Interpreting the behavior of a quarter-wave transmission line resonator in a magnetized plasma

The quarter wave resonator immersed in a strongly magnetized plasma displays two possible resonances occurring either below or above its resonance frequency in vacuum, f_o. This fact was demonstrated in our recent articles [G. S. Gogna and S. K. Karkari, Appl. Phys. Lett. 96, 151503 (2010); S. K. Karkari, G. S. Gogna, D. Boilson, M. M. Turner, and A. Simonin, Contrib. Plasma Phys. 50(9), 903 (2010)], where the experiments were carried out over a limited range of magnetic fields at a constant electron density, n_e. In this paper, we present the observation of dual resonances occurring over the frequency scan and find that n_e calculated by considering the lower resonance frequency is 25%–30% smaller than that calculated using the upper resonance frequency with respect to f_o. At a given magnetic field strength, the resonances tend to shift away from f_o as the background density is increased. The lower resonance tends to saturate when its value approaches electron cyclotron frequency, f_ce. Interpretation of these resonance conditions are revisited by examining the behavior of the resonance frequency response as a function of n_e. A qualitative discussion is presented which highlights the practical application of the hairpin resonator for interpreting n_e in a strongly magnetized plasma.