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

Abstract

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 2.85ρ bi for the full threshold island width, predicted for our equilibrium.

Drift kinetic theory of the NTM magnetic islands in a finite beta general geometry tokamak plasma

“…Their balance determines the threshold island width that is found numerically to be a few ion banana widths for a chosen equilibrium scenario, qualitatively matching data from DIII-D, ASDEX-U and JT-60U. Although the threshold scaling with the inverse aspect ratio as ε 1/2 , recovered in [19], indicates a role for trapped particles, the theory shows that the threshold mechanism originates from the drift orbits associated with passing particles. Specifically, passing particles are shown to follow 'drift islands' which are of the same shape as the magnetic island, but shifted radially relative to it by a few ρ ϑi .…”

“…In [16][17][18][19] we have developed a new self-consistent drift kinetic theory and associated drift island formalism to describe how plasma responds to the NTM magnetic perturbation. To implement this, two numerical codes have been developed: 4D DK- [18] and 3D RDK-NTM [19] (the 3D version, developed in [19], averages the distribution function over streamlines to reduce the 4D version and is valid for small, ITER-relevant collisions). They both assume a low beta large aspect ratio tokamak and consider the limit of small islands, comparable to ρ bi , to retain the effects of finite orbit widths relevant for the NTM threshold island width.…”

“…They both assume a low beta large aspect ratio tokamak and consider the limit of small islands, comparable to ρ bi , to retain the effects of finite orbit widths relevant for the NTM threshold island width. [19] considers how the parallel current density varies as the magnetic island width approaches the ion poloidal Larmor radius. For large islands of half-width w ≫ ρ ϑi , no parallel current is supported inside the magnetic island, providing a strong drive for NTMs, in agreement with the conventional theory of large magnetic islands.…”

Localized compressional self-heating in magnetic islands

“…2017 a ; Dudkovskaia et al. 2021) have already been found to limit the flattening of the pressure profile expected (Fitzpatrick 1995) and observed (Snape et al. 2012) to happen in a magnetic island.…”

“…2021), the effect of finite Larmor radius effects (Dudkovskaia et al. 2021) and some instances of experimental observations of magnetic islands with non-flat pressure profile or localized heating (Choi et al. 2021).…”