The magnetic presheath is a boundary layer occurring when magnetized plasma is in contact with a wall and the angle
$\unicode[STIX]{x1D6FC}$
between the wall and the magnetic field
$\boldsymbol{B}$
is oblique. Here, we consider the fusion-relevant case of a shallow-angle,
$\unicode[STIX]{x1D6FC}\ll 1$
, electron-repelling sheath, with the electron density given by a Boltzmann distribution, valid for
$\unicode[STIX]{x1D6FC}/\sqrt{\unicode[STIX]{x1D70F}+1}\gg \sqrt{m_{\text{e}}/m_{\text{i}}}$
, where
$m_{\text{e}}$
is the electron mass,
$m_{\text{i}}$
is the ion mass,
$\unicode[STIX]{x1D70F}=T_{\text{i}}/ZT_{\text{e}}$
,
$T_{\text{e}}$
is the electron temperature,
$T_{\text{i}}$
is the ion temperature and
$Z$
is the ionic charge state. The thickness of the magnetic presheath is of the order of a few ion sound Larmor radii
$\unicode[STIX]{x1D70C}_{\text{s}}=\sqrt{m_{\text{i}}(ZT_{\text{e}}+T_{\text{i}})}/ZeB$
, where e is the proton charge and
$B=|\boldsymbol{B}|$
is the magnitude of the magnetic field. We study the dependence on
$\unicode[STIX]{x1D70F}$
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
$\unicode[STIX]{x1D70F}$
. The kinetic model is shown to be asymptotically equivalent to Chodura’s fluid model at small ion temperature,
$\unicode[STIX]{x1D70F}\ll 1$
, for
$|\text{ln}\,\unicode[STIX]{x1D6FC}|>3|\text{ln}\,\unicode[STIX]{x1D70F}|\gg 1$
. 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,
$\unicode[STIX]{x1D70F}\gg 1$
, 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
$\sqrt{\unicode[STIX]{x1D6FC}}$
or
$1/\sqrt{\unicode[STIX]{x1D70F}}$
, depending on which is largest.
The Effect of Ionization and Recombination on the Resistivity of a Partially Ionized Plasma in a Magnetic Field
