Three-Dimensional Simulations with Fields and Particles in Software and Inflector Designs


Particles and fields represent two major modeling paradigms in pure and applied science at all. In this paper a methodology and some of the results for three-dimensional (3D) simulations that include both field and particle abstractions are presented. Electromagnetic field calculations used here are based on the discrete differential form representation of the finite elements method, while the Monte Carlo method makes foundation of the particle part of the simulations. The first example is the simulation of the feature profile evolution during SiO2 etching enhanced by Ar + /CF4 non-equilibrium plasma based on the sparse field method for solving level set equations. Second example is devoted to the design of a spiral inflector which is one of the key devices of the axial injection system of the VINCY Cyclotron.

Share and Cite:

B. Radjenović, M. Radmilović-Radjenović and P. Beličev, "Three-Dimensional Simulations with Fields and Particles in Software and Inflector Designs," Journal of Software Engineering and Applications, Vol. 6 No. 8, 2013, pp. 390-395. doi: 10.4236/jsea.2013.68048.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] G. C. Birdsall and A. Langdon, “Plasma Physics via Computer Simulation,” McGraw-Hill, New York, 1985.
[2] Fltk.
[3] Vtk.
[4] Pthreads.
[5] A. Bossavit, “Computational Electromagnetism,” Academic Press, Boston, 1998.
[6] K. Warnick, R. Selfridge and T. Arnold, “Teaching Electromagnetic Field Theory Using Differential Form,” IEEE Transactions on Education, Vol. 40, No. 1, 1997, pp. 53-68. doi:10.1109/13.554670
[7] C. Geuzaine, “High Order Hybrid Finite Element Schemes for Maxwell’s Equations Taking Thin Structures and Global Quantities into Account,” Ph.D. Thesis, Universite de Liege, Liege, 2001.
[8] GetDP.
[9] TetGen.
[10] J. Sethian, “Level Set Methods and Fast arching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision and Materials Sciences,” Cambridge University Press, Cambridge, 1998.
[11] S. Osher and R. Fedkiw, “Level Set Method and Dynamic Implicit Surfaces,” Springer, New York, 2002.
[12] L. Evans, “Partial Differential Equations,” American Mathematical Society, Providence, 1998.
[13] R. Whitaker, “A Level-Set Approach to 3D Reconstruction From Range Data,” International Journal of Computer Vision, Vol. 29, No. 3, 1998, pp. 203-231. doi:10.1023/A:1008036829907
[14] Insight Segmentation and Registration Toolkit.
[15] B. Radjenovic, J. K. Lee and M. Radmilovic-Radjenovic, “Sparse Field Level Set Method for Non-Convex Hamiltonians in 3D Plasma Etching Profile Simulations,” Computer Physics Communications, Vol. 174, No. 2, 2006, pp. 127-132. doi:10.1016/j.cpc.2005.09.010
[16] M. Lieberman and A. Lichtenberg, “Principles of Plasma Discharges and Materials Processing,” John Wiley & Sons, Inc., Hoboken, 1994.
[17] C. K. Birdsall, “Particle-in-Cell Charged-Particle Simulations, Plus Monte Carlo Collisions with Neutral Atoms,” IEEE Transactions on Plasma Science, Vol. 19, No. 2, 1991, pp. 65-85. doi:10.1109/27.106800
[18] J. P. Verboncoeur, M. V. Alves, V. Vahedi and C. Birdsall, “Simultaneous Potential and Circuit Solution for 1D Bounded Plasma Particle Simulation Codes,” Journal of Computational Physics, Vol. 104, No. 2, 1993, pp. 321-328. doi:10.1006/jcph.1993.1034
[19] H. C. Kim, F. Iza, S. S. Yang, M. Radmilovic-Radjenovic and J. K. Lee, “Particle and Fluid Simulations of LowTemperature Plasma Discharge: Benchmarks and Kinetic Effects,” Journal of Physics D: Applied Physics, Vol. 38, No. 19, 2005, pp. R283-R301. doi:10.1088/0022-3727/38/19/R01
[20] B. Radjenovic and J. K. Lee, “3D Feature Profile Evolution Simulation for SiO2 Etching in Fluorocarbon Plasma,” Proceeding of the XXVIIth ICPIG, Eindhoven, 18-22 July 2005.
[21] G. Hwang and K. Giapis, “On the Origin of the Notching Effect during Etching in Uniform High Density Plasmas,” Journal of Vacuum Science and Technology, Vol. B15, No. 1, 1997, pp. 70-87.
[22] A. Mahorowala and H. Sawin, “Etching of Polysilicon in Inductively Coupled Cl2 and HBr Discharges. IV. Calculation of Feature Charging in Profile Evolution,” Journal of Vacuum Science and Technology, Vol. B20, No. 3, 2002, pp. 1084-1095.
[23] H. S. Park, S. J. Kim, Y. Q. Wu and J. K. Lee, “Effects of Plasma Chamber Pressure on the etching of Micro Structures in SiO2 with the Charging Effects,” IEEE Transactions on Plasma Science, Vol. 31, 2003, pp. 703-710. doi:10.1109/TPS.2003.815245
[24] N. Neskovic, et al., “Status Report on the VINCY Cyclotron,” Nukleonika, Vol. 48, 2003, pp. S135-S139.
[25] W. B. Powell and B. L. Reece, “Injection of Ions into a Cyclotron from an External Source,” Nuclear Instruments and Methods, Vol. 32, No. 2, 1965, pp. 325-332. doi:10.1016/0029-554X(65)90531-8
[26] J. L. Belmont and J. L. Pabot, “Study of Axial Injection for the Grenoble Cyclotron,” IEEE Transactions on Nuclear Sciences, Vol. NS-13, 1966, pp. 191-193. doi:10.1109/TNS.1966.4324204
[27] R. W. Müller, “Novel Inflectors for Cyclic Accelerators,” Nuclear Instruments and Methods, Vol. 54, 1967, pp. 29-41. doi:10.1016/S0029-554X(67)80004-1

Copyright © 2024 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.