Safety Factor and q-Profile Control
Controlling the winding of the magnetic field, which governs stability, through the current profile.
What the safety factor is
The safety factor q measures how many times a magnetic field line goes around the torus the long way for each time it goes around the short way. It varies across the plasma, forming the q profile. q governs stability: low-order rational values of q (like 1, 3/2, 2) are where tearing modes and kinks live, and the overall q level sets kink stability limits.
Why it must be controlled
The q profile determines which instabilities the plasma is prone to. Keeping the edge q above 2 avoids the most dangerous external kinks; controlling where rational surfaces sit manages tearing modes; shaping the central q enables advanced high-performance regimes. Much of stability control is, at root, control of the q profile.
Controlling q through current
q is set by the current profile - specifically, it is inversely related to how the current is distributed. So controlling q means controlling the current profile, using non-inductive current drive (neutral beams, radio-frequency waves) to add current at chosen radii, plus the bootstrap current the pressure profile generates. This is slow, because the current profile evolves on the resistive diffusion timescale.
The observability challenge
- External magnetics constrain q at the edge but weakly inside
- The motional Stark effect diagnostic measures internal field pitch, hence q
- Real-time equilibrium reconstruction with kinetic constraints estimates the profile
- Uncertainty in the internal q profile limits how tightly it can be controlled
A slow, foundational loop
Because the current profile changes slowly, q-profile control is a patient, model-based loop acting over seconds, often planned into the scenario from ramp-up. Get the q profile right early and stability follows; get it wrong and modes appear that faster loops must then fight. It is control of the plasma's foundations rather than its surface.