The CAMILA (co-axial magneto-isolated longitudinal anode) concept was introduced to improve the ionization efficiency in low-power Hall thrusters. With relatively large coaxial anode surfaces and longitudinal magnetic strength, the CAMILA represents a significant departure from conventional Hall thrusters. In order to investigate the physical processes inside the CAMILA thruster, a two-dimensional particle-in-cell simulation of the thruster channel is used. The discharge parameters are analysed in two magnetic configurations: simplified CAMILA with a conventional magnetic field and full CAMILA with strengthened longitudinal component of the magnetic field. The simulation is fully kinetic with electrons, ions and gas atoms (xenon) represented as particles. Electron-neutral interactions are included together with particle-boundary interactions such as recombination and secondary emission. In addition, dielectric boundaries float and the cathode is represented as a free-space boundary, emitting electrons to satisfy quasi-neutrality on its surface. The high anode efficiency, observed in experiments, can be explained by several mechanisms found in this work. In the simplified case (magnetic configuration similar to the experiments) a focusing potential is created near the anode-dielectric boundary that directs ions away from the walls. It is created due to a combination of anode placement, in parallel with the channel, penetration of the plasma inside the anode cavity and the shape of magnetic force lines. Simulated steady-state results show good agreement with experimental measurements. In the full CAMILA case we demonstrate that the ionization region is found in the anode cavity. The electric field inside the anode cavity is substantial and it is directed towards the anode cavity centreline. Electrons are heated sufficiently to reach a high degree of ionization inside the anode cavity while ion currents to the anode surfaces are reduced significantly.