The magnetic pitch at the plasma edge that governs the boundary between stable confinement and catastrophic disruption
The safety factor q quantifies how many times a magnetic field line winds around the torus the long way (toroidally) for each complete loop the short way (poloidally). The subscript "95" denotes that this value is evaluated at the flux surface enclosing 95% of the poloidal magnetic flux—effectively the plasma edge, just inside the last closed flux surface. q95 is one of the most operationally critical parameters in tokamak physics because it directly controls MHD stability, energy confinement, and the threshold for disruptions.1
The Kruskal–Shafranov criterion establishes that the edge safety factor must exceed unity to avoid the catastrophic m=1, n=1 external kink mode. In practice, tokamaks require q95 > 2 to remain reliably stable, and most experiments operate with q95 between 3 and 5. Below q95 ≈ 2, the plasma becomes increasingly susceptible to large-scale MHD modes—particularly the 2/1 tearing mode—that can lock to the wall and precipitate a disruption.2
For a circular cross-section tokamak, q at the edge is approximately:
qedge ≈ 2π a² BT / (μ0 R Ip)
where a is the minor radius, R the major radius, BT the toroidal field, and Ip the plasma current. Plasma shaping (elongation and triangularity) modifies this relationship, allowing higher current at the same q95. The q-profile across the plasma radius—not just its edge value—determines the spectrum of MHD modes that can be destabilized. Advanced scenarios with reversed magnetic shear maintain qmin > 1 in the core while keeping q95 ≥ 4, suppressing sawteeth and neoclassical tearing modes simultaneously.4
Accurate real-time reconstruction of q95 is essential for plasma control systems; most tokamaks derive it from external magnetic measurements and equilibrium reconstruction codes such as EFIT.