In Hall propulsion, the thrust is provided by the acceleration of ions in a plasma generated in a cross-field configuration. Standard thruster configurations have annular channels with an almost radial magnetic field at the channel exit. A potential difference is imposed in the axial direction and the intensity of the magnetic field is calibrated in order to hinder the electron motion, while leaving the ions non-magnetised. Magnetic field lines can be assumed, as a first approximation, as lines of constant electron temperature and of thermalized potential. In typical thruster configurations, the discharge occurs inside a ceramic channel and, due to plasma-wall interactions, the electron temperature is typically low, less than few tens of eV. Hence, the magnetic field lines can be effectively used to tailor the distribution of the electrostatic potential. However, the erosion of the ceramic walls caused by the ion bombardment represents the main limiting factor of the thruster lifetime and new thruster configurations are currently under development. For these configurations, classical first order models of the plasma dynamics fail to grasp the influence of the magnetic topology on the plasma flow. In the present paper, a novel approach to investigate the correlation between magnetic field topology and thruster performance is presented. Due to the anisotropy induced by the magnetic field, the gradients of the plasma properties are assumed to be mainly in the direction orthogonal to the local magnetic field, thus enabling a quasi-one-dimensional description in magnetic coordinates. Theoretical and experimental investigations performed on a 5 kW class Hall thruster with different magnetic field configurations are then presented and discussed.