Safety Factor and the q-Profile

The safety factor q counts toroidal turns per poloidal turn of a field line; its radial profile governs which instabilities the plasma is prone to.

A geometric stability number

The safety factor q measures how many times a magnetic field line wraps the long way around the torus for each time it wraps the short way. It is set by the ratio of toroidal field to plasma current and varies with radius, giving a q-profile from the magnetic axis to the edge. The name is apt: q is a first-order indicator of stability.

Low-order rational surfaces — where q equals simple fractions like 1, 3/2, or 2 — are where tearing modes and other instabilities like to grow. A well-designed q-profile keeps these surfaces where they do the least harm and keeps the edge q high enough to avoid disruptive limits. Hyperion's 9.66 MA current and toroidal field are chosen with the resulting q-profile in mind.

Coupling to current drive

Because q depends on the current distribution, and the current distribution depends on bootstrap and external drive, the q-profile is not a free input — it emerges from the self-consistent current profile. Shaping it to be stable while keeping a high bootstrap fraction is one of the central design-and-simulation balancing acts.

• q = toroidal turns per poloidal turn, varying with radius
• Rational-q surfaces host tearing and kink instabilities
• The q-profile follows from the self-consistent current profile

This page describes a design-and-simulation study, not a built machine. Construction begins Q2 2027; first-of-a-kind first tritium is targeted near 2030. No hardware net-gain is claimed before FOAK.