Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-23T20:13:54.350Z Has data issue: false hasContentIssue false

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

Published online by Cambridge University Press:  27 March 2019

G. Gallina
Affiliation:
Department of Physics and Astronomy, University of British Columbia, 6224 Agricultural Road, Vancouver BC V6T 1Z1, CA TRIUMF, 4004 Wesbrook Mall, Vancouver BC V6T 2A3, CA
M. Magarotto*
Affiliation:
Department of Industrial Engineering, University of Padova, Via Gradenigo 6/a 35131 Padova, IT Centro di Ateneo di Studi e Attività Spaziali ‘Giuseppe Colombo’ – CISAS, University of Padova, Via Venezia 15 35131 Padova, IT
M. Manente
Affiliation:
Technology for Propulsion and Innovation S.r.l., Via della Croce Rossa 112 35129 Padova, IT
Daniele Pavarin
Affiliation:
Department of Industrial Engineering, University of Padova, Via Gradenigo 6/a 35131 Padova, IT Centro di Ateneo di Studi e Attività Spaziali ‘Giuseppe Colombo’ – CISAS, University of Padova, Via Venezia 15 35131 Padova, IT Technology for Propulsion and Innovation S.r.l., Via della Croce Rossa 112 35129 Padova, IT
*
Email address for correspondence: [email protected]

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.

