Tearing Mode and Island Modeling
Specialized codes track magnetic islands from onset to saturation, predicting when tearing modes threaten confinement and how to suppress them.
Islands at rational surfaces
Where the safety factor takes a rational value, field lines close on themselves and are vulnerable to reconnection. A tearing mode reorganizes the field there into a chain of magnetic islands. Inside an island, heat short-circuits across what were nested flux surfaces, flattening the profile and lowering confinement.
The modified Rutherford equation
Island evolution is often modeled with the modified Rutherford equation, an ordinary differential equation for the island width. It balances the classical tearing drive against stabilizing and destabilizing terms: bootstrap-current loss, curvature, and any externally driven current placed inside the island. Codes integrate this equation to predict whether an island grows or heals.
Inputs and outputs
- Inputs: equilibrium and profiles, resistivity, bootstrap fraction, and any current-drive deposition
- Outputs: island width over time, saturation width, onset thresholds, and stabilization requirements
Active stabilization
Neoclassical tearing modes can be suppressed by driving localized current at the island with electron-cyclotron waves, replacing the missing bootstrap current. Island codes coupled to ray-tracing and current-drive models predict how much power, and how precise an aiming, is needed, informing the design of real-time stabilization systems.
Why it matters for design
Because neoclassical tearing modes appear at high pressure, they can cap performance below the ideal limit. Modeling them defines a practical operating boundary and motivates the current-drive capability a design must carry to stay stable.
For the Hyperion breeder, island analysis is part of confirming that the high-performance design point can be held without confinement-destroying modes, given realistic stabilization tools.