Theory of anomalous tearing mode growth and the major tokamak disruption

Abstract

An analytic theory of turbulence in reduced resistive magnetohydrodynamics is developed and applied to the major disruption in tokamaks. The renormalized equations for a long-wavelength tearing instability are derived. The theory predicts two principal nonlinear effects: an anomalous flux diffusivity due to turbulent fluid convection in Ohm’s law and a vorticity damping term due to turbulent magnetic stresses in the equation of motion. In the final phase of the disruption, when fine-scale fluid turbulence has been generated, detailed considerations show that anomalous diffusivity has the dominant effect at long wavelengths. For a low-m tearing mode, the solution of the renormalized equations during the turbulent phase yields a growth rate analogous to the classical case but increased by turbulent resistivity: γ∼(∑k′ k′2θ‖φk′‖2)3/8 ×(Δ′)1/2. This analytical prediction is in good accord with computational results.