The Radial Electric Field and Flow Shear
How a sheared radial electric field suppresses turbulence and enables transport barriers.
The force balance for E_r
The radial electric field in a magnetized plasma is set by the radial force balance of a species, combining the pressure gradient and the flows:
E_r = (1/n q) dp/dr - v_theta B_phi + v_phi B_thetaIt has contributions from the diamagnetic (pressure-gradient) term and from the poloidal and toroidal rotation. E_r itself does not directly transport heat, but its radial variation, the shear, is decisive for turbulence.
Shear suppression of turbulence
A sheared E cross B flow stretches and tears apart turbulent eddies before they can grow, reducing their radial size and the transport they cause. When the E cross B shearing rate exceeds the turbulence growth rate, turbulence is quenched:
omega_shear = |d(E_r/B)/dr| > gamma_turbulence => suppressionTransport barriers
- The edge barrier (H-mode pedestal) forms when edge E_r shear suppresses turbulence
- Internal transport barriers form in the core by the same mechanism
- Barriers are self-reinforcing: steeper gradients raise the diamagnetic E_r, increasing shear
How it is computed
E_r is obtained from the radial force balance using neoclassical predictions for the flows (or measured rotation), then the shearing rate is compared against gyrokinetic growth rates to predict suppression. This coupling between E_r, flows, and turbulence is a key part of predictive transport modeling.
Why it matters
Access to and control of transport barriers, governed by radial-electric-field shear, is what makes high-confinement operation possible. Predicting barrier formation and strength is part of projecting the confinement of high-performance scenarios, including for the Hyperion breeder, where flow shear and negative-triangularity shaping both influence edge stability and turbulence.