Abstract
Hybrid codes, in which the ions are treated kinetically and the electrons are assumed to be a massless fluid, have been widely used in space physics over the past two decades. These codes are used to model phenomena on ion inertial and gyro-radius scales, which fall between longer scales obtained by magnetohydrodynamic simulations and shorter scales attainable by full particle simulations. In this tutorial, the assumptions and equations of the hybrid model are described along with some most commonly used numerical implementations. Modifications to include finite electron mass are also briefly discussed. Examples of results of two-dimensional hybrid simulations are used to illustrate the method, to indicate some of the tradeoffs that need to be addressed in a realistic calculation, and to demonstrate the utility of the technique for problems of contemporary interest. Some speculation about the future direction of space physics research using hybrid codes is also provided.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Auer, P.L., Kilb, R.W., Crevier, W.F. (1971): Thermalization in the Earth’s bow shock. J. Geophys. Res., 76, 2927
Forslund, D.W., Freidberg, J.P. (1971): Theory of laminar collisionless shocks. Phys. Rev. Lett., 27, 1189
Mason, R.J. (1971): Computer simulation of ion-acoustic shocks: The diaphragm problem. Phys. Fluids, 14, 1943
Chodura, R. (1975): A hybrid fluid-particle model of ion heating in high-Machnumber shock waves. Nucl. Fusion, 15, 55
Sgro, A.G., Nielson, C.W. (1976): Hybrid model studies of ion dynamics and magnetic field diffusion during pinch implosions. Phys. Fluids, 19, 126
Hamasaki, S., Krall, N.A., Wagner, C.E., Byrne, R.N. (1977): Effects of turbulence on theta pinch modeling by hybrid numerical methods. Phys. Fluids, 20, 65
Hewett, D.W. (1980): A global method for solving the electron-field equations in a zero-inertial electron hybrid plasma simulation code. J. Comput. Phys., 38, 378
Leroy, M.M., Goodrich, C.C., Winske, D., Wu, C.S., Papadopoulos, K. (1981): Simulation of a perpendicular bow shock. Geophys. Res. Lett., 8, 1269
Winske, D., Leroy, M.M. (1984): Hybrid simulation techniques applied to the Earth’s bow shock. In: Matsumoto, H., Sato, T. (ed) Computer Simulations of Space Plasmas. D. Reidel/Terra Sci., Hingham MA
Winske, D. (1985): Hybrid simulation codes with application to shocks and upstream waves. Space Sci. Rev., 42, 53
Quest, K.B. (1989): Hybrid simulation. In: Lembege, B., Eastwood, J. W. (ed) Tutorial Courses: Third International School for Space Simulation. Cepadues Ed., Toulouse, France
Winske, D., Omidi, N. (1993): Hybrid codes: Methods and applications. In: Matsumoto, H., Omura, Y. (ed) Computer Space Plasma Physics: Simulations and Software. Terra, Tokyo
Pritchett, P.L. (2002): Particle-in-cell simulations of plasmas. This volume
Bagdonat, T., Motschmann, U. (2001): 3-D hybrid simulation of the solar wind interaction with comets. In: Buechner, J., Dum, C.T., Scholer, M. (ed) Space Plasma Simulation: Proc. Sixth International School/Symposium ISSS-6. Copernicus Gesellschaft, Katlenburg-Lindau, Germany
Lipatov, A.S. (2001): Hybrid codes with finite electron mass. In: Buechner, J., Dum, C.T., Scholer, M. (ed) Space Plasma Simulation: Proc. Sixth International School/Symposium ISSS-6. Copernicus Gesellschaft, Katlenburg-Lindau, Germany
Omidi, N., Karimabadi, H., Quest, K.B. (2001): Global hybrid simulations of solar wind interaction with the magnetosphere. In: Buechner, J., Dum, C.T., Scholer, M. (ed) Space Plasma Simulation: Proc. Sixth International School/Symposium ISSS-6. Copernicus Gesellschaft, Katlenburg-Lindau, Germany
