Particle-in-Cell electrostatic numerical algorithm

• Autorzy: Konior W.

Warianty tytułu

PL

Algorytm numeryczny Particle-in-Cell dla problemu elektrostatycznego

• Języki publikacji: EN

Abstrakty

EN

Existing global models of interaction between the solar wind (SW) and the local interstellar medium (LISM) describe the heliosphere that arises as a result of this interaction. There is a strong motivation to develop a kinetic model using the Particle-in-Cell (PIC) method to describe phenomena which appear in the heliosphere. This is however a long term scientific goal. This paper describes an electrostatic Particle-in-Cell numerical model developed in the Institute of Aviation in Warsaw, winch includes mechanical and charge exchange collisions between particles in the probabilistic manner using Direct Simulation Monte Carlo method. This is the first step into developing simulations of the heliosphere incorporating kinetic effects in collisionless plasmas. In this paper we focus only on presenting the work, which have been done on the numerical PIC algorithm.

PL

Istniejące globalne modele oddziaływania wiatru słonecznego (SW) z lokalną materią międzygwiazdową (LISM) opisują heliosferę, która powstaje w wyniku interakcji tych dwóch ośrodków. Istnieje silna motywacja do opracowania modelu kinetycznego wykorzystującego metodę Particle-in-Cell (PIC) w celu opisu zjawisk, które zachodzą w heliosferze. Jednakże jest to długoterrninowy cel naukowy. W artykule przedstawiono elektrostatyczny model numeryczny PIC. opracowany w Instytucie Lotnictwa w Warszawie, który obejmuj e kolizje mechaniczne i rezonansową wymianę ładunków pomiędzy cząstkami w sposób probabilistyczny metodą Direct Simulation Monte Carlo. Jest to pierwszy krok w opracowywaniu symulacji heliosfery zawierającej efekty kinetyczne w plazmach bezzderzeniowych. W tym artykule koncentrujemy się tylko na prezentowaniu prac, które zostały wykonane z wykorzystaniem algorytmu numerycznego PIC.

Słowa kluczowe

EN

plasma; neutral particles; Particle-In-Cell; Monte-Carlo method

PL

plazma; heliosfera; Particle-in-Cell; Monte-Carlo

• Wydawca: Wydawnictwa Naukowe Instytutu Lotnictwa
• Czasopismo: Prace Instytutu Lotnictwa
• Rocznik: 2017
• Tom: Nr 3 (248)
• Strony: 24--45
• Opis fizyczny: Bibliogr. 25 poz., rys., tab., wzory

Twórcy

autor

Konior W.

