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The vertical motion of a tokamak plasma is analytically modelled during itsnon-linear phase by a free-moving current-carrying rod inductively coupled to aset of fixed conducting wires or a cylindrical conducting shell. The solutionscapture the leading term in a Taylor expansion of the Green's function for theinteraction between the plasma column and the surrounding vacuum vessel. Theplasma shape and profiles are assumed not to vary during the vertical driftingphase such that the plasma column behaves as a rigid body. In the limit ofperfectly conducting structures, the plasma is prevented to come in contactwith the wall due to steep effective potential barriers created by the inducedEddy currents. Resistivity in the wall allows the equilibrium point to drifttowards the vessel on the slow timescale of flux penetration. The initialexponential motion of the plasma, understood as a resistive verticalinstability, is succeeded by a non-linear "sinking" behaviour shown to bealgebraic and decelerating. The acceleration of the plasma column oftenobserved in experiments is thus concluded to originate from an early sharing oftoroidal current between the core, the halo plasma and the wall or from thethermal quench dynamics precipitating loss of plasma current.

Algebraic motion of vertically displacing plasmas