ECAMP 15

The neutral alkali beams, such as lithium and sodium, were shown to be invaluable for measuring turbulence and electron density profiles in the boundary plasma [1]. These beams have also been proven to be useful for measuring local impurity properties using charge-exchange recombination spectroscopy [2]. The cross section calculations are vital to determine which spectral line can be significantly modulated by the charge-exchange (CX) processes between beam atoms and plasma ions.
In this work, the 3-body classical trajectory Monte Carlo (CTMC) method was used to determine the principal quantum number (n) and the orbital angular momentum quantum number (l) depend-ent CX cross sections for sodium atom and carbon ion collisions. The projectile carbon ion charge state was taken into account from the single charge till the fully stripped ion state. We performed the calculations for 35 keV and 50 keV impact energies. The CTMC method is a non-perturbative method, based on the calculation of a large number of individual particle trajectories when the initial atomic states are chosen randomly [3-4]. In the present work, the CTMC simulations were made in the three-body approximation, where the many-electron target atom was replaced by a one-electron atom and the projectile ion was taken into account as one particle. The three particles are characterized by their masses and charges and Coulomb force is acting between the colliding particles. The effective charge of the target core was calculated according to the Slater’s rules [5]. The initial conditions of the individual collisions are chosen at sufficiently large inter-nuclear separations from the collision center, where the interactions among the particles are negligible. The classical equations of motion were integrated with respect to the time as independent variable by the standard Runge-Kutta method.
We found that higher the charge state higher value of n shows the maximum cross sections. In the similar fashion, for high n capture states the maximum l capture cross sections also shift toward to higher values of l. Moreover, we found that the CTMC modelling and the experiments on the alka-li beam of stellarator Wendelstein 7-X agree that for q=6 carbon ions the electron capture to the n=8 state occurs with the largest probability, while in case of the q=5 carbon ions the same holds for the n=7 states. The CTMC calculations indicate that in these cases the cross sections have a positive correlation with l.

This work has been carried out within the framework of the EUROfusion Consortium, funded by the European Union via the Euratom Research and Training Programme (GrantAgree ment No 101052200 — EUROfusion). Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or the European Commission. Neither the European Union nor the European Commission can be held responsible for them.

References

[1] S. Zoletnik et al., Rev. Sci. Instrum., 89 063503 (2018)
[2] R.P Schorn et al., Nuclear Fusion, 32 351 (1992)
[3] K. Tőkési and G. Hock, Nucl. Instrum. Meth., B 86 201 (1994)
[4] K. Tőkési and Á. Kövér, J. Phys. B, 33 3067 (2000)