# FLYCHK

## Contents |

## History

The K-shell spectroscopy code FLY^{[1]} and its predecessors have been employed to study hot dense plasmas for decades. FLY has provided a basis for studies of K-shell ions up to Z=26, where its ease of use, PC application base, and synthetic spectral production have made it attractive to both experimentalists and modelers. However, the application has been focused on K-shell ions where less ionized species are represented as a ground state only.

To predict the ionization and recombination through the less ionized stages, the model was extended to include kinetics models for all ion stages and the code is named as FLYCHK^{[2]}^{[3]}. The code is developed into a straightforward, rapid tool to provide ionization and population distributions of plasmas in zero dimension with accuracy sufficient for most initial estimates and in many cases is applicable for more sophisticated analysis.

Numerous experimental and calculational comparisons performed in recent years show that FLYCHK provides meaningful estimates of ionization distributions for most laboratory applications. Since 2006, the code is available at a password-protected NIST website.

## Code Description

FLYCHK solves rate equations for level population distributions by considering collisional and radiative atomic processes. The code is designed to be straightforward to use and yet is general enough to apply for most laboratory plasmas. Further, it can be applied for low-to-high Z ions in either steady-state or time-dependent situations. Plasmas with arbitrary electron energy distributions, single or multiple electron temperatures can be studied as well as radiation-driven plasmas.

To achieve this versatility and accuracy in a code that provides rapid response we employ schematic atomic structures, scaled hydrogenic cross-sections and read-in tables. It also employs the jj configuration averaged atomic states and oscillator strengths calculated using the Dirac-Hartree-Slater model^{[4]} for spectrum synthesis.

## Limitations and Validity ranges

The goal of FLYCHK development is to provide a simple and general capability for a wider range of plasmas. FLYCHK has evolved as the understanding of atomic processes in plasmas improved. The assumptions in FLYCHK will continously change so that the code will generate the results that are benchmarked in experiments. Unfortunately, the benchmark experiments or calculations are very scarce and the limitations and validity ranges are not entirely checked yet. Here the general trend is outlined and users should apply FLYCHK results at their discretion.

### Charge state distributions

FLYCHK calculations have been benchmarked against more sophisticated NLTE Kinetics code results at NLTE Kinetics workshops and a few of well-characterized experiments. Since this code is applied to a wide range of plasma conditions, it is difficult to give a simple statement on its limitation. However, as a rule of thu
mb, the code is __best suited to highly ionized plasmas__ and intermediate densities out of coronal equilibrium and yet not in the complete LTE state. The results __near the neutral state should NOT be taken seriously__.

Since the code uses an averaged model of atomic states, it predicts the level population distributions within the same hydrogenic configuration to be statistical and hence the state populations excited by the Δn=0 transition are overestimated in the coronal equilibrium. This leads to the small dielectronic recomb ination (DR) rate of M-shell (or N-shell) ions at low temperatures where Δn=0 channels are dominant in DR process. The radiative power loss rates from the bound-bound transitions are also affected when Δn=0 transitions dominate the rates at the coronal equilibrium.

Atomic data for FLYCHK are generated for all elements up to Z=79(Gold): oscillator strength, collisional excitation gaunt factors, photo-ionization cross-sections and autoionization rates with one exception of autoionization rates for ions with more than 60 electrons. For those ions, analytic formula is used to generat e autoionization rates. FLYCHK code has never been validated against ions with more than 60 electrons and it is highly recommended for users to give us feedback on those results.

### Spectral calculations

The original FLY model is implemented in FLYCHK and hence the K-shell spectroscopy analysis using FLYCHK provides a good diagnostic for elements up to z=26 (Iron). The FLY spectral calculations include not only Doppler but also Stark broadening and hence the results can be applied for both line intensity and line shape analysis. For the K-shell ions of elements with z>26, HULLAC atomic data are generated for atomic levels, oscillator strength and collisional excitation rates. Currently, the Stark broadening is not included for the K-shell ions of elements with z>26.

For ions with more than 3 electrons, STA <Super-configuration Transition Array> intensities are employed for a simple and fast calculation. Nevertheless,the K-shell lines such as K-α and K-β are found to give a reasonable result comparable to observations in the short-pulse laser experiments. The non-K-shell spectra give an overall shape of averaged spectral intensities. Users should take caution when applying these averaged spectra for plasma diagnostics.

## References

- ↑
**A time-dependent model for plasma spectroscopy of K-shell emitters**R. W. Lee and J.T. Larsen, Journal of Quantitative Spectroscopy and Radiative Trans fer, Volume 56, October 1996, Page 535-556 - ↑
**FLYCHK: Generalized population kinetics and spectral model for rapid spectroscopic analysis for all elements**, H.-K. Chung, M.H. Chen, W.L. Morgan, Y. Ralchenko and R.W. Lee, High Energy Density Physics, Volume 1, Issue 1, Decembe r 2005, Pages 3-12 - ↑
**FLYCHK: an extension to the K-shell spectroscopy kinetics model FLY**H. -K. Chung, W. L. Morgan and R. W. Lee, Journal of Quantitative Spectroscopy and Radiative Transfer, Volume 81, November 2003, Pages 107-115 - ↑
**Relativistic L-shell Auger and CosterKronig rates and fluorescence yields**M.H. Chen, E. Laiman, B. Casemann, M. Aoyagi and H. Mark, Phys. Rev. A 19 (1979), p. 2253