Type
Research Article
Copyright
© Cambridge University Press 2019 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Anderson, D., Fedele, R. & Lisak, M. 2001 A tutorial presentation of the two stream instability and Landau damping. Amer. J. Phys. 69 (12), 12621266.Google Scholar
Balay, S.2001 Petsc official web site. https://www.mcs.anl.gov/petsc/, accessed: 2018-09-19.Google Scholar
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.Google Scholar
Birdsall, C. K. & Langdon, A. B. 2004 Plasma Physics via Computer Simulation. CRC Press.Google Scholar
Bittencourt, J. A. 2013 Fundamentals of Plasma Physics. Springer Science & Business Media.Google Scholar
Bossavit, A. 1998 Computational Electromagnetism: Variational Formulations, Complementarity, Edge Elements. Academic.Google Scholar
Brieda, L.2005 Development of the draco es-pic code and fully-kinetic simulation of ion beam neutralization. PhD thesis, Virginia Tech.Google Scholar
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.Google Scholar
Buneman, O. 1959 Dissipation of currents in ionized media. Phys. Rev. 115 (3), 503.Google Scholar
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.Google Scholar
Carlsson, J., Manente, M. & Pavarin, D. 2009 Implicitly charge-conserving solver for Boltzmann electrons. Phys. Plasmas 16 (6), 062310.Google Scholar
Che, H. 2016 Electron two-stream instability and its application in solar and heliophysics. Modern Phys. Lett. A 31 (19), 1630018.Google Scholar
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.Google Scholar
Chen, F. F. 1984 Introduction to Plasma Physics and Controlled Fusion, 2nd edn. Plenum.Google Scholar
Chen, F. F. 1991 Plasma ionization by helicon waves. Plasma Phys. Control. Fusion 33 (4), 339.Google Scholar
Colella, P. & Norgaard, P. C. 2010 Controlling self-force errors at refinement boundaries for amr-pic. J. Comput. Phys. 229 (4), 947957.Google Scholar
D’Agostini, G. 2003 Bayesian Reasoning in Data Analysis: A Critical Introduction. World Scientific.Google Scholar
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.Google Scholar
Dawson, J. 1962 One-dimensional plasma model. Phys. Fluids 5 (4), 445459.Google Scholar
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.Google Scholar
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.Google Scholar
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.Google Scholar
Fehske, H., Schneider, R. & Weiße, A. 2007 Computational Many-Particle Physics. Springer.Google Scholar
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.Google Scholar
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.Google Scholar
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).Google Scholar
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.Google Scholar
Girault, V. & Raviart, P.-A. 2012 Finite element methods for Navier–Stokes equations: theory and algorithms. Springer Science & Business Media.Google Scholar
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.Google Scholar
Hockney, R. W. & Eastwood, J. W. 1988 Computer Simulation Using Particles. CRC Press.Google Scholar
Hu, Y.2016 Particle in cell simulation. http://theory.ipp.ac.cn/yj/, accessed: 2018-09-19.Google Scholar
Inan, U. S. & Gołkowski, M. 2010 Principles of Plasma Physics for Engineers and Scientists. Cambridge University Press.Google Scholar
Jacobs, G. & Hesthaven, J. S. 2006 High-order nodal discontinuous Galerkin particle-in-cell method on unstructured grids. J. Comput. Phys. 214 (1), 96121.Google Scholar
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.Google Scholar
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.Google Scholar
Lapenta, G., Iinoya, F. & Brackbill, J. 1995 Particle-in-cell simulation of glow discharges in complex geometries. IEEE Trans. Plasma Sci. 23 (4), 769779.Google Scholar
Lindman, E. 1970 Dispersion relation for computer-simulated plasmas. J. Comput. Phys. 5 (1), 1322.Google Scholar
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.Google Scholar
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.Google Scholar
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.Google Scholar
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.Google Scholar
Markidis, S. & Lapenta, G. 2011 The energy conserving particle-in-cell method. J. Comput. Phys. 230 (18), 70377052.Google Scholar
Meeker, D.2014 Femm official web site. http://www.femm.info, accessed: 2018-09-19.Google Scholar
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.Google Scholar
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.Google Scholar
Nieter, C. & Cary, J. R. 2004 Vorpal: a versatile plasma simulation code. J. Comput. Phys. 196 (2), 448473.Google Scholar
Osada, R., Funkhouser, T., Chazelle, B. & Dobkin, D. 2002 Shape distributions. ACM Trans. Graph. (TOG) 21 (4), 807832.Google Scholar
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.Google Scholar
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.Google Scholar
Polycarpou, A. C. 2005 Introduction to the finite element method in electromagnetics. Synth. Lectures Comput. Electromagn. 1 (1), 1126.Google Scholar
Quarteroni, A., Sacco, R. & Saleri, F. 2010 Numerical Mathematics. Springer Science & Business Media.Google Scholar
Rao, S. & Singh, N. 2012 Numerical simulation of current-free double layers created in a helicon plasma device. Phys. Plasmas 19 (9), 093507.Google Scholar
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.Google Scholar
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.Google Scholar
Sagdeev, R. Z. & Galeev, A. A. 1969 Nonlinear Plasma Theory. Benjamin.Google Scholar
Seiler, H. 1983 Secondary electron emission in the scanning electron microscope. J. Appl. Phys. 54 (11), R1R18.Google Scholar
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.Google Scholar
Spitkovsky, A. 2005 Simulations of relativistic collisionless shocks: shock structure and particle acceleration. AIP Conf. Proc. 801 (1), 345350.Google Scholar
Taccogna, F., Longo, S. & Capitelli, M. 2004 Plasma-surface interaction model with secondary electron emission effects. Phys. Plasmas 11 (3), 12201228.Google Scholar
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.Google Scholar
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.Google Scholar
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.Google Scholar
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.Google Scholar
Vay, J. L. 2008 Simulation of beams or plasmas crossing at relativistic velocity. Phys. Plasmas 15 (5), 056701.Google Scholar
Verboncoeur, J. P. 2005 Particle simulation of plasmas: review and advances. Plasma Phys. Control. Fusion 47 (5A), A231.Google Scholar
Verboncoeur, J. P., Langdon, A. B. & Gladd, N. 1995 An object-oriented electromagnetic PIC code. Comput. Phys. Commun. 87 (1–2), 199211.Google Scholar
Villasenor, J. & Buneman, O. 1992 Rigorous charge conservation for local electromagnetic field solvers. Comput. Phys. Commun. 69 (2–3), 306316.Google Scholar