Quest, K.B., Karimabadi, H. (2001): Physics of solar wind magnetosphere interactions: 3-D hybrid simulations. In: Buechner, J., Dum, C.T., Scholer, M. (ed) Space Plasma Simulation: Proc. Sixth International School/Symposium ISSS-6. Copernicus Gesellschaft, Katlenburg-Lindau, Germany
Yin, L., Winske, D., Gary, S.P., Birn, J. (2001): Hybrid and Hall-MHD simulations of collisionless reconnection: Effects of plasma pressure tensor. In: Buechner, J., Dum, C.T., Scholer, M. (ed) Space Plasma Simulation: Proc. Sixth International School/Symposium ISSS-6. Copernicus Gesellschaft, Katlenburg-Lindau, Germany
Winske, D., Omidi, N. (1996): A nonspecialist’s guide to kinetic simulations of space plasmas. J. Geophys. Res., 101, 17287
Pritchett, P.L. (2000): Particle-in-cell simulations of magnetosphere electrodynamics. IEEE Trans. Plasma Sci., 28, 1976
Omura, Y., Huba, J.D., Winske, D. (1999): Theory and simulations of nonlinear kinetic processes in space plasmas. In: Stone, W.R. (ed) The Review of Radio Science 1996-1999. Oxford Univ. Press, Oxford
Lipatov, A.S. (2001): The Hybrid Multiscale Simulation Technology. Springer-Verlag, Heidelberg, Germany
Vu, H.X., Brackbill, J.U. (1992): CELEST1D: An implicit fully kinetic model for low frequency electromagnetic plasma simulation. Comput. Phys. Comm., 69, 253
Oppenheim, M., Otani, N., Ronchi, C. (1996): Saturation of the Farley-Buneman instability via nonlinear electron E × B drifts. J. Geophys. Res., 101, 17273
Mankofsky, A., Sudan, R.N., Denavit, J. (1987): Hybrid simulation of ion beams in background plasma. J. Comput. Phys., 70, 89
Omelchenko, Yu.A., Sudan, R.N. (1997): A 3-D Darwin-EM hybrid PICco de for ion ring studies. J. Comput. Phys., 133, 146
Vu, H.X. (1998): A massively parallel three-dimensional hybrid code for simulating ion-driven parametric instabilities. J. Comput. Phys., 144, 257
Birdsall, C.K., Langdon, A.B. (1985): Plasma Physics Via Computer Simulation. McGraw-Hill, New York
Swift, D.W. (1995): Use of a hybrid code to model the Earth’s magnetosphere. Geophys. Res. Lett., 22, 311
Byers, J.A., Cohen, B.I., Condit, W.C., Hanson, J.D. (1978): Hybrid simulations of quasi-neutral phenomena in magnetized plasmas. J. Comput. Phys., 27, 363
Harned, D.S. (1982): Quasineutral hybrid simulation of macroscopic plasma phenomena. J. Comput. Phys., 47, 452
Winske, D., Quest, K.B. (1986): Electromagnetic ion beam instabilities: Comparison of one-and two-dimensional simulations. J. Geophys. Res., 91, 8789
Brecht, S.H., Thomas, V.A. (1988): Multidimensional simulations using hybrid particle codes. Computer Phys. Comm., 48, 135
Fujimoto, M. (1991): Instabilities in the magnetopause velocity shear layer. Thesis, U. Tokyo
Thomas, V.A., Winske, D., Omidi, N. (1990): Reforming supercritical quasiparallel shocks: 1. One-and two-dimensional simulations. J. Geophys. Res., 95, 18809
Winske, D., Quest, K.B. (1988): Magnetic field and density fluctuations at perpendicular supercritical collisionless shocks. J. Geophys. Res., 93, 9681
Matthews, A.P. (1994): Current advance method and cyclic leapfrog for 2-D multispecies hybrid plasma simulations. J. Comput. Phys., 112, 102
Horowitz, E.J., Shumaker, D.E., Anderson, D.V. (1989): QN3D: A threedimensional quasi-neutral hybrid particle-in-cell code with applications to the tilt instability in field reversed configurations. J. Comput. Phys., 84, 279
Terasawa, T., Hoshino, M., Sakai, J.I., Hada, T. (1986): Decay instability of finite amplitude circularly polarized Alfvénwaves: A numerical simulation of stimulated Brillouin scattering. J. Geophys. Res., 91, 4171
