Dependence on ion temperature of shallow-angle magnetic presheaths with adiabatic electrons

The magnetic presheath is a boundary layer occurring when magnetized plasma is in contact with a wall and the angle $\alpha$ between the wall and the magnetic field $\vec{B}$ is oblique. Here, we consider the fusion-relevant case of a shallow-angle, $\alpha \ll 1$, electron-repelling sheath, with the electron density given by a Boltzmann distribution, valid for $\alpha / \sqrt{\tau+1} \gg \sqrt{m_{$\text{e}$}/m_{$\text{i}$}}$,where$m_{$\text{e}$}$ is the electron mass, $m_{\text{i}}$ is the ion mass, $\tau = T_{$\text{i}$}/ZT_{$\text{e}$}$,$T_{$\text{e}$}$istheelectrontemperature,$T_{$\text{i}$}$istheiontemperature,and$Z$ is the ionic charge state. The thickness of the magnetic presheath is of the order of a few ion sound Larmor radii $\rho_{$\text{s}$} = \sqrt{m_{$\text{i}$} \left(ZT_{$\text{e}$} + T_{$\text{i}$} \right) } / ZeB$,where$e$istheprotonchargeand$B = |\vec{B}|$ is the magnitude of the magnetic field. We study the dependence on $\tau$ of the electrostatic potential and ion distribution function in the magnetic presheath by using a set of prescribed ion distribution functions at the magnetic presheath entrance, parameterized by $\tau$. The kinetic model is shown to be asymptotically equivalent to Chodura’s fluid model at small ion temperature, $\tau \ll 1$, for $\mathrm{\mid }\ln \alpha \mathrm{\mid }>3\mathrm{\mid }\ln \tau \mathrm{\mid }\gg 1$. In this limit, despite the fact that fluid equations give a reasonable approximation to the potential, ion gyro-orbits acquire a spatial extent that occupies a large portion of the magnetic presheath. At large ion temperature, $\tau \gg 1$, relevant because $T_{\text{i}}$ is measured to be a few times larger than $T_{\text{e}}$ near divertor targets of fusion devices, ions reach the Debye sheath entrance (and subsequently the wall) at a shallow angle whose size is given by $\sqrt{\alpha }$ or $1\mathrm{/}\sqrt{\tau }$, depending on which is largest.