A class of neighbouring resistive equilibria for a cylindrical tokamak is constructed, characterized by the invariance of the helical flux χ and of the quantity K = ∫ dV. The equilibria of this class bifurcate for critical values of the distance of the current channel from the metallic wall, while a cold plasma remains in contact with the wall. The bifurcation only exists for q < m/n in the current channel and for a peaked current, the critical distance from the wall depending solely on the degree of peaking. Any helically deformed equilibrium with a sufficiently peaked and constricted current (so as to reach the bifurcation point) is unstable with respect to a dissipative purely radial compressible mode which conserves approximately K and χ. The building up of the mode implies a decrease of the current, accompanied by a negative axial voltage near the wall. The resistive mode evolves towards a non-linear phase in which the instability exhibits an explosive behaviour. This phase, however, can only be reached if the radial mode is triggered by a helical deformation with sufficiently large amplitude as can be provided by a non-linearly saturated tearing or kink mode.
Linear stability studies for a quasi-axisymmetric stellarator configuration including effects of parallel viscosity, plasma flow, and resistive walls
Pressure-driven relaxation instability in a current-free high-shear helical system