J. Phys. IV France 133 (2006) 973–975 C EDP Sciences, Les Ulis DOI: 10.1051/jp4:2006133195
An improved version of the HULLAC code M. Busquet1 , A. Bar-Shalom1 , M. Klapisch1 and J. Oreg1 1
ARTEP # , Inc., Ellicott City, Maryland 21042, USA
Abstract. Accurate and detailed atomic structure codes are needed for simulation of of spectrally resolved x-ray output of laser driven target. As such, the HULLAC code [1] has already been presented several times. Recently, cooperation was proposed to anyone interested in extending/developing the code. Until now, however, it needed to be worked on before distribution. We present here this development and the new added possibilities. HULLAC is now ready to be distributed on a basis of collaboration.
1. INTRODUCTION Atomic physics is useful to Inertial Confinement Fusion (ICF) in several ways, e.g. to compute opacities required in simulations, or as a basis for spectroscopic diagnostics. For opacities of heavy atoms, involving extremely complex spectra in conditions of Local Thermodynamic Equilibrium (LTE), the STA code has proven itself very reliable [2]. This code treats the spectra in the framework of super transition arrays . The same concept was developed for non LTE plasmas in the SCROLL code [3]. This concept is extremely efficient for unresolved spectra, but for many elements commonly found in ICF plasmas–e.g. H, Be, C, O, N, Si, Ar, Ti, Cu, etc. . . – the spectra are well resolved, and the distinction between individual lines is very important for opacities and vital for spectroscopic diagnostics. Even for more complex spectra such as Xe, the statistical treatments of super transition arrays may not be good enough, because it prevents taking into account configuration interactions (CI) and other effects, as shown below. For this purpose, our involvement in the HULLAC code [1] has been recently revived. The previous versions of this code [4, 5], that is now in use in several places, had limitations preventing extensive use. On the other hand, the modular structure of the code enables easy addition of other modules, e.g. line shapes, pressure ionization, etc. . . Accordingly, in view of our manpower and time constraints, we proposed a collaboration with whoever wanted at the APIP meeting 2002 [6]. However, the code was not yet in a state that could be distributed, and extensive work has been done since then for this purpose. In the following we first very concisely describe the theory and algorithms used in the code. Then we present the recent modifications and improvements. Finally an example is given, involving CI onXe8+ . 2. SHORT DESCRIPTION OF HULLAC The atomic structure in HULLAC is described in the framework of the central field model, using fully relativistic wavefunctions [7] with configuration interaction (CI). The central field follows the parametric potential model [4, 8]. The angular momentum coefficients of all processes are computed with efficent graph theoretical methods [9]. What makes HULLAC extremely efficient for collisional excitations is the factorization-linearization method [5], combined with a phase-amplitude algorithm [10], applied also to integrals. Electron-ion collisions are treated in the Distorted Wave approximation. The processes currently included are radiative decay, collisional excitation and ionization, radiative recombination, autoionization, and their reverse processes. All these processes are computed with the same wavefunctions. HULLAC is a Collisional Radiative Model (CRM) generator, and thanks to its efficiency, numerous
# ARTEP
is a contractor to the Naval Research Laboratory, Washington, DC 20375, USA.
