Interactive system for the interpretation of atomic spectra

Transcription

1 J. Straus, K. Kolacek, V. Bohacek, O. Frolov, V. Prukner, M. Ripa, V. Sember, J. Schmidt, P. Vrba Institute of Plasma Physics AS CR, Za Slovankou 3, P.O. Box 17, Prague 8 D. Klir Faculty of Electrical Engineering of Czech Technical University Technicka 2, Praha 6 Received 29 April 2004 A method described in this paper enables the simplification and specification of the process of interpreting some spectroscopic measurements. Tabulated spectroscopic data are transformed into the form that provides a clear idea of mutual proportions of spectral line intensities of the given element depending on the selected temperature. PACS: Rj, Ye Key words: spectroscopy, soft x ray, spectra interpretation 1 Introduction The system has been developed for the soft X ray spectroscopic diagnostics of the pulse argon capillary discharge [1], but its utilization is broader. A general procedure for interpreting the experimental atomic spectra is based on the idea that the probable presence of various ionization stages is deduced from the predicted temperature. Their tabulated spectrum is then compared with the experimental data. Since more ionization stages correspond to the given temperature, several sets of lines will be present in the spectrum with temperature dependant proportions. If we do not know the temperature precisely enough in advance, the orientation in large number of the compared data can be too difficult. This system enables to simplify the situation as follows. 2.1 Function principle 2 Description of the interactive system Principle of the interactive system functioning is clear from the flow diagram indicated in Fig. 1. The database of tabulated spectroscopic data is stored in the FILE module. The SELECTION 1 module enables to select the required element whose behavior is to be evaluated. The MODEL 1 module contains the program for iterating model calculation of the ion function for all available ionisation stages of the selected atom in dependence on the electron temperature. The temperature can be continuously changed in the SELECTION 2 module. C314 Czechoslovak Journal of Physics, Vol. 54 (2004), Suppl. C

2 The last MODEL 2 module carries out the calculation of radiation intensity for ions with non zero function. SELECTION 1: Element FILE: Element databaze for all available ionization stages SELECTION 2: Electron temperature 50 ev MODEL 1: Calculation of of individual ionization stages MODEL 2: Calculation of line intensities for active ionization stages Fig. 1. Flow diagram of the interactive system. 2.2 Function description to be evaluated are graphically displayed. We select an element whose behavior is to be monitored and into the same graph the system displays its spectral lines transformed into the form corresponding to the selected temperature of the plasma. Now the temperature can be continuously changed. On greater changes in the temperature some lines are disappearing, other ones are emergingdepending mainly on changes in population of various ionization stages of the given element. 3 Applied mathematical models Both applied mathematical models are very simple and just rough approximation to the real status can be expected. Their application enables practical testing of the interactive system and the verification of its benefit. On the other hand, general applicability of these models without relation to specific types of atoms is a great advantage. Nevertheless, probably more realistic models should be used in next versions of the system. Czech. J. Phys. 54 (2004) C315

3 J. Straus et al. 3.1 Model 1 calculation of of individual ionization stages Lets consider a system consisting of P atoms of the element A with N protons. Ionization stages of this atom will be marked with symbols from A1 to AN, where Al represents the neutral atom A with full number of N electrons, A2 means once ionized atom A and AN +1 represents fully ionized state free from all N electrons. Number of i stage ions will be marked by p i symbols. Let us suppose that ions of higher stage originate from ions of the previous stage at ionizing collisions with free electrons with corresponding kinetic energy. Symbol e i will mark the parameter, proportional to number of such electrons in the system. So we will assume that p i+1 = e i p i and together with the condition that the total number of ions of all stages in the system equals P, we get generally N +1 equations for N +1 variables from p 1 to p N+1. Solving this set of equations, we get for the first variable the expression p 1 = P 1 + N i e k i=1 k=1 and the other variables p i can be expressed by the method of successive substitution to the original equations. To calculate the root of these equations we need to know the values of parameters e i, i.e. the numbers of electrons with sufficient energy for relevant ionization. We assume, therefore, that these parameters will be proportional to the value of a definite integral from the energetic Maxwell function of free electrons of the selected electron temperature calculated from the value of the ionization energy of the respective ion to infinity. Furthermore, for the searched parameters e i we assume to be proportional to the total number of electrons in the system. On the assumption of plasma quasi neutrality, this number can be easily expressed on the basis of the given of ionization stages. Since this is, however, just what we want to calculate, to keep the transparency of the whole solution, nothing else remains, but to use the iteration method that with a small restriction at low temperatures reliably converges. Considering the required computing speed a linear interpolation in numerically calculated chart was used to figure out the integral from the Maxwell function. 3.2 Model 2 calculation of line intensities for active ionization stages Description of model 2 comes from the description of the system we dealt with in model 1. The radiation intensity of the spectral line corresponding to the transition from level i to level j is E ij = k A ij n i λ ij where k is constant, A ij is Einstein coefficient, n i is the number of electrons ready in the excited state i and λ ij is the wavelength. The task of this model is to define C316 Czech. J. Phys. 54 (2004)