Kazeminezhad, F., Dawson, J.M., Leboeuf, J.N., Sydora, R., Holland, D. (1992): A Vlasov particle ion zero mass electron model for plasma simulations. J. Comput. Phys., 102, 277
Hewett, D.W., Nielson, C.W. (1978): A multidimensional quasineutral plasma simulation model. J. Comput. Phys., 29, 219
Shay, M., Drake J.F., Denton, R.E., Biskamp, D. (1998): Structure of the dissipation region during collisionless magnetic reconnection. J. Geophys. Res., 103, 9165
Kuznetsova, M.M., Hesse, M., Winske, D. (1998): Kinetic quasi-viscous and bulk flow inertia effects in collisionless magnetotail reconnection. J. Geophys. Res., 103, 199
Omidi, N., Winske, D. (1992): Kinetic structure of slow shocks: Effects of the electromagnetic ion/ion cyclotron instability. J. Geophys. Res., 97, 14801
Winske, D., Omidi, N. (1992): Electromagnetic ion/ion cyclotron instability: Theory and simulations. J. Geophys. Res., 97, 14779
Cremer, M., Scholer, M. (1999): Collisionless slow shocks in magnetotail reconnection. Geophys. Res. Lett., 26, 2709
Cremer, M., Scholer, M. (2000): Structure of the reconnection layer and the associated slow shocks: Two-dimensional simulations of a Riemann problem. J. Geophys. Res., 105, 27621
Daughton, W., Gary, S.P., Winske, D. (1999): Electromagnetic proton/proton instabilities in the solar wind: Simulations. J. Geophys. Res., 104, 4657
Nakamura, M.S., Fujimoto, M. (1998): A three-dimensional hybrid simulation of magnetic reconnection. Geophys. Res. Lett., 25, 2917
Krauss-Varban, D., Omidi, N. (1995): Large-scale hybrid simulations of the magnetotail during reconnection. Geophys. Res. Lett., 22, 3271
Kuznetsova, M.M., Hesse, M., Winske, D. (1996): Ion dynamics in a hybrid simulation of magnetotail reconnection. J. Geophys. Res., 101, 27351
Nakabayashi, J., Machida, S. (1997): Electromagnetic hybrid code simulation of magnetic reconnection: Velocity distribution functions of accelerated ions. Geophys. Res. Lett., 24, 1339
Nakamura, M.S., Fujimoto, M. (1998): Ion dynamics and resultant velocity space distributions in the course of magnetotail reconnection. J. Geophys. Res., 103, 4531
Lottermoser, R.F., Scholer, M., Matthews, A.P. (1998): Ion kinetics in magnetic reconnection: Hybrid simulations. J. Geophys. Res., 103, 4547
Hesse, M., Winske, D. (1993): Hybrid simulations of collisionless ion tearing. Geophys. Res. Lett., 20, 1207
Hesse, M., Winske, D. (1994): Hybrid simulations of collisionless reconnection in current sheets. J. Geophys. Res., 99, 11177
Hesse, M., Winske, D., Kuznetsova, M.M. (1995): Hybrid modeling of collisionless reconnection in two-dimensional current sheets: Simulations. J. Geophys. Res., 100, 21815
Yin, L., Winske, D., Gary, S.P., Birn, J. (2001): Hybrid and Hall-MHD simulations of collisionless reconnection: Dynamics of the electron pressure tensor. J. Geophys. Res., 106, 10761
Yin, L., Winske, D., Gary, S.P., Birn, J. (2001): Particle Hall-MHD simulation of collisionless reconnection: Finite ion gyro-orbit correction. Geophys. Res. Lett., 28, 2173
Yin, L., Winske, D., Gary, S.P., Birn, J. (2002): Hybrid and Hallmagnetohydrodynamics simulations of collisionless reconnection: Effect of the ion pressure tensor and particle Hall-magnetohydrodynamics. Phys. Plasmas, 9, 2575–2584
Brecht, S.H., Ferrante, J.R. (1991): Global hybrid simulation of unmagnetized planets: Comparison of Venus and Mars. J. Geophys. Res., 96, 11209
Brecht, S.H., Ferrante, J.R., Luhmann, J.G. (1993): Three-dimensional simulations of the solar wind interaction with Mars. J. Geophys. Res., 98, 1345
