On profiles of hydrogenic spectral lines under stochastic electric fields of plasma turbulence: Applications to diagnostics of the Langmuir turbulence

Abstract

Studies of the effects of various oscillatory electric fields on hydrogenic spectral lines have a long history. Over the years various effects of a monochromatic linearly-polarized electric field were analyzed and applied to spectroscopic diagnostics of laboratory and astrophysical plasmas.Then in 1996 a paper was published where the author analyzed how profiles of hydrogen spectral lines are affected by a multi-mode non-monochromatic linearly-polarized electric field E(t). Specifically it concerned the situation where the power spectrum of the field E(t) has the Lorentzian form. In the present paper we obtained a general analytical result for the shape of hydrogenic (i.e., hydrogen and hydrogenlike) spectral lines under the same kind of the field E(t), but whose power spectrum has the Gaussian form. We consider this kind of electric field to be caused by the Langmuir turbulence in plasmas. We show that if the power spectrum of the field is Gaussian, then for the relatively small value of the average Langmuir field, the profile of each Stark component is Lorentzian, while for the relatively large value of the average Langmuir field, the profile of each Stark component is Gaussian. We analyze theoretical profiles of the hydrogenic Ly-beta line under the Langmuir field of either one of the above two kinds of the power spectrum. On the basis of this analysis, we propose a new diagnostic method allowing for the first time not only to measure experimentally the average field of the Langmuir turbulence in dense plasmas, but also to find out the information on the power spectrum of the Langmuir turbulence. This diagnostic method is not limited to using the Ly-beta line: it would work while using other intense hydrogenic spectral lines that do not have the central Stark components, such as, e.g., Ly-delta, Balmer-beta, and Balmer-delta.