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Enhanced biDimensional pIc: an electrostatic/magnetostatic particle-in-cell code for plasma based systems

  • G. Gallina (a1) (a2), M. Magarotto (a3) (a4), M. Manente (a5) and Daniele Pavarin (a3) (a4) (a5)

Abstract

EDI (enhanced biDimensional pIc) is a two-dimensional (2-D) electrostatic/magnetostatic particle-in-cell (PIC) code designed to optimize plasma based systems. The code is built on an unstructured mesh of triangles, allowing for arbitrary geometries. The PIC core is comprised of a Boris leapfrog scheme that can manage multiple species. Particle tracking locates particles in the mesh, using a fast and simple priority-sorting algorithm. A magnetic field with an arbitrary topology can be imposed to study the magnetized particle dynamics. The electrostatic fields are then computed by solving Poisson’s equation with a a finite element method solver. The latter is an external solver that has been properly modified in order to be integrated into EDI. The major advantage of using an external solver directly incorporated into the EDI structure is its strong flexibility, in fact it is possible to couple together different physical problems (electrostatic, magnetostatic, etc.). EDI is written in C, which allows the rapid development of new modules. A big effort in the development of the code has been made in optimization of the linking efficiency, in order to minimize computational time. Finally, EDI is a multiplatform (Linux, Mac OS X) software.

