Valeriy Sysun, Alexander Sysun, Vladimir Ignakhin^*, Viktor Titov, Alexander Tikhomirov

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Department of Physical Engineering, Petrozavodsk State University, Petrozavodsk, Russia.
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Abstract: The main ion-atomic collision treatment methods based on Monte-Carlo simulation are considered and discussed. We have proposed an efficient scheme for simulation of time between collisions taking into account cross-section dependence on ion velocity and random generation of ion velocities and scattering angles after collisions. The developed algorithm of simulation of interval between collisions takes into account the change of relative velocity of ion-atom pair as well as the change of cross-section of collision and atomic concentration. At the same time, unlike the widely used “null-collision” method, both the probability of collision and change of particles’ state which determines this probability are taken into consideration for each particle independently in time. The simulation results according to the techniques proposed are found to be close to the theoretical values of ion drift velocities. It is revealed that the “null-collision” method results in exceeding of drift velocity in strong and intermediate fields. At the same time the proposed method of accumulation of probability under the same conditions gives values close to theoretical ones. In weak fields calculated values of drift velocity in both methods exceed theoretical values to some small extent.

Keywords: PIC-MC Simulation, Ion-Atomic Collisions, Discharge Plasma

Cite this paper: Sysun, V. , Sysun, A. , Ignakhin, V. , Titov, V. and Tikhomirov, A. (2014) Comparison of Simulation Methods of Ion-Atomic Collisions in PIC-MC. Journal of Applied Mathematics and Physics, 2, 1233-1241. doi: 10.4236/jamp.2014.213144.

References

[1]   Birdsall, C.K. (1991) Particle-in-Cell Charged-Particle Simulations, plus Monte Carlo Collisions with Neutral Atoms, PIC-MCC. IEEE Transactions on Plasma Science, 19, 65-85.
http://dx.doi.org/10.1109/27.106800

[2]   Vahedi, V. and Surendra, M. (1995) A Monte Carlo Collision Model for the Particle-in-Cell Method: Applications to Argon and Oxygen Discharges. Computer Physics Communications, 87, 179-198.
http://dx.doi.org/10.1016/0010-4655(94)00171-W

[3]   Zobnin, A.V., Nefedov, A.P., Sinel’Shchikov, V.A. and Fortov, V.E. (2000) On the Charge of Dust Particles in a Low-Pressure Gas Discharge Plasma. Journal of Experimental and Theoretical Physics, 91, 483-487.
http://dx.doi.org/10.1134/1.1320081

[4]   Cenian, A., Chernukho, A., Bogaerts, A., Gijbels, R. and Leys, C. (2005) Particle-in-Cell Monte Carlo Modeling of Langmuir Probes in an Ar Plasma. Journal of Applied Physics, 97, Article ID: 123310.
http://dx.doi.org/10.1063/1.1938275

[5]   Sysun, A.V., Sysun, V.I., Khakhaev, A.D. and Shelestov, A.S. (2008) Charge and Potential of a Dust Grain versus the Intergrain Distance and Establishment of the Latter in a Low-Pressure Plasma. Plasma Physics Reports, 34, 501-507.
http://dx.doi.org/10.1134/S1063780X08060068

[6]   Sysun, V.I. and Ignakhin, V.S. (2014) Simulations of the Ion Current to a Probe in Plasma with Allowance for Ionization and Ion-Neutral Collisions: I. Spherical Probe. Plasma Physics Reports, 40, 101-109.
http://dx.doi.org/10.1134/S1063780X14010097

[7]   Kim, H.C., Iza, F., Yang, S.S., Radmilovic-Radjenovic, M. and Lee, J.K. (2005) Particle and Fluid Simulations of Low-Temperature Plasma Discharges: Benchmarks and Kinetic Effects. Journal of Physics D: Applied Physics, 38, Article ID: R283.
http://dx.doi.org/10.1088/0022-3727/38/19/R01

[8]   Vaulina, O.S., Repin, A.Y. and Petrov, O.F. (2006) Empirical Approximation for the Ion Current to the Surface of a Dust Grain in a Weakly Ionized Gas-Discharge Plasma. Plasma Physics Reports, 32, 485-488.
http://dx.doi.org/10.1134/S1063780X06060055

[9]   Simek, J. and Hrach, R. (2006) Comparison of Collision Treatment Methods in PIC-MC Plasma Simulation. Czechoslovak Journal of Physics, 56, B1086-B1090.
http://dx.doi.org/10.1007/s10582-006-0331-z

[10]   May, P.W., Field, D. and Klemperer, D.F. (1992) Modeling Radio-Frequency Discharges: Effects of Collisions upon Ion and Neutral Particle Energy Distributions. Journal of Applied Physics, 71, 3721-3730.
http://dx.doi.org/10.1063/1.350882

[11]   Nanbu, K. and Kitatani, Y. (1995) An Ion-Neutral Species Collision Model for Particle Simulation of Glow Discharge. Journal of Physics D: Applied Physics, 28, 324.
http://dx.doi.org/10.1088/0022-3727/28/2/015

[12]   Boeuf, J.P. and Marode, E. (1982) A Monte Carlo Analysis of an Electron Swarm in a Nonuniform Field: The Cathode Region of a Glow Discharge in Helium. Journal of Physics D: Applied Physics, 15, 2169.
http://dx.doi.org/10.1088/0022-3727/15/11/012

[13]   Skullerud, H.R. (1968) The Stochastic Computer Simulation of Ion Motion in a Gas Subjected to a Constant Electric Field. Journal of Physics D: Applied Physics, 1, 1567.
http://dx.doi.org/10.1088/0022-3727/1/11/423

[14]   Maiorov, S.A. (2009) Ion Drift in a Gas in an External Electric Field. Plasma Physics Reports, 35, 802-812.
http://dx.doi.org/10.1134/S1063780X09090098

[15]   McDaniel, E.W. and Mason, E.A. (1973) Mobility and Diffusion of Ions in Gases. Wiley, New York.

[16]   Smirnov B.M. (2008) The Sena Effect. Physics-Uspekhi, 51, 291-293.
http://dx.doi.org/10.1070/PU2008v051n03ABEH006542