J. Oreg

HULLAC, an integrated computer package for atomic processes in plasmas

Abstract We describe H ULLAC , an integrated code for calculating atomic structure and cross sections for collisional and radiative atomic processes. This code evolved and has been used over the years, but so far, there was no coherent, comprehensive, and in-depth presentation of it. It is based on relativistic quantum mechanical calculations including configuration interaction. The collisional cross sections are calculated in the distorted wave approximation. The theory and code are presented, emphasizing the various novel methods that has been developed to obtain accurate results very efficiently. In particular we describe the parametric potential method used for both bound and free orbitals, the factorization–interpolation method applied in the derivation of collisional rates, the phase amplitude approach for calculating the continuum orbitals and the N JGRAF graphical method used in the calculation of the angular momentum part of the matrix elements. Special effort has been made to insure the simplicity of use, which is demonstrated in an example.

Configuration interaction in LTE spectra of heavy elements

Abstract We present a method for including the effects of configuration interaction (CI) between relativistic subconfigurations of an electron configuration in the calculation of emission and absorption spectra of plasmas in local thermodynamic equilibrium (LTE). Analytical expressions for the correction to the intensities, owing to CI, of an unresolved transition array (UTA) and of a supertransition array (STA) are obtained when the correction is small compared to the spin-orbit splitting, bypassing the need to diagonalize energy matrices. These expressions serve as working formulas in the STA model and, in addition, reveal a priori the conditions under which CI effects are significant. Examples of the effect are presented.

Non-LTE superconfiguration collisional radiative model

Abstract We have developed a non-LTE collisional radiative model which takes into account the overwhelming multiplicity of excited levels of heavy elements in hot and dense plasmas. The model, ‘SCROLL’ (Super Configuration Radiative cOLLisional), treats superconfigurations as effective levels and reproduces detailed configuration accounting results by an iterative procedure which splits superconfiguration until convergence. The fundamental assumption in the model is that within a superconfiguration levels are populated according to Boltzmann statistics. This assumption is effectively relaxed by the convergence procedure. The populations of the superconfigurations are obtained by solving the set of collisional radiative rate equations. For this purpose we have derived analytical formulae for the average transition rates between superconfigurations for collisional excitation and ionization, radiative transitions, photoionization and autoionization. These analytical formulae are obtained using the ‘Partition Function Algebra’ developed in our previous LTE STA model. The calculation of the average rates are performed in the distorted wave approximation framework. Using the resulting superconfiguration populations we can then calculate charge distribution, opacities and emissivities. The model is applicable to any atom. In the present work it was applied to investigate non-LTE thin plasmas of Al and Au for several temperatures and densities. Comparison with detailed calculations when these are possible gave excellent agreement. Both theory and results are addressed.

Recent developments in the SCROLL model

Abstract We present the recent developments in the SCROLL model for simulating non-LTE plasma spectra. The model accounts for the overwhelming multiplicity of excited levels of heavy elements in hot and dense plasmas, treating superconfigurations as effective levels. The detailed configuration accounting results are obtained by an iterative scheme that splits superconfigurations until convergence. We present here a binary tree splitting procedure that enables a practical convergence algorithm. With an eye on future non-LTE database production, we have extended the model to include radiation fields. Some preliminary attempts to simulate the effects of radiation by using dilute Planckian radiation fields are presented. Comparison between the SCROLL results and an experiment performed recently on gold non-LTE plasma, show good agreement.

The effect of configuration interaction on relativistic transition arrays

Abstract The theory for the inclusion of configuration interaction shifts, widths and intensity redistribution effects on relativistic transition arrays is presented. These effects become important when the electrostatic interaction is strong enough, in particular for Δ n =0 transitions. Analytic expressions for the corrected array moments are obtained for both UTAs and STAs, bypassing the impractical need for matrix diagonalizations. Comparison of the theoretical results with detailed calculations and with experiments are presented.

A NEW APPROACH TO INCLUDING DOUBLY EXCITED LEVELS IN THE COLLISIONAL RADIATIVE MODEL

Abstract A severe limitation on the application of the collisional radiative model is the need to include an exceedingly high number of relevant doubly excited and inner shell excited levels. The direct inclusion of all these levels is simply impractical. In a previous theory we have included doubly excited configurations as effective levels assuming statistical distribution of the populations within these configurations. In the present work we develop a new approach which minimizes even further the amount of effective levels, and leading, paradoxically, to weaker statistical assumptions. It is shown that the outer Rydberg orbital of the doubly excited configuration resembles a continuum electron, and is only weakly coupled to the internal core. This fact allows the application of the Factorization Interpolation method, reducing the cross-sections of the various collisional radiative processes to one electron multipole transitions between core states only. The radial integrals include the outer orbital and the summation over all the involved continuum orbitals. It is also shown that the assumption of a statistical distribution can be extended to groups of states with neighboring Rydberg orbitals. Each group then contains effective levels characterized by the core state designation and therefore has the same dimension as the original core. A convergence procedure is described that involves reducing the number of Rydberg orbitals within a group. It is shown that a small number of groups is sufficient for convergence, reducing drastically the number of effective levels in the model. The simple example of the Ne-like ion is discussed. The many thousands of relevant doubly excited states are reduced in this case to the 37 levels of the core multiplied by the small number of groups. This reduction is even more striking in more complex ions and in cases where the core is far from closed shell configurations.

A simplified approach to line broadening in dense plasmas

A simplified approach is presented for the analysis of broadening and shift of emission lines in hot dense plasmas. The basic approximation which allows this simplified approach is the factorization of the wavefunction for the many-body problem into the wavefunction for the plasma particles, and the wavefunction which describes the internal degrees of freedom.