The modeling of atom – neutral collisions for beam emission spectroscopy applications

Eur. Phys. J. D (2019) 73: 116 https://doi.org/10.1140/epjd/e2019-90690-2 THE EUROPEAN PHYSICAL JOURNAL D Regular Article The modeling of atom – neutral collisions for beam emission spectroscopy applications? O. Asztalos1,a , B. Szondy1 , K. Tőkési2,3 , and G.I. Pokol1,4 1 2 3 4 Institute of Nuclear Techniques, Budapest University of Technology and Economics, Muegyetem rkpt 3, 1111 Budapest, Hungary Institute for Nuclear Research, Hungarian Academy of Sciences (Atomki), 4001 Debrecen, Hungary ELI-ALPS, ELI-HU Non-profit Ltd., Dugonics ter 13, 6720 Szeged, Hungary Wigner RCP, Hungarian Academy of Science, 1121 Konkoly-Thege Miklos 29-33, Budapest, Hungary Received 18 December 2018 / Received in final form 11 March 2019 Published online 1 June 2019 c The Author(s) 2019. This article is published with open access at Springerlink.com Abstract. The collisional radiative models used in the modeling of beam emission spectroscopy diagnostics neglect atom–atom collisions because of a lack of sufficiently detailed atomic data. Filling this scantiness we performed a classical trajectory Monte Carlo simulations to calculate the cross sections for various channels in collisions between H + H2 and Li + H2 for a wide range of projectile energies. Based on the calculated cross sections, a simplified version of the collisional radiative model has been derived. We show that the model is suitable to obtain the beam attenuation in neutral gases outside of the confined plasma region. A strong density dependence has been found for each beam species. 1 Introduction Beam emission spectroscopy (BES) is an active plasma diagnostic used for density measurements, which has sufficient spatial and temporal resolutions for the study of turbulent density fluctuations and associated flows [1]. A high energy neutral beam of 20–100 keV is shot into the plasma, consisting of hydrogen isotopes or light alkali metal isotopes with only one valence electron. While attenuating, the beam atoms can be excited into higher states through various collisional processes with plasma particles (electrons, ions, impurities and neutrals) and spontaneously emit photons, which can be detected by an independent observation system. Plasma density [2] and fluctuations [3] measurement are based on the detected light signal and its fluctuations, respectively. Forward modeling of BES diagnostics is integral to the plasma density reconstruction [4] and spatial localization of density fluctuation [5], which strongly depend on the range and accuracy of underlying collisional radiative models (CRMs). Forward modeling BES codes, e.g., RENATE [6], are equipped with a CRM for alkali atom and hydrogenic beam emission modeling which accounts for collisional excitation, de-excitation, charge exchange, ionization and spontaneous emission. Existing CRMs do not include beam atom interaction with neutral particles, due to a general lack of cross-sections ? Contribution to the Topical Issue “Many Particle Spectroscopy of Atoms, Molecules, Clusters and Surfaces (2018)”, edited by Károly Tőkési, Béla Paripás, Gábor Pszota, and Andrey V. Solov’yov. a e-mail: handling collisional interactions of higher atomic states at BES relevant impact energies. Recent trends in fusion research show a renewed interest in the contribution of neutral particles located outside of magnetic confinement region, enforcing the need to extend current CRMs. Applications include: – improved estimation of beam attenuation, relevant for diagniostics and high powered heating beams [7], – validation of BES relative calibration procedures also shown in Fisher et al. [8], – improvement of synthetic BES diganostics [9] aiding the study on the effect of neutrals on the dynamics of scrape-off layer (SOL) turbulence [10]. A classical trajectory Monte Carlo (CTMC) method [11] has been used to reproduce the existing measured neutral with neutral ionization cross-sections found in literature to establish the method as a suitable tool for the computation of new, not yet measured, beam atom impact with neutral cross-sections. Collisional radiative models used in the modeling of beam emission spectroscopy diagnostics neglect the atomatom collisions due to a lack of sufficiently detailed atomic data. In this work, filling this scantiness we present a classical trajectory Monte Carlo method to calculate the cross sections for various channels in collisions between H + H2 and Li + H2 in a wide range of projectile energies. Based on the calculated cross sections, a simplified version of the collisional radiative model has been derived. We show that the model is suitable to obtain the beam attenuation in neutral gases outside of the confined plasma region. Page 2 of 6 Eur. Phys. J. D (2019) 73: 116 described by a set of non-relativistic Newtonian equations: mi Fig. 1. The relative vectors involved in a 4 body interactions. We organize the paper as follows: Section 2 introduces a CTMC method, ionization cross-section computations and comparisons are made with experimental measurements. Section 3 describes a CRM for neutral particle beam interaction. Beam attenuation is calculated using computed ionization cross-sections. It is shown that this model is suitable to improve the beam attenuation calculations in fusion experiments. Section 4 concludes on the viability of the CTMC method for cross-section generation as well as the inclusion of neutral particle with beam atom collisions into existing CRMs. 2 Beam–neutral cross-sections Extensive work has been perfomed in the procurement of cross-sections for atomic rate calculations used by BES modeling, such as, Wutte et al. [12] which features an extended cross-section table with nl resolved collisional cross-sections for lithium impact excitation, ionisation and charge exchange with electrons, protons and impurities for atomic levels up to 4f. This work also includes Li + H2 ground state ionization cross-sections of the valence electron and collisional excitation to 2p. Similar work was done for sodium projectiles [13]. Earlier hydrogen impact cross-section work is more extensive, with regard to high energy H + H2 collisions [14–16] but this lacks the detailed cross-section tables as featured for electron and proton impact interactions needed for beam evolution calculations. 2.1 Classical trajectory Monte Carlo The classical trajectory Monte Carlo (CTMC) is a nonperturbative method that classically deals with collisions. CTMC has been shown to be effective in the calculation of ionization and capture cross-sections for ion atom collisions [21,22]. In this work, a four body approximation is applied for the modeling of collisions between Li and H projectiles with H2 targets, (see Fig. 1). The interaction between the colliding particles is governed by the Coulomb force and d2 ri = dt2 4 X Zi Zj j=1,i6=j (ri − rj ) |ri − rj |3 (1) where mi , Zi and ri are the mass, charge and relative position of the ith particle, resp (...truncated)