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Thomson scatter radars have successfully measured plasma parameters in the ionosphere for over 60 years. Fundamentally, the radars measure increased power returns when the Bragg scattering condition is met by a source of density fluctuations in the plasma. Typically, wave modes of the plasma provide the source of structuring, and the radars measure strong power returns at the ion line which is associated with the ion-acoustic mode, the gyro line which is associated with the electrostatic whistler mode, and the plasma line that comes from the Langmuir mode. However, the existence of an ion-acoustic mode or electrostatic whistler mode is not guaranteed in the ionosphere. In this study, a formalism is developed to explain non-resonant wave modes as features occurring at frequencies where the dielectric function has a local minimum as opposed to a root corresponding to the typical resonant wave mode. With this formalism, the frequency of non-resonant waves is numerically solved as a function of basic plasma parameters. By solving for minima of the dielectric function, the frequency and intensity of gyro lines is determined for a wide range of plasma temperatures and densities. This analysis explains why Arecibo gyro lines are typically weak in intensity and result from non-resonant waves. For VHF systems like EISCAT, gyro lines are shown to be strong spectral peaks corresponding to standard resonant solutions for electrostatic whistler waves.