The vertical displacement of a tokamak plasma is modelled during itsnon-linear phase by considering a free-moving current-carrying rod inductivelycoupled to a set of fixed conducting wires or a cylindrical conducting shell.The models capture the leading term in a Taylor expansion of the Green'sfunction for the interaction between the plasma column and the surroundingvacuum vessel. The plasma shape and profiles are assumed not to vary during thevertical drifting phase such that the plasma column behaves as a rigid body. Inthe limit of perfectly conducting structures, the plasma is prevented to comein contact with the wall due to steep effective potential barriers created bythe induced Eddy currents. Consequently, the plasma wire oscillates atAlfv\'enic frequencies about a given force-free position. In addition todamping oscillations, resistivity in the wall allows for the equilibrium pointto drift towards the vessel on the slow timescale of flux penetration. Theinitial exponential motion of the plasma, understood as a resistive verticalinstability, is succeeded by a non-linear "sinking" behaviour, that isanalytically shown to be algebraic and decelerating. The acceleration of theplasma column often observed in experiments is thus conjectured to originatefrom an early sharing of toroidal current between the core, the halo plasma andthe wall or from the thermal quench dynamics precipitating loss of plasmacurrent.
展开▼
