The Third Non-LTE (Local Thermodynamic Equilibrium) Kinetics Workshop (NLTE-3)

 

December 1-5, 2003

NIST, Gaithersburg MD

 

 

Submission of Calculations

 

 

This document is intended to define the particulars of the workshop submissions. In the sections below, we will define the case problems, the comparison quantities which we require, and the detailed format of the data files which we will be expecting. The case problems are of two types:  steady-state and time-dependent. These problems are completely defined by a specification of the electron temperature and electron or ion density. For the time-dependent cases, these quantities are provided as a time history. With the large number of case studies included in these two categories, we have avoided additional variations on the general NLTE problem, i.e. we specifically request that there be no consideration of optical depth, radiative transfer, or heavy-particle interactions. (The non-Maxwellian electron effects, however, are included in one of the cases.)  These interesting topics are best deferred to later meetings.

 

An ftp/http server will be set up early summer 2003 to serve our needs for this workshop, and an email containing the relevant details will be distributed among the potential participants. Although the specific data transfer mode is still under consideration (ftp uploading being the primary candidate), it would be most convenient if the contributor created an archive file containing all the individual result files. Submissions employing such data compression techniques as zip/gzip/bzip2/arj/lha/rar along with the Unix tar archiving utility will be accepted. Please contact Yuri Ralchenko (email: yuri.ralchenko@nist.gov) if other compression/archiving options are necessary. An example submission file will be provided on the ftp server for comparisons.

 

Timeline:

 

1. June  2003 – web server is set up
2. October 1 2002 – submission deadline
3. December 1 2003 – workshop opens
4. December 5 2003 – workshop closes

 

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I.       STATEMENT OF STEADY-STATE CASES

 

Notations: electron temperature T_e, electron density N_e, ion density N_i, hot electron temperature T_hot, radiation field temperature T_rad 

We have selected a number of atoms to consider, and for each atom are requesting results on a grid of electron temperatures and electron or ion (for the Xe case only) densities.  In the following, temperatures are given in eV (1 eV = 1.602 176 462 · 10^-19 J) and particle densities in cm^-3. 

 

The following problems have been established for the steady-state cases:

 

 

 

 

                        Table I.  Steady-state case definitions.

 

The grid of plasma temperatures and densities is given in Table I. If your calculation requires an ion temperature, then you should assume it is identical to the electron temperature.

 

In case of argon calculations, 10% of the hot electrons means 10% of the total electron density given by N_e. Thus, for instance, for N_e = 10¹⁸ cm^-3 the density of hot electrons would be 10¹⁷ cm^-3 while the density of the bulk thermal electrons would be 9×10¹⁷ cm^-3. The hot electrons are to be presented as a second Maxwellian with the temperature of 10 000 eV.

 

Each calculation will be referenced by a case name, which is to be given in the submissions data file (as described further below). The case name is constructed by appending a suffix to the Case_ID shown in the preceding table. The suffix consists of a digit, a letter and, for Ar and GeTr cases only, a digit. The first digit identifies the problem temperature, while the letter indicates the electron density. For the Ar case, the final digit is 1 for 0% of hot electrons and 2 for 10% of hot electrons. For the GeTr case, the final digit is 1, 2 or 3 for T_rad = T_e/2, T_e or 300, respectively. Thus, the case name Al3b refers to the third temperature and second density of the aluminum steady-state grid, namely 100 eV and 10²² cm^-3. The name GeTr4a2 refers to germanium at T_e = 600 eV, N_e = 3×10²² cm³, and T_rad = T_e.

 

The quantities to be computed for each case are described below. The Xe case additionally requires calculation of emission spectra. The emissivity of the xenon plasma is to be calculated in the wavelength range of 9-120 Å[1].

 

In all the above cases, the calculations are to be solved in steady-state, at the specified electron densities and temperatures. In all but the GeTr cases the radiation field should be zero − only spontaneous radiative decays and radiative recombination shall be included –  while for the GeTr case we request the photoinduced processes (photoionization, photoexcitation, stimulated emission, etc.) to be added as well.

 

For both steady-state and time-dependent cases the submissions file should be named as <case>.<contributor_name>.<code_name>, so that Dr. A. Einstein’s calculations for one of the hot-electron cases in Argon with his code GTOE would be in the file ar2c2.einstein.gtoe (case insensitive).

