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A new drift kinetic theory for the plasma response to the neoclassical tearing mode (NTM) magnetic perturbation is presented. Small magnetic islands of width,  w ≪ a ( a  is the tokamak minor radius) are assumed, retaining the limit  w  ∼  ρ bi ( ρ bi is the ion banana orbit width) to include finite orbit width effects. When collisions are small, the ions/electrons follow streamlines in phase space; for passing particles, these lie in surfaces that reproduce the magnetic island structure but have a radial shift by an amount, proportional to  ρ ϑ i / e , where  ρ ϑ i / e is the ion/electron poloidal Larmor radius. This shift is associated with the curvature and ∇ B  drifts and is found to be in opposite directions for  V ∥ ≶ 0 , where  V ∥ is the component of velocity parallel to the magnetic field. The particle distribution function is then found to be flattened across these shifted or  drift  islands rather than the magnetic island. This results in the pressure gradient being sustained across the magnetic island for  w ∼ ρ ϑ i and hence reduces the neoclassical drive for NTMs when  w  is small. This provides a physics basis for the NTM threshold, which is quantified. In Imada  et al  (2019  Nucl. Fusion  59  046016, and references therein), a 4D drift kinetic non-linear code has been applied to describe these modes. In the present paper, the drift island formalism is employed. Valid at low collisionality, it allows a dimensionality reduction to a 3D problem, simplifying the numerical task and efficiently resolving the collisional boundary layer across the trapped-passing boundary. An improved model is adopted for the magnetic drift frequency. This decreases the NTM threshold, compared to the results shown in Imada  et al  (2019  Nucl. Fusion  59  046016, and references therein), making it in quantitative agreement with experimental observations, with  w c = 0.45 ρ ϑ i , where  w c is the threshold magnetic island half-width, or 2.85 ρ bi for the full threshold island width, predicted for our equilibrium.

Drift kinetic theory of neoclassical tearing modes in a low collisionality tokamak plasma: magnetic island threshold physics