The cathodic arc thruster is a newly developed electric propulsion system. It provides a stream of ions with very high velocities from a solid conducting cathode. This high ion velocity in combination with a high ionization fraction makes the cathodic arc thruster attractive for spacecraft propulsion. In the past, a record-high specific impulse was measured for such thrusters. The thruster uses a voltage of −220 V at the cathode for several microseconds, producing plasma from the cathode material which then streams out of the thruster producing thrust. In this work, a two-dimensional axial-symmetric particle-in-cell code with Monte-Carlo collisions is used to simulate the plasma of a cathodic arc thruster with a simplified wall model for the initial triggering of the arc. The work concentrates on the plasma transport and aims not at a self-consistent description of the arc, including plasma-wall interaction, e.g., description of the erosion and surface heating. The interaction of the arc beam with the background plasma results in a plasma-beam instability. Due to this instability charge separation can be detected that leads to large electric fields. By this electric field, plasma particles are accelerated and contribute to the thrust.