A helicon thruster consists of a cylindrical helicon source, where the plasma is generated and heated, and a magnetic nozzle, where the plasma beam is accelerated supersonically. Two dimensional models of the plasma flow inside the source and in the external magnetic nozzle are derived, for a known amount of absorbed power from rf waves. 2D plasma structure and response inside the source are described, comprising the processes of neutral depletion, losses to chamber walls, and backward and forward flows. Conditions for high propellant utilization and high current efficiency are determined. The matching with the magnetic nozzle model yields the overall characterization of helicon thruster performances in terms of power, thrust and efficiency.