Electromagnetic bounded States and challenges of plasma spectroscopy

We review the foundations and observational support for a new plasma wave mode that has been proposed to explain emissions stimulated by satellite-born high-power radio-frequency sounders. These sounders, which are designed to derive remote electron density profiles from electromagnetic-wave echoes, stimulate plasma resonances in the local plasma. In addition to stimulating resonances at the electron plasma frequency f_pe, harmonics of electron gyrofrequency f_ce, and at the upper hybrid frequency f_uh, resonances are also stimulated at frequencies below f_pe between the gyroharmonics. The first such resonance, with frequency between f_ce and 2f_ce, was discovered by Nelms and Lockwood in 1967 using the topside sounder on Alouette 2. From its appearance, it was called a diffuse resonance (D₁ in modern notation) and was originally thought to have a frequency of 3/2f_ce. Further observations, and theoretical insights, indicated that f_D1 is dependent on f_pe and f_ce, namely, f_D1=(3/π)(f_pef_ce)¹2/. The theoretical concepts used to obtain this expression indicated that the D_n resonances (n=1,2,3,...) are electron eigenmodes (electromagnetic bounded states) and led to equations describing the frequencies of the entire D_n sequence and their subsidiary resonances D_n⁺ and D_n^-. Such formulas, based on a combined theoretical and empirical approach, describe a √n spectrum with the frequency of each mode split by the magnetic field analogous to the Zeeman splitting in quantum mechanics. The √n spectrum was first predicted for force-free electromagnetic cylindrical plasma oscillations by Osherovich in 1986. The main theoretical challenge remains to derive the frequency f_D1 from first principles. Although the D_n resonances have been stimulated in the terrestrial ionosphere for decades by topside sounder satellites such as Alouette 2 and by electron guns on several rocket experiments, and in Jupiter´s Io plasma torus by the sounder on the Ulysses space probe, and are currently being stimulated in the terrestrial magnetosphere by the sounder on the IMAGE spacecraft, they have yet to be observed in laboratory experiments.