Characteristics of monotonic sheaths near a wall with grazing magnetic incidence

TL;DR

This paper develops a gyrokinetic model and a computational scheme to analyze the electrostatic potential and particle distributions in a magnetized plasma near a wall with grazing magnetic incidence, relevant for fusion devices.

Contribution

It introduces the GYRAZE code that simultaneously solves for the magnetic presheath and Debye sheath, extending previous models to include the ratio of electron gyroradius to Debye length.

Findings

Critical magnetic field angle increases with gamma.

Monotonic potential profiles exist only above a certain angle.

The critical angle remains smaller than typical divertor angles.

Abstract

We consider a magnetised plasma in contact with an absorbing planar wall, where the angle $\alpha$ between the magnetic field and the wall is small, $\alpha \ll 1$ (in radians) and the system is symmetric tangential to the wall. The finite ratio $\gamma$ of the characteristic electron gyroradius $\rho_{\rm e}$ to the Debye length $\lambda_{\rm D}$, $\gamma = \rho_{\rm e} / \lambda_{\rm D}$, is retained via a grazing-incidence ($\alpha \ll 1$) gyrokinetic treatment [1,2]. Building on a previously developed iterative scheme [2,3] to solve for the steady-state electrostatic potential in the quasineutral magnetic presheath of width $\sim \rho_{\rm S}$, we developed a scheme that simultaneously solves for both the presheath and the non-neutral Debye sheath of width $\sim \lambda_{\rm D}$ in the limit $\lambda_{\rm D} / \rho_{\rm S} \rightarrow 0$. The code, called GYRAZE, thus provides the energy-angle distribution of ions at the wall and the velocity distributions of electrons reflected by the wall for different values of wall potential. A monotonic electrostatic potential profile, assumed in this work, can only exist for magnetic field angles larger than a critical value [3]. While the critical angle is shown here to significantly increase with $\gamma$, it is still typically smaller than the magnetic field angle at divertor targets of a fusion device.