Electron temperature resonances of a plasma column described to full first order in the temperature

An inhomogeneous plasma column surrounded by a glass wall is described through full first order in temperatures T_e and T_i using a complete electromagnetic treatment. We study the response of this system to a purely TE wave with K perpendicular to the axis. Comparison with existing theories and experimental results is made in the electron-wave domain (ions play no role) with zero steady magnetic field, i.e. in the case of temperature (Tonks-Dattner) resonances. Perhaps surprising at first sight, there is poor agreement with experiment at low density, the classic T^½_e theory (scalar perturbed pressure approximation) giving far better results. Simple arguments concerning the different levels of approximation in the description of the longitudinal k² enable us to distinguish the crucial difference existing between a scalar pressure and a complete T description and to understand this result. We generalize these findings, demoastrating that a description is always more realistic than a one in the range ω_pe<ω.