• Institute of Aviation, Aleja Krakowska 110/114, 02-256 Warsaw, Poland

Bibliografia

• [1] Davis, L., 1955. "Interplanetary Magnetic Fields and Cosmic Rays'1, Physical Review, Volume 100, Issue 5, pp. 1440-1444.
• [2] Parker, E., 1963, "Interplanetary dynamical processes", Interscience Publishers, New York, NY.
• [3] Axford, W. I., 1972, "The Interaction of the Solar Wind With the Interstellar Medium", Solar Wind. Edited by Charles P Sonett, Paul J. Coleman, and John M. Wilcox, Washington, Scientific and Technical Information Office, NASA, p. 609.
• [4] Baranov, V. B., Malama, Yu. G., 1993, "Model of the solar wind interaction with the local interstellar medium - Numerical solution of self-consistent problem", Journal of Geophysical Research, Volume 98, Issue A9, pp. 15157-15163.
• [5] Pauls, H. L., Zank, G. P., Williams, L. L.; 1995, "Interaction of the solar wind with the local interstellar medium". Journal of Geophysical Research, Volume 100, Issue All, pp. 21595-21604.
• [6] Zank, G. P., Pauls, H. L., Williams, L. L., Hall, D. T, 1996, "Interaction of the solar wind with the local interstellar medium: A multifluid approach", Journal of Geophysical Research, Volume 101, Issue A10, pp. 21639-21656.
• [7] Washimi, H., Tanaka, 1996, "3-D Magnetic Field and Current System in the Heliosphere", Space Science Reviews, Volume 78, Issue 1-2, pp. 85-94.
• [8] Ratkiewicz, R., Barnes, A., Molvik, G. A., Spreiter, J. R., Stahara, S. S., Vinokur, M., Venkateswaran, S., 1998, "Effect of varying strength and orientation of local interstellar magnetic field on configuration of exterior heliosphere: 3D MHD simulations", Astronomy and Astrophysics, Volume 335, pp. 363-369.
• [9] Pogorelov, N. V.: Matsuda, T.: 1998, "Influence of the interstellar magnetic field direction on the shape of the global heliopause". Journal of Geophysical Research, Volume 10, pp. 237.
• [10] Opher, M., Stone, E. C., Liewer, P. C., 2006, "The Effects of a Local Interstellar Magnetic Field on Voyager 1 and 2 Observations", Astrophysical Journal, Volume 640, Issue 1, pp. L71-L74..
• [11] Heerikhuisen, J., Pogorelov, N. V, 2010 ''Kinetic Modeling of Interstellar Hydrogen in the Heliosphere”, Numerical Modeling of Space Plasma Flows, Astronum-2009, Astronomical Society of the Pacific, San Francisco, pp. 227.
• [12] M. Strumik, A. Czechowski, S. Grzedzielski, W. M. Macek, and R. Ratkiewicz, 2013, "Small-Scale Local Phenomena Related to the Magnetic Reconnection and Turbulence in the Proximity of the Heliopause", Astrophysical Journal Letters, Volume 773, L23 pp. 1-5.
• [13] Kunz, M. W., Schekochihihin, A. A, Chen, C. H. K., Abel, I., Cowley, S. C., 2015, "Inertial-range kinetic turbulence in pressure-anisotropic astrophysical plasmas", J. Plasma Phys., Volume 81, Issue 5, pp. 1-61.
• [14] Howes, G. G., Cowley, S. C., Dorland, W., Hammett, G. W., Quataert, E., Schekocliihin, A. A., 2006, "Astrophysical Gyrokinetics: Basic Equations and Linear Theory", The Astrophysical Journal. Volume 651, Issue 1, pp. 590-614.
• [15] Valentini, F., Travnicek, P., Califano, F., Hellinger, P., Mangeney, A., 2007, "A hybrid-Vlasov model based on the current advance method for the simulation of collisionless magnetized plasma", Journal of Computational Physics, Vol. 225, Issue 1, pp. 753.
• [16] Ren, C., 2011, “Introduction to Particle-in-cell Methods in Plasma Simulations”, The 2011 HEDP Summer School, University of Rochester, from http://hedpschool.lle.rochester.edu/2011SummerSchool/lectures/Ren.pdf.
• [17] Birdsall, C. K. and Langdon A. B., 2005, “Plasma Physics via Computer Simulation”, Taylor & Francis Group, New York, NY.
• [18] Brieda, L., 2010, “The Electrostatic Particle In Cell (ES-PIC) Method”, from https://www.particleincell.com/2010/es-pic-method/.
• [19] Griffiths, D. J., 1999, “Introduction to Electrodynamics”, 3th Edition, Prentice Hall, Upper Saddle River, New Jersey, NJ.
• [20] Kahan, W., 1958, “Gauss-Seidel Methods of Solving Large Systems of Linear Equations”, Ph. D. thesis, University of Toronto.
• [21] Brieda, L., 2016, “Fundamentals of the Particle In Cell Method 2016”, lecture materials, Particle In Cell Consulting LLC, California, CA.
• [22] Deuflhard, P., 2004, “Newton Methods for Nonlinear Problems. Affine Invariance and Adaptive Algorithms”, Volume 35, Springer, Berlin.
• [23] Barrett, R., Berry, M., Chan, T. F., Demmel, J., Donato, J., Dongarra, J., Eijkhout, V., Pozo, R., Romine. C., van der Vorst, H., 1994, “Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods”, SIAM, Philadelphia.
• [24] Blum, P. W., Fahr, H. J., 1970, “Interaction between Interstellar Hydrogen and the Solar Wind”, Astronomy & Astrophysics Volume 4, pp. 280-290.
• [25] Bird, G. A., 1994, “Molecular Gas Dynamics and the Direct Simulation of Gas Flows”, Clarendon Press, Oxford.

Uwagi

EN

The work was carried out as part of a research project funded by the Institute of Aviation. WK also thanks prof. R. Ratkiewicz for all the support and reviewers for their remarks.

PL

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).