Magnetic Shear

The radial variation of the field-line pitch, a primary stabilizing ingredient for pressure-driven and current-driven instabilities.

Definition

Magnetic shear measures how the pitch angle of the helical field lines changes across flux surfaces. It is usually written as the dimensionless quantity s = (r/q)(dq/dr), where q is the safety factor, r the minor radius coordinate, and dq/dr its gradient. Positive shear means q rises outward, so field lines on neighboring surfaces wind at progressively different rates.

Stabilizing Role

Shear stabilizes many instabilities by decorrelating perturbations on adjacent flux surfaces. A mode resonant at one rational surface cannot easily extend to neighbors whose field-line pitch differs, so the mode is localized and its drive limited. Shear enters the Mercier and ballooning stability criteria directly, where sufficient shear can hold off pressure-driven interchange and ballooning modes.

Reversed and Weak Shear

Where dq/dr is negative the shear is reversed, producing a q profile with an off-axis minimum. Reversed-shear configurations can form internal transport barriers because the reversal region suppresses turbulence, and they modify the location of rational surfaces. Weak or zero shear near the axis, by contrast, can leave low-order rational surfaces vulnerable to tearing and infernal modes.

Relevance

Tailoring the shear profile is a central lever in advanced tokamak scenarios, balancing turbulence suppression, MHD stability, and bootstrap-current alignment. For the Hyperion spherical-tokamak breeder concept, the safety-factor and shear profiles are design variables in the stability and transport analysis. Such profiles are computational targets for a machine still in simulation, with construction of first hardware targeted no earlier than 2027.