Review of recent analytical advances in the spectroscopy of hydrogenic lines in plasmas

Broadening of hydrogenic spectral lines is an important tool in spectroscopic diagnostics of various laboratory and astrophysical plasmas. We review recent analytical advances in three areas. First, we review the analytical solution for the splitting of hydrogenic lines under the combination of a circularly polarized electromagnetic wave with a strong magnetic field. Practical applications of this solution relate to the spectroscopic diagnostic of the electron cyclotron waves and to the relativistic laser-plasma interactions. Second, we review analytical results concerning the Stark-Zeeman broadening of the Lyman-alpha (Ly-alpha) line in plasmas. These results allow for the Stark width of the Ly-alpha pi-component to be used for the experimental determination of the ion density or of the root-mean-square field of a low-frequency electrostatic plasma turbulence in the situation where the Zeeman effect dominates over the Stark effects. Third, we review recent analytical advances in the area of the intra-Stark spectroscopy: three different new methods, based on the emergent phenomenon of the Langmuir-wave-caused structures ("L-dips") in the line profiles, for measuring super-strong magnetic fields of the GigaGauss range developing during relativistic laser-plasma interactions. We also review the rich physics behind the L-dips phenomenon - because there was a confusion in the literature in this regard.