Atomic Data for Calculation of the Intensities of Stark Components of Excited Hydrogen Atoms in Fusion Plasmas

Oleksandr Marchuk,David Schultz,Yuri Ralchenko

doi:10.3390/atoms8010008

Abstract

Motional Stark effect (MSE) spectroscopy represents a unique diagnostic tool capable of determining the magnitude of the magnetic field and its direction in the core of fusion plasmas. The primary excitation channel for fast hydrogen atoms in injected neutral beams, with energy in the range of 25–1000 keV, is due to collisions with protons and impurity ions (e.g., He 2 + and heavier impurities). As a result of such excitation, at the particle density of 10 13 –10 14 cm − 3 , the line intensities of the Stark multiplets do not follow statistical expectations (i.e., the populations of fine-structure levels within the same principal quantum number n are not proportional to their statistical weights). Hence, any realistic modeling of MSE spectra has to include the relevant collisional atomic data. In this paper we provide a general expression for the excitation cross sections in parabolic states within n = 3 for an arbitrary orientation between the direction of the motion-induced electric field and the proton-atom collisional axis. The calculations make use of the density matrix obtained with the atomic orbital close coupling method and the method can be applied to other collisional systems (e.g., He 2 + , Be 4 + , C 6 + , etc.). The resulting cross sections are given as simple fits that can be directly applied to spectral modeling. For illustration we note that the asymmetry detected in the first classical cathode ray experiments between the red- and blue-shifted spectral components can be quantitatively studied using the proposed approach.

Highlights

Beam-assisted spectroscopy represents a special class of diagnostics in plasma spectroscopy, as here, in contrast to passive emission spectroscopy, the heavy-particle collisions at the energies of a few atomic units (1 a.u. ≈ 25 keV) play a dominant role [1]
We provided a set of proton-hydrogen excitation cross sections for calculation of the line intensities for radiative transitions between n ≤ 3 parabolic states in the low-density limit
These data are required for Motional (translational) Stark effect (MSE) diagnostics under typical conditions of fusion plasmas

Summary

Introduction

Beam-assisted spectroscopy represents a special class of diagnostics in plasma spectroscopy, as here, in contrast to passive emission spectroscopy, the heavy-particle collisions at the energies of a few atomic units (1 a.u. ≈ 25 keV) play a dominant role [1]. Stark effect measurements with beam atoms and Zeeman effect measurements for the cold atoms at the plasma edge can clearly detect the spectral line components using high resolution spectroscopy [12,13]. For the applied external magnetic field of 1–5 T the energy separation due to the Zeeman effect is a few times larger than the fine-structure splitting of cold atoms in the plasma. Calculations of relative MSE line intensities in laboratory plasmas are based on either a statistical (static) or dynamical assumption [15]. In the former case the populations of levels are considered to be proportional to their statistical weights. The aim of this paper is to present a concise tabulated set of atomic data that has been found to be the most successful one, at least for fusion plasmas, by applying a density matrix formalism

Theoretical Approach

Lines Ratio of Stark Components in the Low Density Limit

Conclusions