The plasma column's tendency to bend or twist when the current it carries grows too large relative to the confining field.
A kink instability is a macroscopic MHD displacement in which the entire plasma column (or a large fraction of it) shifts, bends, or helically distorts. The instability is driven by the free energy stored in the plasma current: the poloidal magnetic field generated by the current can overwhelm the stabilizing tension of the toroidal field, causing the column to "kink" outward or inward like a pressurized garden hose.1
Kinks are classified by their toroidal mode number n and poloidal mode number m. The most dangerous is the external kink (n = 1, m = 1), which displaces the plasma as a whole and can terminate a discharge in milliseconds. Internal kinks (resonant inside the plasma at a rational surface where q = m/n) produce sawtooth oscillations and related core relaxation events.2
The foundational stability criterion states that the edge safety factor qa must exceed unity—practically, qa > 2 for a circular cross-section tokamak—to avoid the n = 1 external kink. This Kruskal–Shafranov limit sets an upper bound on the total plasma current for a given toroidal field and geometry, and is one of the oldest and most consequential results in fusion stability theory.1
When the safety factor drops below unity on axis (q0 < 1), the m = 1/n = 1 internal kink goes unstable and drives the sawtooth crash—a periodic relaxation that flattens the core temperature and density profiles. While sawteeth can be beneficial (flushing impurities from the core), large sawteeth can seed neoclassical tearing modes (NTMs) that degrade confinement.3
External kinks are controlled by limiting the plasma current (staying well above qa = 2), by plasma shaping (elongation and triangularity raise the current limit), and by close-fitting conducting structures. Internal kinks and their sawtooth consequences can be managed with ion-cyclotron resonance heating (ICRH) to create fast-ion populations that modify the internal kink drive, or with localized electron-cyclotron current drive (ECCD) to keep q0 just above unity.4