Tracking electron capture processes in classical molecular dynamics simulations for spectral line broadening in plasmas

TL;DR

The paper addresses recombination broadening in Stark-broadened plasmas by introducing a global, history-based criterion to identify trapped electrons in classical MD for emitters with charge $Z \ge 1$. The method combines a threshold energy $\mathscr{E}_{th} = -\frac{2}{3} V_i$, a $Z+1$ neighbor tracking rule, and a bound-interval test $\tau_{\text{bound}} = 3\tau_T$ derived from plasma parameters, all within a regularized Coulomb potential. Application to a $Z=2$ plasma demonstrates that captured electrons yield characteristic field histories and that the ionization balance inferred from trapping agrees with a potential-energy distribution method, validating the approach. This provides a practical route to improve line-shape calculations in strongly coupled plasmas, while noting limitations such as the condition $a<r_e$ and the absence of dissipative radiative processes in the classical framework.

Abstract

Plasma spectroscopy is a fundamental tool for diagnosing laboratory and astrophysical plasmas. Accurate interpretation of spectra depends upon precise modeling and comprehension of Stark broadening and other mechanisms affecting spectral lines. In this context, computer simulations have emerged as valuable tools, offering idealized experiments with well-defined conditions. Molecular dynamics simulations, in particular, excel at replicating the particle interactions within the plasma and their impact on the state of a radiating atom or ion. However, these simulations present challenges in tracking electron capture processes, since setting an unambiguous criterion to distinguish between bound and free electrons is not trivial. In this paper we introduce a new algorithm that, within a classical framework, precisely identifies the scenario in which an electron is captured by an ion and then follows a stable orbit around it. The algorithm's applicability extends to emitters with charges Z >= 1. The procedure enables the correct identification of valid time-histories of the electric microfield perturbing the emitting ion, which will be used for subsequent line shape calculations. The ionization balance results obtained from the application of this algorithm are compared with an additional method based on the potential energy of the particles in the simulations, finding good agreement, therefore validating the use of this approach.

Figures (5)

• Figure 1: Time-history of a plasma with $\rho = 0.6$ and emitters with charge 2. From top to bottom: potential energy of an emitter as a function of time, indices of the three closest electrons at each moment, and electric field. The shaded regions correspond to the moments when a particle is trapped. The potential energy is given in units of $\mathscr{E}_0$, a characteristic energy of the simulation, and the electric field in units of $E_0$, the electric field produced by a single electron at the typical distance $r_e$.
• Figure 2: Distribution of the potential energy of ions (left) and its integral (right). Data correspond to a Helium plasma ($Z=2$), with an ionization potential $V_i = \unit[30]{\mathscr{E}_0}$, and a coupling parameter $\rho_N = 1.0$. The mean total energy per particle of the system is $\mathscr{E}_t = -2.12\mathscr{E}_0$.
• Figure 3: Same as in Fig. \ref{['fig:418']}, with a mean total energy for particle of $-10.00\mathscr{E}_0$.
• Figure 4: Fractional population of the different ion species as a function of the temperature for a plasma of ions with charge 2, and an ionization potential of $V_i = 30\mathscr{E}_0$. Each dot corresponds to a set of simulations with the same temperature at equilibrium.
• Figure 5: Mean ion charge obtained by applying the new criterion for selecting electric field sequences, compared to the values obtained by integrating the potential energy distributions. It can be seen that the results are in very good agreement.