plasma Article A Supersensitive Method for Spectroscopic Diagnostics of Electrostatic Waves in Magnetized Plasmas Eugene Oks 1, *, Elisabeth Dalimier 2,3 and Paulo Angelo 2,3   Citation: Oks, E.; Dalimier, E.; Angelo, P. A Supersensitive Method for Spectroscopic Diagnostics of Electrostatic Waves in Magnetized Plasmas. Plasma 2021, 4, 780–788. https://doi.org/10.3390/ plasma4040040 Academic Editor: Andrey Starikovskiy Received: 19 November 2021 Accepted: 6 December 2021 Published: 10 December 2021 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affil- iations. Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). 1 Physics Department, Auburn University, 380 Duncan Drive, Auburn, AL 36849, USA 2 Laboratoire Pour L’utilisation des Lasers Intenses, Sorbonne Université, CEDEX 05, F-75252 Paris, France; elisabeth.dalimier@upmc.fr (E.D.); paulo.angelo@upmc.fr (P.A.) 3 Centre National de la Recherche Scientifique, Ecole Polytechnique, CEA—Université Paris-Saclay, CEDEX 05, F-75252 Paris, France * Correspondence: goks@physics.auburn.edu Abstract: For relatively strong magnetic fields, hydrogen atoms can have delocalized bound states of almost macroscopic dimensions. Therefore, such states are characterized by a Giant Electric Dipole Moment (GEDM), thus making them very sensitive to an external electric field. We con- sidered the manifestations of the GEDM states in hydrogen spectral line profiles in the presence of a quasimonochromatic electrostatic wave of a frequency ω in a plasma. We demonstrated that in this situation, hydrogen spectral lines can exhibit quasi-satellites, which are the envelopes of Blochinzew-type satellites. We showed that the distinctive feature of such quasi-satellites is that their peak intensity is located at the same distance from the line center (in the frequency scale) for all hydrogen spectral lines, the distance being significantly greater than the wave frequency ω. At the absence of the GEDM (and for relatively strong electrostatic waves), the maxima of the satellite envelopes would be at different distances from the line center for different hydrogen lines. We demonstrated that this effect would constitute a supersensitive diagnostic method for measuring the amplitude of electrostatic waves in plasmas down to ~10 V/cm or even lower. Keywords: strong magnetic fields; center-of-mass effects; giant electric dipole moments; supersensi- tive diagnostics of electrostatic waves in plasmas 1. Introduction There are numerous methods for spectroscopic diagnostics of plasmas (see, e.g., books [1–11] listed in chronological order). Among these methods are those designed for spectroscopic diagnostics of various electrostatic waves in plasmas (see, e.g., books [3,10,11]). These methods, based on the shape of spectral lines of atoms and ions, cover the range of amplitudes of the electrostatic waves from ~1 kV/cm to ~1 GV/cm. In the present paper we describe a possibility to extend the sensitivity of such methods to ~10 V/cm or even lower, as follows. There are plenty of studies showing that for hydrogenic atoms/ions in a uniform magnetic field, the center-of-mass motion and the relative (internal) motion are coupled by the magnetic field and, rigorously speaking, cannot be separated (see, e.g., papers [12–14] and references therein). A pseudoseparation is possible for hydrogen atoms. It leads to a Hamiltonian for the relative motion that depends on a center-of-mass integral of the motion K called pseudomomentum but does not depend on the center-of-mass coordinate [14]. We remind that the pseudomomentum K is the canonical variable conjugated to the center- of-mass coordinate. A diamagnetic potential term in the Hamiltonian for the relative motion is responsible for the formation of an additional potential well far away from the hydrogen nucleus (proton). For relatively strong magnetic fields, the new bound states inside this well are delocalized states of almost macroscopic dimensions. Therefore, the bound state inside this Plasma 2021, 4, 780–788. https://doi.org/10.3390/plasma4040040 https://www.mdpi.com/journal/plasma