Atomic collisional data for neutral beam modeling in fusion plasmas

Abstract

The injection of energetic neutral particles into the plasma of magnetic confinement fusion reactors is a widely-accepted method for heating such plasmas; various types of neutral beam are also used for diagnostic purposes. Accurate atomic data are required to properly model beam penetration into the plasma and to interpret photoemission spectra from both the beam particles themselves and from plasma impurities with which they interact. 

This paper reviews and compares theoretical methods for calculating ionization, excitation and charge exchange cross sections applied to several important processes relevant to neutral hydrogen beams, including H + Be4+ and H + H+. In particular, a new cross section for the proton-impact ionization of H (1s) is recommended which is significantly larger than that previously accepted at fusion-relevant energies. Coefficients for an empirical fit function to this cross section and to that of the first excited states of H are provided and uncertainties estimated. The propagation of uncertainties in this cross section in modeling codes under JET-like conditions has been studied and the newly-recommended values determined to have a significant effect on the predicted beam attenuation. In addition to accurate calculations of collisional atomic data, the use of these data in codes modeling beam penetration and photoemission for fusion-relevant plasma density and temperature profiles is discussed. In particular, the discrepancies in the modelling of impurities are reported.

The present paper originates from a Coordinated Research Project (CRP) on the topic of fundamental atomic data for neutral beam modeling that the International Atomic Energy Agency (IAEA) ran from 2017 – 2022; this project brought together 10 research groups in the fields of fusion plasma modeling and collisional cross section calculations. Data calculated during the CRP is summarized in an Appendix and is available online in the IAEA's atomic database, CollisionDB.

Time-Dependent Density Functional Theory for Atomic Collisions: A Progress Report

“…The theoretical results displayed in Figure 5 were again obtained from BGM calculations. In addition to exact time-dependent screening and exchange contributions, the effective electron-electron potential (10) used here includes an accurate ground state correlation potential determined numerically by an inversion procedure [31]. The correlation potential was found to be unimportant for the collision calculations; thus, the single-particle solutions are in fact very similar to the exchange-only results (cf.…”

“…Although it did not explicitly include bound projectile states in the basis, the (time-dependent) pseudostates had a two-center character, and capture probabilities were extracted from their population at asymptotic times using a projection technique. The effective electron-electron potential (10) was taken at the exchange-only level, i.e., correlation was neglected while exchange was included exactly. For helium, this is accomplished by multiplying the Hartree potential (11) by a factor of one half, as the elimination of the unphysical self-interaction contributions is the only role of exchange in this two-electron spin-singlet system.…”

“…The effect is relatively small, however, and comparison with the experimental data does not provide a clear-cut answer as to whether the response results are superior. In an ideal world in which the experimental data had negligible error bars and the theoretical results had exceedingly high numerical accuracy, it could be concluded from Figures 3 and 4 that any remaining discrepancy between theory and experiment would be resolved if we knew how to include correlation in the effective electron-electron potential (10). Total cross-sections for net ionization in proton (top) and He 2+ (bottom) collisions with helium as functions of collision energy.…”

“…As a matter of fact, the community has struggled to reach agreement even on the most basic one-electron ion-atom scattering problem, namely, the proton-hydrogen system, for which one does not need TDDFT or any other many-body approach. Only recently has this changed, with consensus being reported regarding the magnitude of the total ionization cross-section in the intermediate energy region, where it peaks and competes with capture and target excitation [10].…”

CollisionDB: A New Database of Atomic and Molecular Collisional Processes with an Interactive API

“…As is evident in Listing 9, data visualization allows users to intuitively identify inconsistencies in the data. This serves as a first step in evaluating the data quality and requires further in-depth analysis of the data [16]. In the context of querying the database through the API, filtering is based on the search for the text representation of the objects, such as reactants and products, where applicable.…”