We propose and put to use a new approach to studying magnetised plasmas sustained by a high frequency (HF) field, particularly aiming at examining the case of discharges achieved at electron cyclotron resonance (ECR). This approach considers the methodology and the formalism of the modelling of cylindrical plasma columns produced by electromagnetic surface waves and extends them to the case where these discharges are submitted to an axial, static magnetic field B0. It leads to a variety of waves that are guided by the plasma column, these waves differing in particular by the spatial distribution of their electric field intensity. This distribution, as we show, plays on the power transfer from the HF field to the plasma and it influences the spatial density distribution of excited atoms. This led us to analyse, as a function of B0, the respective effects of the wave attenuation coefficient, wave polarization and HF power required to maintain an electron-ion pair in the discharge upon the plasma density and upon the electric field for the gas breakdown. In the latter case, we have introduced the novel concept of effective electric conductivity that appears to be more instructive here than that of the effective electric field. This first analysis has been conducted using a hydrodynamic and linearized description for the plasma assumed to be cold and collisional and not within the kinetic context as required by a complete description of the ECR phenomenon. Nevertheless, the results obtained permit one to identify better the most efficient operating conditions in terms of HF power transfer to the plasma at ECR. Such a wealth of results proves the potential and the interest of this new approach that should now be completed by using a kinetic theory.