Monopole Contribution to the Stark Width of Hydrogenlike Spectral Lines in Plasmas: Analytical Results

Abstract

One of the most reliable and frequently used methods for diagnosing various laboratory and astrophysical plasmas is based on the Stark broadening of spectral lines. It allows for determining from the experimental line profiles important parameters, such as the electron density and temperature, the ion density, the magnetic field, and the field strength of various types of the electrostatic plasma turbulence. Since, in this method, radiating atoms or ions are used as the sensitive probes of the above parameters, these probes have to be properly calibrated. In other words, an accurate theory of the Stark broadening of spectral lines in plasmas is required. In the present paper, we study, analytically, the monopole contribution to the Stark width of hydrogen-like spectral lines in plasmas. For this purpose, we use the formalism from paper by Mejri, Nguyen, and Ben Lakhdar. We show that the monopole contribution to the width has a non-monotonic dependence on the velocity of perturbing electrons. Namely, at relatively small electron velocities, the width decreases as the velocity increases. Then it reaches a minimum and (at relatively large electron velocities), as the velocity further increases, the width increases. The non-monotonic dependence of the monopole contribution to the width on the electron velocity is a counter-intuitive result. The outcome that at relatively large electron velocities, the monopole contribution to the width increases with the increase in the electron velocity is in a striking distinction to the dipole contribution to the width, which decreases as the electron velocity increases. We show that, in the situation encountered in various areas of plasma research (such as in magnetically-controlled fusion), where there is a relativistic electron beam (REB) in a plasma, the monopole contribution to the width due to the REB exceeds the corresponding dipole contribution by four orders of magnitude and practically determines the entire Stark width of hydrogenic spectral lines due to the REB.