The outward displacement of the plasma magnetic axis from the geometric center of the vacuum vessel — a direct consequence of finite plasma pressure in toroidal geometry.
In a tokamak or any toroidal confinement device, the magnetic axis — the innermost closed flux surface, which degenerates to a single field line — does not coincide with the geometric center of the plasma cross-section. It is displaced outward (toward the low-field side) by a distance called the Shafranov shift, denoted Δ. This shift arises because the outward-pointing "hoop force" and the pressure-gradient-driven "tire-tube force" push the plasma column toward larger major radius, and the external vertical field that opposes this displacement cannot eliminate it entirely within the plasma interior.[1]
The Shafranov shift has two primary drivers:
1. Finite pressure (β). Higher plasma pressure inflates the flux surfaces on the outboard side more than the inboard side, pushing the magnetic axis outward. The shift scales roughly as Δ ∼ βp a² / R0, where βp is the poloidal beta, a is the minor radius, and R0 is the major radius.[2]
2. Internal inductance (li). A peaked current profile concentrates magnetic energy near the core and adds to the outward displacement. Broad current profiles reduce the shift, while peaked profiles increase it.
A large Shafranov shift compresses the flux surfaces on the outboard side and stretches them on the inboard side. This has several consequences:
Stability limit. When the shift becomes comparable to the minor radius (Δ ∼ a), the flux surfaces near the magnetic axis become highly compressed, local magnetic shear is reduced, and the plasma approaches the ideal ballooning stability boundary. The Shafranov shift therefore sets a practical upper limit on achievable β.[3]
Transport. The asymmetry introduced by the shift modifies trapped-particle orbits and affects neoclassical and turbulent transport. In some scenarios, a moderate Shafranov shift can stabilize certain microinstabilities by enhancing local magnetic shear on the outboard midplane.
Diagnostics and control. Real-time knowledge of the Shafranov shift is essential for accurate equilibrium reconstruction, position control, and heating-beam aiming in experiments.
The Shafranov shift is routinely determined by equilibrium reconstruction codes (EFIT and similar), constrained by external magnetic measurements, motional Stark effect (MSE) diagnostics for the internal field pitch, and soft X-ray tomography that images the flux-surface geometry directly.