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Corresponding author

Email address for correspondence: magamir91@gmail.com

References

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Anderson, D., Fedele, R. & Lisak, M. 2001 A tutorial presentation of the two stream instability and Landau damping. Amer. J. Phys. 69 (12), 12621266.
Balay, S.2001 Petsc official web site. https://www.mcs.anl.gov/petsc/, accessed: 2018-09-19.
Barber, C. B., Dobkin, D. P., Dobkin, D. P. & Huhdanpaa, H. 1996 The quickhull algorithm for convex hulls. ACM Trans. Math. Softw. (TOMS) 22 (4), 469483.
Birdsall, C. K. & Langdon, A. B. 2004 Plasma Physics via Computer Simulation. CRC Press.
Bittencourt, J. A. 2013 Fundamentals of Plasma Physics. Springer Science & Business Media.
Bossavit, A. 1998 Computational Electromagnetism: Variational Formulations, Complementarity, Edge Elements. Academic.
Brieda, L.2005 Development of the draco es-pic code and fully-kinetic simulation of ion beam neutralization. PhD thesis, Virginia Tech.
Bukowski, J., Graves, D. & Vitello, P. 1996 Two-dimensional fluid model of an inductively coupled plasma with comparison to experimental spatial profiles. J. Appl. Phys. 80 (5), 26142623.
Buneman, O. 1959 Dissipation of currents in ionized media. Phys. Rev. 115 (3), 503.
Cardinali, A., Melazzi, D., Manente, M. & Pavarin, D. 2014 Ray-tracing WKB analysis of Whistler waves in non-uniform magnetic fields applied to space thrusters. Plasma Sources Sci. Technol. 23 (1), 015013.
Carlsson, J., Manente, M. & Pavarin, D. 2009 Implicitly charge-conserving solver for Boltzmann electrons. Phys. Plasmas 16 (6), 062310.
Che, H. 2016 Electron two-stream instability and its application in solar and heliophysics. Modern Phys. Lett. A 31 (19), 1630018.
Che, H., Drake, J., Swisdak, M. & Goldstein, M. 2013 The adiabatic phase mixing and heating of electrons in Buneman turbulence. Phys. Plasmas 20 (6), 061205.
Chen, F. F. 1984 Introduction to Plasma Physics and Controlled Fusion, 2nd edn. Plenum.
Chen, F. F. 1991 Plasma ionization by helicon waves. Plasma Phys. Control. Fusion 33 (4), 339.
Colella, P. & Norgaard, P. C. 2010 Controlling self-force errors at refinement boundaries for amr-pic. J. Comput. Phys. 229 (4), 947957.
D’Agostini, G. 2003 Bayesian Reasoning in Data Analysis: A Critical Introduction. World Scientific.
Damyanova, M., Sabchevski, S. & Zhelyazkov, I. 2010 Pre-and post-processing of data for simulation of gyrotrons by the gyreoss software package. J. Phys.: Conf. Ser. 207 (1), 012032.
Dawson, J. 1962 One-dimensional plasma model. Phys. Fluids 5 (4), 445459.
Dular, P. & Geuzaine, C.2016 GetDP reference manual: the documentation for GetDP, a general environment for the treatment of discrete problems. http://getdp.info, accessed: 2018-09-19.
Dular, P., Henrotte, F., Robert, F., Genon, A. & Legros, W. 1997 A generalized source magnetic field calculation method for inductors of any shape. IEEE Trans. Magn. 33 (2), 13981401.
Fabris, A. L., Young, C. V., Manente, M., Pavarin, D. & Cappelli, M. A. 2015 Ion velocimetry measurements and particle-in-cell simulation of a cylindrical cusped plasma accelerator. IEEE Trans. Plasma Sci. 43 (1), 5463.
Fehske, H., Schneider, R. & Weiße, A. 2007 Computational Many-Particle Physics. Springer.
Fonseca, R. A., Silva, L. O., Tsung, F. S., Decyk, V. K., Lu, W., Ren, C., Mori, W. B., Deng, S., Lee, S., Katsouleas, T. et al. 2002 Osiris: a three-dimensional, fully relativistic particle in cell code for modeling plasma based accelerators. In International Conference on Computational Science, pp. 342351. Springer.
Geuzaine, C. 2007 Getdp: a general finite-element solver for the de rham complex. In PAMM: Proceedings in Applied Mathematics and Mechanics, vol. 7, pp. 10106031010604. Wiley Online Library.
Geuzaine, C. & Remacle, J. F. 2009 Gmsh: a three-dimensional finite element mesh generator with built-in pre- and post-processing facilities. Intl J. Numer. Meth. Engng 79 (11).
Ghorbanalilu, M., Abdollahzadeh, E. & Rahbari, S. E. 2014 Particle-in-cell simulation of two stream instability in the non-extensive statistics. Laser Part. Beams 32 (3), 399407.
Girault, V. & Raviart, P.-A. 2012 Finite element methods for Navier–Stokes equations: theory and algorithms. Springer Science & Business Media.
Haselbacher, A., Najjar, F. M. & Ferry, J. P. 2007 An efficient and robust particle-localization algorithm for unstructured grids. J. Comput. Phys. 225 (2), 21982213.
Hockney, R. W. & Eastwood, J. W. 1988 Computer Simulation Using Particles. CRC Press.
Hu, Y.2016 Particle in cell simulation. http://theory.ipp.ac.cn/yj/, accessed: 2018-09-19.
Inan, U. S. & Gołkowski, M. 2010 Principles of Plasma Physics for Engineers and Scientists. Cambridge University Press.
Jacobs, G. & Hesthaven, J. S. 2006 High-order nodal discontinuous Galerkin particle-in-cell method on unstructured grids. J. Comput. Phys. 214 (1), 96121.
Jacobs, G. & Hesthaven, J. S. 2009 Implicit–explicit time integration of a high-order particle-in-cell method with hyperbolic divergence cleaning. Comput. Phys. Commun. 180 (10), 17601767.
Jacobs, G., Kopriva, D. & Mashayek, F. 2001 A particle-tracking algorithm for the multidomain staggered-grid spectral method. In 39th Aerospace Sciences Meeting and Exhibit, p. 630.
