The systematic particle drift caused by spatial gradients in magnetic field strength — the fundamental reason a simple toroidal field cannot confine a plasma
When a charged particle gyrates in a magnetic field whose strength varies across space, the radius of its circular orbit (the Larmor radius) changes within each gyration cycle: the orbit is tighter on the strong-field side and wider on the weak-field side. This asymmetry produces a net drift perpendicular to both the magnetic field B and its gradient ∇B. The drift velocity is given by v∇B = (mv⊥²/2qB³)(B × ∇B), where m is the particle mass, v⊥ is the velocity component perpendicular to the field, and q is the particle charge.[1]
Crucially, the drift direction depends on the sign of the charge: ions and electrons drift in opposite directions. In a torus, where the toroidal field falls off as 1/R (with R the major radius), the resulting grad-B drift is vertical — ions drift up and electrons drift down (or vice versa, depending on the field direction).
The vertical charge separation driven by grad-B drift creates a vertical electric field inside the plasma. This electric field, crossed with the toroidal magnetic field, produces an outward E × B drift that is the same for both species and pushes the entire plasma column toward the outboard wall. Left uncorrected, this sequence would expel the plasma in microseconds.[2]
In a torus the magnetic field lines are curved, and particles following those curves experience an additional centrifugal drift — the curvature drift — that has the same direction and comparable magnitude as the grad-B drift. In practice the two drifts are always present together and are often combined into a single expression for the total VB-plus-curvature drift. Both are proportional to the particle energy, so hotter plasmas drift faster and are harder to confine in simple geometries.[3]
The primary mitigation in a tokamak is rotational transform: the helical twist of field lines ensures that each field line spends equal time on the top and bottom of the torus, averaging out the vertical drift over a magnetic surface. Stellarators achieve the same cancellation through external coil geometry rather than plasma current. In both cases the design challenge is to make the drift orbit closures tight enough that particle losses remain acceptably small for reactor-relevant confinement times.[4]