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.

[1]  J. Belmont,et al.  Study of Axial Injection for the Grenoble Cyclotron , 1966 .

[2]  Ross T. Whitaker,et al.  A Level-Set Approach to 3D Reconstruction from Range Data , 1998, International Journal of Computer Vision.

[3]  C. Birdsall,et al.  Plasma Physics via Computer Simulation , 2018 .

[4]  Hyunchul Kim,et al.  Particle and fluid simulations of low-temperature plasma discharges: benchmarks and kinetic effects , 2005 .

[5]  P. Belicev,et al.  Status report of the VINCY Cyclotron , 2003 .

[6]  G. M.,et al.  Partial Differential Equations I , 2023, Applied Mathematical Sciences.

[7]  James A. Sethian,et al.  Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid , 2012 .

[8]  Charles K. Birdsall,et al.  Particle-in-cell charged-particle simulations, plus Monte Carlo collisions with neutral atoms, PIC-MCC , 1991 .

[9]  R. W. Müller Novel inflectors for cyclic accelerators , 1967 .

[10]  Jae Koo Lee,et al.  Sparse field level set method for non-convex Hamiltonians in 3D plasma etching profile simulations , 2006, Comput. Phys. Commun..

[11]  Karl F. Warnick,et al.  Teaching Electromagnetic Field Theory Using Differential Forms , 1997, Teaching Electromagnetics.

[12]  Arpan P. Mahorowala,et al.  Etching of polysilicon in inductively coupled Cl2 and HBr discharges. IV. Calculation of feature charging in profile evolution , 2002 .

[13]  K. Giapis,et al.  On the origin of the notching effect during etching in uniform high density plasmas , 1997 .

[14]  S. Kim,et al.  Effects of plasma chamber pressure on the etching of micro structures in SiO/sub 2/ with the charging effects , 2003 .

[15]  J. Sethian Level set methods : evolving interfaces in geometry, fluid mechanics, computer vision, and materials science , 1996 .

[16]  W. B. Powell,et al.  INJECTION OF IONS INTO A CYCLOTRON FROM AN EXTERNAL SOURCE , 1965 .

[17]  A. Lichtenberg,et al.  Principles of Plasma Discharges and Materials Processing , 1994 .

[18]  Christophe Geuzaine,et al.  High order hybrid finite element schemes for Maxwell's equations taking thin structures and global quantities into account , 2001 .

[19]  John P. Verboncoeur,et al.  Simultaneous potential and circuit solution for 1D bounded plasma particle simulation codes , 1990 .

[20]  Thomas Rylander,et al.  Computational Electromagnetics , 2005, Electronics, Power Electronics, Optoelectronics, Microwaves, Electromagnetics, and Radar.

[21]  Ronald Fedkiw,et al.  Level set methods and dynamic implicit surfaces , 2002, Applied mathematical sciences.