Lapenta, G., Iinoya, F. & Brackbill, J. 1995 Particle-in-cell simulation of glow discharges in complex geometries. IEEE Trans. Plasma Sci. 23 (4), 769779.
Lindman, E. 1970 Dispersion relation for computer-simulated plasmas. J. Comput. Phys. 5 (1), 1322.
Lotov, K., Timofeev, I., Mesyats, E., Snytnikov, A. & Vshivkov, V. 2015 Note on quantitatively correct simulations of the kinetic beam-plasma instability. Phys. Plasmas 22 (2), 024502.
Magarotto, M., Bosi, F. J., de Carlo, P., Manente, M., Trezzolani, F., Pavarin, D., Alotto, P. & Melazzi, D. 2016 Numerical investigation into the power deposition and transport phenomena in helicon plasma sources. In COMSOL Conference.
Manente, M., Trezzolani, F., Magarotto, M., Fantino, E., Selmo, A., Bellomo, N., Toson, E. & Pavarin, D. 2019 Regulus: a propulsion platform to boost small satellite missions. Acta Astronautica 157, 241249.
Manzolaro, M., Manente, M., Curreli, D., Vasquez, J., Montano, J., Andrighetto, A., Scarpa, D., Meneghetti, G. & Pavarin, D. 2012 Off-line ionization tests using the surface and the plasma ion sources of the spes project. Rev. Sci. Instrum. 83 (2), 02A907.
Markidis, S. & Lapenta, G. 2011 The energy conserving particle-in-cell method. J. Comput. Phys. 230 (18), 70377052.
Meeker, D.2014 Femm official web site. http://www.femm.info, accessed: 2018-09-19.
Melzani, M., Winisdoerffer, C., Walder, R., Folini, D., Favre, J. M., Krastanov, S. & Messmer, P. 2013 Apar-t: code, validation, and physical interpretation of particle-in-cell results. Astron. Astrophys. 558, A133.
Moon, H., Teixeira, F. L. & Omelchenko, Y. A. 2015 Exact charge-conserving scatter–gather algorithm for particle-in-cell simulations on unstructured grids: a geometric perspective. Comput. Phys. Commun. 194, 4353.
Nieter, C. & Cary, J. R. 2004 Vorpal: a versatile plasma simulation code. J. Comput. Phys. 196 (2), 448473.
Osada, R., Funkhouser, T., Chazelle, B. & Dobkin, D. 2002 Shape distributions. ACM Trans. Graph. (TOG) 21 (4), 807832.
Pavarin, D., Ferri, F., Manente, M., Curreli, D., Melazzi, D., Rondini, D. & Cardinali, A. 2011 Development of plasma codes for the design of mini-helicon thrusters, IEPC-2011-240. In 32nd International Electric Propulsion Conference.
Pinto, M. C., Jund, S., Salmon, S., Sonnendrücker, E. & Lorraine, C.-I. 2008 Charge-conserving FEMPIC schemes on general grids. Comptes Rendus Mecanique 157, 570582.
Polycarpou, A. C. 2005 Introduction to the finite element method in electromagnetics. Synth. Lectures Comput. Electromagn. 1 (1), 1126.
Quarteroni, A., Sacco, R. & Saleri, F. 2010 Numerical Mathematics. Springer Science & Business Media.
Rao, S. & Singh, N. 2012 Numerical simulation of current-free double layers created in a helicon plasma device. Phys. Plasmas 19 (9), 093507.
Ren, J., Godar, T., Menart, J., Mahalingam, S., Choi, Y., Loverich, J. & Stoltz, P. H. 2015 PIC algorithm with multiple Poisson equation solves during one time step. J. Phys.: Conf. Ser. 640 (1), 012033.
Sabariego, R., Gyselinck, J., Dular, P., De Coster, J., Henrotte, F. & Hameyer, K. 2004 Coupled mechanical-electrostatic fe-be analysis with fmm acceleration: application to a shunt capacitive mems switch. COMPEL-The International Journal for Computation and Mathematics in Electrical and Electronic Engineering 23 (4), 876884.
Sagdeev, R. Z. & Galeev, A. A. 1969 Nonlinear Plasma Theory. Benjamin.
Seiler, H. 1983 Secondary electron emission in the scanning electron microscope. J. Appl. Phys. 54 (11), R1R18.
Spirkin, A. M.2006 A three-dimensional particle-in-cell methodology on unstructured Voronoi grids with applications to plasma microdevices. PhD thesis, Worcester Polytechnic Institute.
Spitkovsky, A. 2005 Simulations of relativistic collisionless shocks: shock structure and particle acceleration. AIP Conf. Proc. 801 (1), 345350.
Taccogna, F., Longo, S. & Capitelli, M. 2004 Plasma-surface interaction model with secondary electron emission effects. Phys. Plasmas 11 (3), 12201228.
Trophime, C., Egorov, K., Debray, F., Joss, W. & Aubert, G. 2002 Magnet calculations at the grenoble high magnetic field laboratory. IEEE Trans. Appl. Superconductivity 12 (1), 14831487.
Umeda, T.2003 Study on nonlinear processes of electron beam instabilities via computer simulations. PhD thesis, Department of Communications and Computer Engineering Graduate School of Informatics Kyoto University, Kyoto, Japan.
Umeda, T., Omura, Y., Tominaga, T. & Matsumoto, H. 2003 A new charge conservation method in electromagnetic particle-in-cell simulations. Comput. Phys. Commun. 156 (1), 7385.
Vahedi, V. & Surendra, M. 1995 A Monte Carlo collision model for the particle-in-cell method: applications to argon and oxygen discharges. Comput. Phys. Commun. 87 (1–2), 179198.
Vay, J. L. 2008 Simulation of beams or plasmas crossing at relativistic velocity. Phys. Plasmas 15 (5), 056701.
Verboncoeur, J. P. 2005 Particle simulation of plasmas: review and advances. Plasma Phys. Control. Fusion 47 (5A), A231.
Verboncoeur, J. P., Langdon, A. B. & Gladd, N. 1995 An object-oriented electromagnetic PIC code. Comput. Phys. Commun. 87 (1–2), 199211.
Villasenor, J. & Buneman, O. 1992 Rigorous charge conservation for local electromagnetic field solvers. Comput. Phys. Commun. 69 (2–3), 306316.
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