Tearing Mode Stability
The resistive instability that reconnects field lines into magnetic islands at rational surfaces.
Reconnection at rational surfaces
At a rational surface where q = m/n, a resistive perturbation can reconnect field lines and form a chain of magnetic islands. This tearing mode is slower than ideal instabilities but degrades confinement by flattening the pressure across the island and, if large enough, can trigger a disruption. Its linear drive is measured by the stability index Delta'.
Delta' = [ (dpsi/dr)_outer - (dpsi/dr)_inner ] / psi at the rational surfacePositive Delta' means the outer-region ideal solution wants an island: the mode is classically unstable. Negative Delta' means it is classically stable. Delta' is obtained by solving the Newcomb equation in the outer region and matching across the resistive layer.
Classical versus neoclassical
- Classical tearing modes are driven by the current-gradient term Delta'
- Neoclassical tearing modes are driven by the loss of bootstrap current inside the island
- Neoclassical modes are metastable: they need a seed island to grow but can then persist
How it is analyzed
Linear stability computes Delta' from the equilibrium; nonlinear island evolution uses the Rutherford equation to predict growth and saturated width. Full resistive-MHD simulation captures the coupled dynamics, including how sawteeth or ELMs can seed islands.
Control and design
Tearing modes, especially neoclassical ones, cap the achievable pressure in long pulses. They are suppressed by driving current at the island (electron-cyclotron current drive) to replace the missing bootstrap current. Predicting and controlling tearing stability, using Delta' and the Rutherford equation, is a standard part of qualifying high-beta scenarios for devices such as the Hyperion breeder.