Kinetic theory of tearing instabilities

Abstract

The transition of the tearing instability from the collisional to the collisionless regime is investigated kinetically using a Fokker–Planck collision operator to represent electron‐ion collisions. As a function of the collisionality of the plasma, the tearing instability falls into three regions, which are referred to as collisionless, semi‐collisional, and collisional. The width Δ of the singular layer around k⋅B₀=0 is limited by electron thermal motion along B₀ in the collisional and semi‐collisional regimes and is typically smaller than ρ_i, the ion Larmor radius. Previously accepted theories, which are based on the assumption Δ≫ρ_i, are found to be valid only in the collisional regime. The effects of density and temperature gradients on the instabilities are also studied. The tearing instability is only driven by the temperature gradient in the collisional and semi‐collisional regimes. Numerical calculations indicate that the semi‐collisional tearing instability is particularly relevant to present day high temperature tokamak discharges.