Plasma frequency demand for mode conversion processes from slow Z-mode to LO-mode waves in an inhomogeneous plasma

The mode conversion process responsible for radio wave generation has been studied for several decades; however, the properties of the condition required for an efficient conversion process are still unknown. The aim of this study is to determine the value of plasma frequency required for an efficient mode conversion process from slow Z-mode to left-hand ordinary (LO)-mode waves in the matching cases, where the two branches of the dispersion relation of the two modes are perfectly connected. We derive the dispersion relations for electromagnetic wave propagation in an inhomogeneous plasma considering Snell's law and investigated them in detail. We quantify the minimum variation of plasma frequency required for the efficient mode conversion process, which we call "the plasma frequency demand." We show that the condition required for the efficient mode conversion can be satisfied by waves propagating first toward the high-density region and then returning toward the low-density region before reaching the region where the wave frequency matches the cutoff frequency; therefore, a large inhomogeneity is not always required. We show that the angle between the background magnetic field and the density gradient has a significant effect on the plasma frequency demand.