The Pfirsch-Schluter Current
The parallel return current that keeps a toroidal equilibrium divergence-free despite the outboard-inboard field asymmetry.
Why a return current is needed
In a torus the diamagnetic (pressure-driven) perpendicular current varies around the flux surface because the field is stronger inboard than outboard. Its divergence would build up charge unless a parallel current flows to cancel it. That parallel return current is the Pfirsch-Schluter current, required by current continuity div J = 0.
div J_perp + div J_parallel = 0 => J_PS ~ 2 (dp/dr) (q / B) cos(theta)It flows along field lines, largest on the outboard side, and closes the current loop that the varying diamagnetic current would otherwise leave open.
Consequence for transport
Driving this parallel current against resistivity dissipates energy and enhances cross-field transport by a factor of (1 + 2 q^2) over the classical rate, the Pfirsch-Schluter enhancement. This is the high-collisionality branch of neoclassical transport, important in denser, cooler plasmas such as the edge.
Where it fits
- High-collisionality (Pfirsch-Schluter) regime: transport enhanced by q^2
- It is the collisional-regime counterpart to the banana-regime bootstrap physics
- It also contributes to the equilibrium current balance
How it is computed
The Pfirsch-Schluter current follows from solving the parallel force balance on a flux surface with the divergence-free constraint, part of the neoclassical drift-kinetic calculation. Its resistive dissipation gives the enhanced transport coefficient used in transport codes for collisional regions.
Relevance
In the cooler, more collisional edge of a tokamak, Pfirsch-Schluter transport contributes to the heat and particle balance and to the equilibrium current pattern. It is one component of the full neoclassical picture evaluated for devices like the Hyperion breeder, alongside the banana-regime bootstrap current that dominates the hot core.