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 α between the wall and the magnetic field B is oblique. Here, we consider the fusion-relevant case of a shallow-angle, α << 1, electron-repelling sheath, with the electron density given by a Boltzmann distribution, valid for α/$\sqrt {τ + 1}$ >> $\sqrt {m_e/m_i}$, where m e is the electron mass, m i is the ion mass, τ = T i /ZT e , T e is the electron temperature, T 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 ρ s = p m i (ZT e + T i )/ZeB, where e is the proton charge and B = |B| is the magnitude of the magnetic field. We study the dependence on τ 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 τ. The kinetic model is shown to be asymptotically equivalent to Chodura’s fluid model at small ion temperature, τ << 1, for | ln α| > 3| ln τ| >> 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, τ>> 1, relevant because Ti is measured to be a few times larger than Te 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 $\sqrt α$ or 1/ $\sqrt τ$ , depending on which is largest.