In plasma fluid simulations, data of electron swarm parameters (e.g., mobility and diffusion constant) and reaction rate constants must be prepared in advance, depending on the gas species, its reaction model, pressure, etc. In addition to the conventional method that assumes the Maxwell or Druyvesteyn distribution for electron velocity distribution function (EVDF), we often use a method based on a realistic EVDF obtained by solving the Boltzmann equation using the electron collisional cross section data. In this method, the table data (lookup table: LUT) of the swarm parameters calculated from the EVDF are reffered to during the calculation. It is very important to use a proper EVDF for reliable plasma simulations.

For the calculation methods of EVDF (i.e, solution methods of the Boltzmann equation), there are several methods such as two-term approximation method, Monte Carlo method (MC), and propagator method (PM). There are well-known two-term approximation programs such as BOLSIG+ and LoKI-B. For the MC programs, Magboltz, METHES, and LoKI-MC are known. The MC and the PM are known as exact solution methods. The PM is characterized by higher calculation accuracy than the two-term approximation method and a faster calculation speed than the MC. For details about the PM, please refer to this paper (a PDF e-print of author's version is available here at the HUSCAP collection of Hokkaido University Library).

Prof. Sugawara of Hokkaido University has developed a PM computer code and demonstrated that it can achieve the same accuracy as the MC. However, it was impractical to use for multiple gas species (gas mixture) and to prepare a LUT for plasma models.

With the help of Prof. Sugawara, we have extended the calculation code to be more versatile and developed a graphical user interface (GUI). A newly developed improved calculation method has also been included. This new computer program has been named BOSPROM^® (BOltzmann Solver by PROpagator Method). With this new tool, the LUT for plasma simulations is easily created.

The following is an overview of BOSPROM.

Figure 1 shows the importance of a reliable EVDF in plasma fluid modelings.

Fig. 1

Figure 2 shows methods to solve the Boltzmann equation, where the propagator method is spotlighted.

Fig. 2

Figure 3 shows features of BOSPROM.

Fig. 3

Figure 4 shows the cross section data handling panel of BOSPROM. The free software GNUPLOT is used as a graphical viewer.

Fig. 4

Figure 5 shows an example of the BOSPROM's calculation condition setting panel and calculation convergence status.

Fig. 5

Figure 6 shows an example of the results viewing panel of BOSPROM.

Fig. 6

Figure 7 shows a list of parameters that can be vizualized on the graph.

Fig. 7

Figure 8 shows an example of the oscillating EEDF (electron energy distribution function), EEPF (electron energy probability function), and EVDF (electron velocity distribution function) under the RF (13.56 MHz) electric field in Ar gas.

Fig. 8

Figure 9 shows an example of the BOSPROM's lookup-table creating panel for plasma simulation.

Fig. 9

* Actual calculation examples will be added soon.

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