4 n i values for all lines. Lets assume that n i is proportional to the number of ions of respective ionization stage p k and to the number of free electrons e i, with the kinetic energy at least equal to the excitation energy. The e i value is calculated as a product of the number of all free electrons e and a definite integral from the energetic Maxwell function, this time within excitation energy value of respective excited state and infinity, on the selected temperature of electrons. 4 Example of interactive systems application We will try to demonstrate a basic application of the interactive system to the analysis of data obtained from the flat field spectroscope (working scope from 10 nm to 60 nm) representing the soft X ray spectrum of pulse argon capillary discharge [1]. We will select an element, in this case argon and set the electron temperature at the minimal value 15 ev. In the upper part of Fig. 2, on the bar graph of 15 ev Fig. 2. View of the control panel for at the temperature 15 ev. the actual ionization stages, we can see high representation of the 3 ionization stage, lower of 2 and 4 ionization stages, and minimum of 1 and 5 ionization stages. We can state that although the configuration of displayed lines is roughly copying the experimental curve, with regard to a regularly reached accuracy of measurement this resemblance is not accurate enough. We increase the temperature gradually, observing the changing configuration of lines and compare this pattern with the experimental curve. Fig. 3 shows the situation at temperature 30 ev. In its upper part we can see that ionization stages from 4 to 9 occur and ionization stage 7 prevails. The line configuration has considerably changed lines of lower wavelength have appeared, but again their pattern do not satisfactorily matches the shape of the experimental curve. Even if the line of 26 nm Czech. J. Phys. 54 (2004) C317

5 J. Straus et al. 30 ev Fig. 3. View of the control panel for at the temperature 30 ev. 32 ev Fig. 4. View of the control panel for at the temperature 32 ev. wavelength corresponds to the local maximum of the curve, we cannot be satisfied, because there is another line of 29 nm, very high and the experimental curve shows no corresponding maximum. Situation changes at temperature 32 ev in Fig. 4. The line at 26 nm begins to be greater than that at 29 nm and the rest of the configuration is plausible. This is valid up to the temperature of 78 ev in Fig. 5, with C318 Czech. J. Phys. 54 (2004)

6 78 ev Fig. 5. View of the control panel for at the temperature 78 ev. 90 ev Fig. 6. View of the control panel for at the temperature 90 ev. the highest representation of 9 and occurrence of 7 to 11. When the temperature reach above 78 ev, the line of 17 nm is prevailing without corresponding maximum on the experimental line. It is demonstrated in Fig. 6, where the situation at the temperature 90 ev is depicted. In this way we have gained two pieces of information; it has been found out that within the used models the experimental Czech. J. Phys. 54 (2004) C319

7 J. Straus et al.: Interactive system for the interpretation of atomic spectra spectrum is likely to correspond to the temperature between 32 ev and 78 ev, and one line of 36 nm was identified. This is triplet 2D 2F* transition 2p6.3d2 p6.4f of ion 8 with wavelengths nm, nm and nm. To obtain more information regarding argon it seems to be inevitable to supply some further argon lines to the working database. In addition, it is possible to add another element that can be assumed to be present in the given experimental volume and try to verify, if its lines improve at some temperature agreement between pattern of all considered spectral lines and the experimental curve. 5 Discussion As the next step a verification of the accuracy and limits of used mathematical models should be done. For the improvement of these models, it would be suitable, among other things, put in the temperature dependence into the ionization and excitation cross sections, to include the ion to ion collisions, to consider more precisely the plasma density influence etc. As far as the experimental spectra are concerned, they should be preliminarily evaluated which would involve the verification of the spectroscope calibration constants and the data analyzes considering the background level and signal to noise ratio. 6 Conclusions There was designed, realized and tested a special method, making the process of spectroscopic data interpretation simpler and better arranged. The described method is helpful in the case, when it is to determine a presence of chemical elements, their ionization stages and electron temperature of the plasma source. The theoretical part of this work was supported by Ministry of Education, Youth and Sports of the Czech Republic under Grant 1P2004LA235 and the software development by the Grant Agency of Czech Republic under Grant 2002/03/0711. References [1] K. Kolacek, J. Schmidt, V. Bohacek, M. Ripa, P. Vrba, O. Frolov, A. Jancarek and M. Vrbova, Dominating spectral line at the Wavelength of laser transition in X ray spectrum of the fast gas filled capillary discharge, 20 th Symp. Plasma Physics and Technology, June 10-13, 2002, Prague, Czech Rep., in Proc. 20 th Symp. Plasma Physics and Technology, SPPT 2002, Czechoslov. J. Phys., 52, Suppl. D, D199 D204, Eds. P. Kulhanek, D. Bren, J. Pasek, P. Brichnac, J. Hofman, J. Pichal, (2002) ISSN C320 Czech. J. Phys. 54 (2004)