Low-energy collisions between electrons and : Cross sections and rate coefficients for all the vibrational states of the ion
Introduction
Even though various isotopes of light elements can be coupled to achieve thermonuclear fusion energy release, the next generation of thermonuclear fusion reactors will use deuterium–tritium (D–T) reactions, by far most efficient and accessible plasma fuel for fusion reactors and power plants. As discussed in detail elsewhere [1], [2], [3], [4], [5], [6], beryllium (Be) is meant to enter the composition of the wall of the future fusion devices (ITER). Its performance on preventing tritium retention and, meanwhile, still keeping the benefits of a low Z material (low fuel dilution), is currently being tested in the JET [3], [4]. According to current plans, tungsten (W) will be the plasma facing material in the high heat flux components (the entire divertor). These materials (Be and W) are expected to provide sufficiently low fuel retention, plasma impurity levels, neutron damage, and sufficient heat removal capabilities in the divertor and then, meet ITER requirements [2]. The key challenge in the use of beryllium as main chamber material for experimental and commercial fusion devices is to understand, predict and control the characteristics of the thermonuclear burning plasma, the plasma edge regimes that result in acceptable erosion performance and the divertor plasma (heat and particle exhaust, impurity control, lifetime).
Due to the low mass ratio between beryllium and the D, T plasma fuel ions, beryllium erodes rather easily under plasma exposure by physical and chemical sputtering, a process which releases Be, , and other impurities into the plasma. Significant fractions of the eroded beryllium will be transported towards the divertor and will form compounds with the fuel atoms, molecules and/or molecular ions. Therefore, BeH as well as BeD and BeT molecules are expected to appear in a significant (spectroscopically detectable) amount in the edge and divertor plasmas. Various source mechanisms may lead to their formation, either surface or volumetric (particle rearrangement) processes. The particle interchange reaction [7], where X denotes one of the fuel atoms H, D or T, was suggested as one, possibly dominant, volumetric BeX formation channel, when is in its vibrational ground state. However, the exo- or endothermicity will greatly depend upon the vibrational state of and other channels, including electron transfer channels, may also be open for BeX formation in fusion divertor plasma conditions. The involved particles–atoms, molecules and molecular ions–follow their often quite complex transport pathways in the edge plasma and take part in the complex reactions determining the plasma composition. Its detailed modeling by taking into account reactions between all present species is necessary, first of all, for interpretation of molecular and atomic line spectroscopy and also to understand and predict the overall plasma edge dynamics and the divertor region behavior in particular.
In principle, the rate of beryllium erosion in fusion devices can be measured by spectroscopical techniques of all the states of the atoms and molecules, so primarily of Be, , , BeX, , , . In order to provide a quantitative interpretation of such spectroscopic measurements, one needs a complete set of rate coefficients for excitation, ionization and the various atomic and molecular ions break-up reactions. The inelastic electron-impact processes of vibrationally excited beryllium monohydride play a key role in the reaction kinetics of low-temperature plasmas in general, and potentially also in certain cold regions of fusion reactor relevant (e.g. the divertor) plasmas. In order to model and diagnose plasmas containing it is essential to build a complete database of cross-sections and rate coefficients for electron-impact collision processes. Knowing the loss rates of (and isotopologues) as well as absolutely calibrated spectroscopic emission from this molecular ion will allow to draw conclusions also about the formation rates.
The ion is subject to Dissociative Recombination (DR), competed by Vibrational Transitions (VT)–excitation/de-excitation (VE/VdE)–and Dissociative Excitation (DE) respectively [8]: where are standing for the initial/final vibrational levels of the cation.
Whereas for numerous ions measurements of these reactive collisions have been performed in magnetostatic or electrostatic storage rings (multipass experiments using merged electron and ion beams) [8], this is certainly not the case for , beryllium being highly toxic.
In the current study, we performed large scale computations of cross sections for the reactive collisions DR, VE and VdE displayed in eq. (2), as well as of the corresponding rate coefficients.
More specifically, we have used the molecular structure data computed by some of us [9] in order to model the dynamics of these reactions by our stepwise MQDT-method, neglecting the rotational structure and interactions [10], [11], [12], [13]. Whereas our previous works [9], [13] restricted to the ground and three lowest vibrationally-excited levels of , we have extended here our analysis to the whole range of its vibrational states, i.e. up to .
After briefly reminding the major ideas and steps of our MQDT method, including the main features and parameters of the computational part (Section 2), we present the cross sections and rate coefficients below 2.7 eV–dissociation threshold–and below 5000 K, respectively (Section 3). The coefficients appearing in the analytical functions used to fit the rate coefficients are organized in tables.
At higher energy of the incident electron, a further competing process, dissociation excitation, will become effective. The collisional data for this range are the subject of ongoing calculations.
Section snippets
Theoretical approach of the dynamics
In this paper, we use an MQDT-type method to study the electron-impact collision processes: resulting from the quantum interference between the direct mechanism–involving the doubly excited resonant states –and the indirect one–occurring via Rydberg singly-excited predissociating states .
A detailed description of our theoretical approach was given in [13]. Its main steps are the following:
(i) Building of the interaction matrix : It is based
Results
Using the available molecular data–quasi-diabatic potential energy curves and electronic couplings for , and states displayed in Fig. 1 of [13] (for more details see as well [9], [18])–we have extended our previous calculations–initially restricted to the ground and weakly excited vibrational states–to all vibrational levels (up to ) of the ground electronic state. The energy of the electron is inferior to 2.7 eV, this value corresponding to the dissociation threshold of the
Conclusions
The present paper provides a complete state-to-state information of the reactive collisions with electrons, illustrating quantitatively the competition between the vibrational transitions and dissociative recombination. We display the cross sections or/and the Maxwell rate coefficients for the molecular ion in all of its initial vibrational states and for the entire range of energies of the incident electron below the ion dissociation threshold.
Arrhenius-type formulas are used in order to
Acknowledgments
We acknowledge the French LabEx , via the project PicoLIBS (No. ANR-12-BS05-0011-01), the BIOENGINE project (sponsored by the European fund FEDER and the French CPER), the Fédération de Recherche Fusion par Confinement Magnétique - ITER and the European COST Program CM1401 (Our Astrochemical History). AEO acknowledges support from the National Science Foundation, Grant No PHY-11-60611. In addition some of this material is based on work done while AEO was serving at the NSF. ÅL acknowledges
References (19)
- et al.
J. Nucl. Mater.
(2007) - et al.
J. Nucl. Mater.
(1999) - et al.
Fusion Eng. Des.
(1997) - et al.
Nucl. Fusion
(2001) - et al.
Plasma Phys. Control. Fusion
(2012) - et al.
Nucl. Fusion
(2007) - et al.
Plasma Phys. Control. Fusion
(2008) - et al.
Phys. Rev. A
(2009)
Cited by (15)
Reactive collisions between electrons and BeT<sup>+</sup>: Complete set of thermal rate coefficients up to 5000 K
2021, Atomic Data and Nuclear Data TablesTheoretical study of low energy electron collisions with the BeO molecule
2023, Journal of Physics B: Atomic, Molecular and Optical PhysicsStudy of bound and resonant states of NS molecule in the R-matrix approach
2022, Journal of Physics B: Atomic, Molecular and Optical Physics