  Charged particles gyrate around magnetic field lines, a property that is
exploited to confine plasma in magnetic confinement fusion devices. Typically,
the gyroradius is small compared to the system size and thus the gyromotion can
be averaged out. The resulting charged particle motion closely follows a
magnetic field line. At the edge of fusion devices, the magnetic field usually
impinges on a wall at a shallow angle. A boundary layer forms in which the
plasma density changes over a characteristic distance from the wall of the
order of the ion gyroradius, as ions are absorbed during their gyromotion. This
boundary layer is called magnetic presheath, and is typically collisionless and
quasineutral. Importantly, the electric field in this region distorts the ion
gyro-orbits, making them non-circular and thus affecting the ion density
profile. Solving the magnetic presheath amounts to obtaining the
self-consistent electric field for which the net charge density is zero.
  In this thesis, I assume a small magnetic field angle and small gradients
parallel to the wall to develop an asymptotic theory for the magnetic
presheath, which is used to obtain the ion density. The small, yet crucial,
contribution of the part of the orbit near the wall is included. To demonstrate
the theory for a case without any gradients parallel to the wall, I calculate
numerically the self-consistent electrostatic potential by assuming the
electron density to be a Boltzmann distribution. The model is used to study the
dependence of magnetic presheath characteristics on magnetic field angle and
ion temperature. The distribution function of ions that have traversed the
magnetic presheath is obtained, which is important to predict the amount of
sputtering and erosion at the wall of a fusion device.
