This research work is part of a PhD project aiming to design a new helicon plasma thruster for cargo space missions, within a collaboration between the School of Aerospace Engineering of La Sapienza University and the ENEA Frascati research center. A 0-D global design model of the thruster is first established to identify the main operational conditions of the thruster, starting from a targeted performance in terms of specific impulse and thrust. These operational conditions are tested with dedicated simulations on the electromagnetic plasma-wave interaction within the ionization chamber, and on the electrostatic plasma acceleration within the magnetic nozzle. The former are carried out with a finite element electromagnetic code and confirm the technical feasibility of the identified operational RF power with a predefined chamber geometry. The latter are obtained with an electrostatic particle-in-cell code, which allows to estimate more precisely the achieved thruster performance. A sub-optimal thruster with an absorbed plasma power of around 1 kW, a thrust of around 10 mN and a specific impulse higher than 1000 s is successfully simulated. The established simulation framework will serve as the basis for the next optimization of the thruster geometry and operational conditions, with the ultimate goal of building and testing a new helicon thruster prototype.