Brecht, S.H. (1997): Hybrid simulations of the magnetic topology of Mars. J. Geophys. Res., 102, 4743
Omidi, N., Karimabadi, H., Krauss-Varban, D¿ (1998): Hybrid simulation of the curved dayside magnetopause during southward IMF. Geophys. Res. Lett., 25, 3273
Ogino, T. (1993): Two-dimensional MHD code. In: Matsumoto, H., Omura, Y. (ed) Computer Space Plasma Physics: Simulations and Software. Terra, Tokyo
Sckopke, N., Paschmann, G., Bame, S.J., Gosling, J.T., Russell, C.T. (1983): Evolution of ion distributions across the nearly perpendicular bow shock: Specularly and non-specularly reflected-gyrating ions. J. Geophys. Res., 88, 6121
Dawson, J.M. (1999): Role of computer modeling of plasmas in the 21st century. Phys. Plasmas, 6, 4436
Lin, Y., Xie, H. (1997): Formation of reconnection layer at the dayside magnetopause. Geophys. Res. Lett., 24, 3145
Xie, H., Lin, Y. (2000): Two-dimensional hybrid simulation of the dayside reconnection layer and associated ion transport. J. Geophys. Res., 105, 25171
Nakamura, M., Scholer, M. (2000): Structure of the magnetopause reconnection layer and of flux transfer events: Ion kinetic effects. J. Geophys. Res., 105, 23179
Lin, Y., Swift, D.W. (1996): A two-dimensional hybrid simulation of the magnetotail reconnection layer. J. Geophys. Res., 101, 19859
Scholer, M., Lottermoser, R.F. (1998): On the kinetic structure of the magnetotail reconnection layer. Geophys. Res. Lett., 25, 3281
Galeev, A.A., Lipatov, A.S., Sagdeev, R.Z. (1987): Two-dimensional numerical simulation of the relaxation of cometary ions and MHD turbulence in the flow of the solar wind around a cometary atmosphere. Sov. J. Plasma Phys., 13, 323
Omidi, N., Winske, D. (1990): Steepening of magnetosonic waves into shocklets: Simulations and consequences for planetary shocks and comets. J. Geophys. Res., 95, 2281
Liewer, P.C., Velli, M., Goldstein, B. (1999): Hybrid simulations of wave propagation and ion cyclotron heating in the expanding solar wind. Space Sci. Rev., 87, 257
Miller, R.H., Rasmussen, C.E., Gombosi, T.I., Khazanov, G.V., Winske, D. (1993): Kinetic simulation of plasma flows in the inner magnetosphere. J. Geophys. Res., 98, 19301
Jones, M.E., Lemons, D.S., Mason, R.J., Thomas, V.A., Winske, D. (1996): A grid-based Coulomb collision model for PIC codes. J. Comput. Phys., 123, 169
Thomas, V.A. (1997): Modeling combined collisional/collisionless plasma interpenetration. IEEE Trans. Plasma Sci., 25, 353
Decyk, V.K., Dauger, D.E. (2001): How to build an AppleSeed: A parallel Macintosh cluster for numerically intensive computing. In: Buechner, J., Dum, C.T., Scholer, M. (ed) Space Plasma Simulation: Proc. Sixth International School/Symposium ISSS-6. Copernicus Gesellschaft, Katlenburg-Lindau, Germany
Liewer, P.C., Decyk, V.K. (1989): A general concurrent algorithm for plasma particle-in-cell simulation codes. J. Comput. Phys., 85, 302
Omidi, N., Blanco-Cano, X., Russell, C.T., Karimabadi, H., Acuna, M. (2002): Hybrid simulations of solar wind interaction with magnetized asteroids: General characteristics. J. Geophys. Res., 107, in press
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Winske, D., Yin, L., Omidi, N., Karimabadi, H., Quest, K. (2003). Hybrid Simulation Codes: Past, Present and Future—A Tutorial. In: Büchner, J., Scholer, M., Dum, C.T. (eds) Space Plasma Simulation. Lecture Notes in Physics, vol 615. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36530-3_8
Download citation
DOI: https://doi.org/10.1007/3-540-36530-3_8
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-00698-5
Online ISBN: 978-3-540-36530-3
eBook Packages: Springer Book Archive