavior is part of the core-stability picture that scenario modeling for any tokamak must account for.