Non-Ambipolarity of Microturbulent Transport

TL;DR

The paper investigates how electrostatic microturbulence in magnetized plasmas with chaotic magnetic field lines alters quasi-neutrality and induces non-ambipolar transport. It shows that chaos-enabled electron transport manifests as an effective diffusion $D_{ef}=\frac{\Delta}{a_T}\frac{T_e}{eB}$ and a viscosity-like force $\vec{F}_v$, which can counterbalance non-ambipolar ion diffusion $f_{na}$, thereby influencing impurity confinement via the radial electric field. A shielding constraint tied to plasma beta $\beta$ and the perturbation scale sets when the turbulent magnetic perturbations remain effective, with key thresholds such as $\beta > \frac{\Delta}{a_T}\frac{1}{k_\theta a}$. The results provide criteria for when electron-dominated confinement occurs and how magnetic perturbations may be shielded, offering practical implications for impurity control in stellarators like W7-X.

Abstract

Even what is called electrostatic microturbulence produces a plasma-beta-dependent turbulent magnetic field $\tilde{B}$, which makes the magnetic field lines chaotic. Quasi-neutrality along the chaotic magnetic field lines requires a potential that obeys $\vec{B}\cdot \vec{\nabla} Φ= \vec{B}\cdot \vec{\nabla} p_e$, where $p_e$ is the electron pressure. This potential produces radial transport similar to that of diffusion coefficient $D_{ef}= (Δ/a_T)T_e/eB$. $Δ$ is the radial distance over which the potential $Φ$ is correlated by the electron motion along the chaotic magnetic field, and $|dT_e/dr| = T_e/a_T$. The chaos-produced electron transport gives an effective viscosity on the electron flow, which can counter balance a non-ambipolar part of the ion radial particle diffusion $f_{na}$. This non-ambipolarity would otherwise require a radial electric field that confines ions and hence impurities. The maximum $f_{na}$ that can be counterbalanced and the required plasma beta to avoid shielding the magnetic perturbations $\tilde{B}$ are calculated.

Figures (1)

• Figure 1: A magnetic field $\vec{B}(\vec{x},t)$ can be thought of as consisting of tubes of magnetic flux by placing a gridded surface across the field. Each tube is defined by the magnetic field lines that pass through the perimeters of the grid cells. When the field is chaotic, the perimeter of each cell becomes exponentially longer when the grid is replotted after each line on the perimeters is followed for a distance $\ell$. But, each cell contains exactly the same field lines and has precisely the same neighboring cells. When the magnetic field is evolving ideally with a chaotic velocity $\vec{u}_\bot$, a similar distortion of the grid occurs when the grid is replotted using the location of each line on the perimeters after a time $t$. The figure shows the distortion of a $5\times5$ array. This is Figure 1 of Boozer, Phys. Plasmas 32, 052106 (2025). The distorted grid is part of Figure 5 of Y.-M. Huang and A. Bhattacharjee, Phys. Plasmas 29, 122902 (2022), which was based on a chaotic evolution defined by A. H. Boozer and T. Elder, Phys. Plasmas 28, 062303 (2021). Boozer and Elder illustrated distortions of ideally evolving flux tubes up to a factor $\sim 10^7$.