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The magnetic presheath is a boundary layer occurring when magnetized plasmais in contact with a wall and the angle $\alpha$ between the wall and themagnetic field $\vec{B}$ is oblique. Here, we consider the fusion-relevant caseof a shallow-angle, $\alpha \ll 1$, electron-repelling sheath, with theelectron density given by a Boltzmann distribution, valid for $\alpha /\sqrt{\tau+1} \gg \sqrt{m_{\text{e}}/m_{\text{i}}}$, where $m_{\text{e}}$ isthe electron mass, $m_{\text{i}}$ is the ion mass, $\tau =T_{\text{i}}/ZT_{\text{e}}$, $T_{\text{e}}$ is the electron temperature,$T_{\text{i}}$ is the ion temperature, and $Z$ is the ionic charge state. Thethickness of the magnetic presheath is of the order of a few ion sound Larmorradii $\rho_{\text{s}} = \sqrt{m_{\text{i}} \left(ZT_{\text{e}} + T_{\text{i}}\right) } / ZeB$, where $e$ is the proton charge and $B = |\vec{B}|$ is themagnitude of the magnetic field. We study the dependence on $\tau $ of theelectrostatic potential and ion distribution function in the magnetic presheathby using a set of prescribed ion distribution functions at the magneticpresheath entrance, parameterized by $\tau$. The kinetic model is shown to beasymptotically equivalent to Chodura's fluid model at small ion temperature,$\tau \ll 1$, for $|\ln \alpha| > 3|\ln \tau | \gg 1$. In this limit, despitethe fact that fluid equations give a reasonable approximation to the potential,ion gyro-orbits acquire a spatial extent that occupies a large portion of themagnetic presheath. At large ion temperature, $\tau \gg 1$, relevant because$T_{\text{i}}$ is measured to be a few times larger than $T_{\text{e}}$ neardivertor targets of fusion devices, ions reach the Debye sheath entrance (andsubsequently the wall) at a shallow angle whose size is given by$\sqrt{\alpha}$ or $1/\sqrt{\tau}$, depending on which is largest.

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