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II.                 JUSTIFICATIONS OF THE STEADY-STATE CASES

 

1. C

 

Since the NLTE-1 comparisons for carbon cases have shown quite a good agreement for lower densities of 10¹⁶ and 10²⁰ cm^-3, here we would like to study the highest-density case for which the codes produced the mostly divergent results.

 

2. Al

 

Aluminum cases for NLTE-1 have showed a wide spread for temperatures below 200 eV and all densities. Correspondingly, the number of low-T_e points is increased here.

 

3. Ar

 

For argon, a rather good agreement was found in NLTE-1, mostly since the high temperatures shift the ion distribution towards He- and H-like ions. Here we, first, add lower temperatures and second, ask for calculations with hot electrons.

 

4. Ge

 

To move the comparisons toward higher atomic number we have attempted to take cases motivated by experiment. Thus we choose this Ge (Z=32) steady-state case to provide further information on the same T_e and N_e range that is used in the TD-Ge case which was motivated schematically by the transient collisional laboratory X-ray laser scheme. We have done this in the hopes of a) reducing the number of kinetics models that need to be constructed and b) providing further insight in the TD-Ge case.

 

5. GeTr

 

To test the various aspects of the code with respect to radiation fields we have taken the simplest form of the problem.  That is, we impose a Planckian radiation field at the specified radiation temperature T_rad.

 

6.      Xe

 

This is the most “experiment-related” case inspired by the recent both published (Phys. Rev. E 65, 046418, 2002) and yet unpublished measurements by C. Chenais-Popovics et al. The measurements were aimed “…at validating recent calculation techniques for the emission properties of medium- and high-Z multicharged ions in hot plasmas." The fundamental plasma parameters, such as electron temperature, electron density and average charge state, were deduced from electronic and ionic Thomson scattering spectra, so that the calculated spectra could be directly compared to experimental data.

 

7. Au

 

Here we would like to explore the rapid changes in ion distribution which seems to strongly depend not only on T_e but on N_e as well.

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III.       STATEMENT OF TIME-DEPENDENT CASES

 

Three simple cases have been defined by temperature and density histories:

 

TD-C            Impurity transport in a reversed-field pinch.

TD-Ar           Implosion of argon plasma in a capillary discharge.

TD-Ge         Germanium X-ray laser plasma.

 

For all time-dependent cases the time grid is linear starting from t = 0. The exact time grids as well as the electron temperature and density histories for each case are provided in the Appendix. The calculated data are to be provided at each time step.

 

We would like to emphasize that although the proposed cases are motivated by some particular experiments, the presented time histories are not necessarily identical to those determined in various measurements. This was done intentionally in order to enhance some or to diminish other physical processes taking place in the plasmas.

 

The TD-C case of the NLTE-1 was devoted to recombination of high-density plasma of carbon. Here we propose a low-density case which is related to the reversed-field pinch experiment. The impurity emission during its transport across the experimental device is widely used for diagnostics of this type of plasma. The major process here is also recombination although at a much lower density. The electron temperature and density are presented in Fig. 1. This calculation should be carried out to t = 200 ms. The initial condition is that all the population is in the bare ion. Output should be provided at t = 0 and thereafter at 40 uniformly spaced times spanning the range 5 to 200 ms.  The intensities of the Ly_α and He_α (W) and intercombination (Y) lines in C V and C VI are requested as well.

 

The TD-Ar case is inspired by the implosion of argon inside capillary discharge used in the studies of the collisional X-ray laser. However, the N_e and T_e are, correspondingly, lower and higher than those in the X-ray laser capillaries. For this case all population at time t=0 is in the ground state of Ar VI or, only if Ar VI is not included in the model, in the ground state of the lowest-charge ion. The history of the electron temperature and density is presented in Fig. 2; the calculation should be carried out to t = 50 ns.

 

In Figure 3 we show the time history of T_e (left hand axis) and N_e (right hand axis) for the TD-Ge case, which is motivated by the germanium X-ray laser experiments. This calculation should be carried out to t = 1.975 ns, and the non-uniform time grid along with the corresponding values of T_e and N_e are presented in the Appendix.  The initial condition is LTE. 

 

Case	Initial Condition	# Output Times	Output Δ	Stop Time