Article published by EDP Sciences and available at http://www.edpsciences.org/jp4 or http://dx.doi.org/10.1051/jp4:2006133195
974
JOURNAL DE PHYSIQUE IV
levels can be included in the model. Thus the inclusion of a large number of doubly excited states may reproduce at least part of the resonances effects. 3. RECENT MODIFICATIONS AND IMPROVEMENTS First of all, an overhaul was performed, modernizing many parts to make them easier to understand, and adding many comments. At this occasion, many known bugs and quirks were corrected. The dimensions of relevant arrays were made compatible between the various modules. The source, in FORTRAN 77, was compiled and checked on many different systems with different compilers. Then, the most visible modifications are in the input method : By use of the super-shell and superconfiguration notations, the input can be very compact. A few lines can generate thousands of levels. The standard mode of the HULLAC code is to compute the fine structure levels, for energies and for all the above mentioned processes. In the new version[11], we have added the possiblity to directly compute the (relativistic) configuration averages, skipping the fine structure. However, in this case CI can be accounted for only within each nonrelativistic configuration. Therefore we added the possibility of a mixed description, where not all configurations are described at the fine structure level. Eventually the suite of codes can output superconfiguration averages from the energies and rates computed for configuration or levels, using the statistical equilibrium approximation or a pseudo-LTE with an user defined effective temperature. 4. EXAMPLE The following example is the spectrum of Xe8+ , where singly (i.e. with transitions to the ground state 4d10 ), doubly (to 4d9 4f), and triply (to 4d8 4f2 ) excited configurations are taken into account. The interest in this case is that CI – between non relativistic configurations – plays an important role, because we are looking at n = 0 transitions. The number of levels is 4694, and the number of transitions is 93,058 (without CI) and 642,482 with CI. Nevertheless, HULLAC is able to compute it all very rapidly. Figure 1 shows the results, assuming LTE for the populations. In the right graph, CI was neglected, and in the left graph, full CI was taken into account. Not only does the array lose its symmetry, but there is a significant shift of around 20 Å towards shorter wavelengths. Clearly, without CI, the identification of the spectrum for diagnostics, or the computation of opacities for simulations would be in error. More details about this computation can be found in [12].
Figure 1. HULLAC spectrum, assuming LTE of Xe8+ , without (left) and with (right) CI. Dots: transitions to 4d10 , lower curve: to 4d9 4f, upper curve: to 4d8 4f2 .
IFSA-2005
975
5. FUTURE EXTENSIONS AND COLLABORATION As mentioned above, there are a number of improvements and extensions that could be implemented in HULLAC. For instance, finding a way to include resonances in DWA for collisions, taking into account line profiles, improving level energies with 2nd order perturbation, etc... For this purpose, we are ready to distribute the code source in exchange for collaboration. Also extensive use of the code and feedback is useful, for it can reveal errors. If you are interested, please contact one of us (M.B.) at
[email protected]. Acknowledgment This work was supported by the USDOE through a grant to the Naval Research Laboratory.
References [1] A. Bar-Shalom, M. Klapisch, and J. Oreg, J. Quant. Spectrosc. Radiat. Transfer 71, 169 (2001). [2] A. Bar-Shalom, J. Oreg, J. F. Seely, U. Feldman, C. M. Brown, B. A. Hammel, R. W. Lee, and C. A. Back, Phys. Rev. E 52, 6686 (1995). [3] A. Bar-Shalom, J. Oreg, and M. Klapisch, J. Quant. Spectrosc. Radiat. Transfer 65, 43 (2000). [4] M. Klapisch, Comput. Phys. Comm. 2, 239 (1971). [5] A. Bar-Shalom, M. Klapisch, and J. Oreg, Phys. Rev. A 38, 1773 (1988). [6] A. Bar-Shalom, M. Klapisch, and J. Oreg, in Atomic Processes in Plasmas, edited by D. R. Schultz, F. W. Meyer and F. Ownby (AIP, Gatlinburg, TN, 2002), Vol. 635, p. 92. [7] E. Koenig, Physica(Utrecht) 62, 393 (1972); I. P. Grant, J. Phys. B (At. Mol.) 7, 1458 (1974). [8] M. Klapisch, Ph. D. Dissertation, Une Nouvelle Methode pour le calcul des fonctions d’onde atomique, University of Paris, Orsay, France (1969). (in French) [9] A. Bar-Shalom and M. Klapisch, Comput. Phys. Comm. 50, 375 (1988). [10] A. Bar-Shalom, M. Klapisch, and J. Oreg, Comput. Phys. Comm. 93, 21 (1996). [11] M. Busquet, M. Klapisch, and A. Bar-Shalom, Bull. Am. Phys. Soc. 49, (8)114 (2004). [12] M. Busquet, J. Quant. Spectrosc. Radiat. Transfer, in the press (2005).
