The Ion-Temperature-Gradient Mode

A drift-type microinstability driven by steep ion temperature gradients, a leading cause of core heat loss.

The Drive

The ion-temperature-gradient (ITG) mode is destabilized when the ion temperature gradient exceeds a critical value, usually expressed through the ratio eta_i = (dln T_i/dr)/(dln n/dr). When eta_i is larger than a threshold near one, the mode grows. Physically, ions drifting in unfavorable field-line curvature carry heat in phase with the perturbation, so a temperature bump is convected to reinforce itself.

Slab and Toroidal Branches

There are two variants. The slab branch relies on parallel ion dynamics and Landau resonance and exists even without curvature. The toroidal branch, usually more virulent in a tokamak, is driven by the bad-curvature region on the outboard side where the grad-B and curvature drifts point down the pressure gradient. The toroidal branch sets the critical gradient for core ion transport.

Profile Stiffness

Because the ITG mode switches on sharply above its critical gradient and drives large transport, the ion temperature profile tends to be stiff: it resists steepening beyond the marginal gradient no matter how much power is added, since extra heat simply drives more turbulence. This stiffness is a dominant constraint on achievable core ion temperature and thus on fusion performance.

Relevance

ITG turbulence is often the largest single contributor to core ion heat loss, so its critical gradient effectively caps the ion temperature. Mitigation through sheared E-cross-B flow, reversed shear, or fast-ion dilution is a main lever in scenario design. For the Hyperion breeder concept, ITG stability sets part of the confinement estimate behind its design point in gyrokinetic modeling of a simulated device.