Hostname: page-component-848d4c4894-8bljj Total loading time: 0 Render date: 2024-07-07T07:47:34.405Z Has data issue: false hasContentIssue false
  • English
  • Français

Collisional relaxation: Landau versus Dougherty operator

Part of: Collisions in Collisionless Plasmas

Published online by Cambridge University Press:  13 October 2014

Oreste Pezzi ,
F. Valentini  and
P. Veltri
Oreste Pezzi*
Affiliation:
Dipartimento di Fisica and CNISM, Universitá della Calabria, 87036 Rende (CS), Italy
F. Valentini
Affiliation:
Dipartimento di Fisica and CNISM, Universitá della Calabria, 87036 Rende (CS), Italy
P. Veltri
Affiliation:
Dipartimento di Fisica and CNISM, Universitá della Calabria, 87036 Rende (CS), Italy
*
†Email address for correspondence: oreste.pezzi@fis.unical.it
Get access Rights & Permissions [Opens in a new window]

Abstract

A detailed comparison between the Landau and the Dougherty collision operators has been performed by means of Eulerian simulations, in the case of relaxation toward equilibrium of a spatially homogeneous field-free plasma in three-dimensional velocity space. Even though the form of the two collisional operators is evidently different, we found that the collisional evolution of the relevant moments of the particle distribution function (temperature and entropy) are similar in the two cases, once an ‘ad hoc’ time rescaling procedure has been performed. The Dougherty operator is a nonlinear differential operator of the Fokker-Planck type and requires a significantly lighter computational effort with respect to the complete Landau integral; this makes self-consistent simulations of plasmas in presence of collisions affordable, even in the multi-dimensional phase space geometry.

Type
Research Article
Information
Journal of Plasma Physics , Volume 81 , Issue 1 , January 2015 , 305810107
Copyright
Copyright © Cambridge University Press 2014 

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

REFERENCES

Anderson, M. W. and O'Neil, T. M. 2007a Eigenfunctions and eigenvalues of the Dougherty collision operator. Phys. Plasmas 14, 052 103.Google Scholar
Anderson, M. W. and O'Neil, T. M. 2007b Collisional damping of plasma waves on a pure electron plasma column. Phys. Plasmas 14, 112 110.Google Scholar
Bhatnagar, P. L., Gross, E. P. and Krook, M. 1954 A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems. Phys. Rev. 94, 511–525.Google Scholar
Dougherty, J. K. 1964 Model Fokker-Planck equation for a plasma and its solution. Phys. Fluids 7, 113–133.Google Scholar
Dougherty, J. K. and Watson, S. R. 1967 Model Fokker-Planck equations: part 2. The equation for a multicomponent plasma. J. Plasma Phys. 1, 317–326.Google Scholar
Driscoll, C. F., Anderegg, F., Dubin, D. H. E. and O'Neil, T. M. 2009 Trapping and frequency variability in electron acoustic waves. In: New Developments in Nonlinear Plasma Physics (AIP Conf. Proc., 1188), (eds.) Eliasson, B. and Shukla, P. K., pp. 272–279.Google Scholar
Filbet, F. and Pareschi, L. 2002 A numerical method for the accurate solution of the Fokker-Planck-Landau equation in the nonhomogeneous case. J. Comput. Phys. 179, 1–26.Google Scholar
Hinton, F. L. and Hazeltine, R. D. 1976 Theory of plasma transport in toroidal confinement systems. Rev. Mod. Phys. 48, 239–303.Google Scholar
Kogan, V. I. 1961 The rate of equalization of the temperatures of charged particles in a plasma. Plasma Phys. Problem Control. Thermonuclear React. 1, 153.Google Scholar
Kumar, K., D. and Das, N. 2014 Electron-ion collisional effect on Weibel instability in a Kappa distributed unmagnetized plasma. Phys. Plasmas 21, 042 106.Google Scholar
Landau, L. D. 1936 The transport equation in the case of the Coulomb interaction. In: Collected Papers of L. D. Landau, Pergamon Press, pp. 163–170.Google Scholar
Lenard, A. and Bernstein, I. B. 1958 Plasma oscillations with diffusion in velocity space. Phys. Rev. 112, 1456–1459.Google Scholar
Livi, S. and Marsch, E. 1986 Comparison of the Bhatnagar-Gross-Krook approximation with the exact Coulomb collision operator. Phys. Rev. A 34, 533–540.Google Scholar
Marsch, E. 2006 Kinetic physics of the solar corona and solar wind. Living Rev. Sol. Phys. 3.1, 1–100.Google Scholar
O'Neil, T. M. 1968 Effects of Coulomb collisions and microturbulence on plasma wave echo. Phys. Fluids 11, 2420–2425.Google Scholar
Pareschi, L., Russo, L. G. and Toscani, G. 2000 Fast spectral methods for the Fokker-Planck-Landau Collision operator. J. Comput. Phys. 165, 216–236.Google Scholar
Peyret, R. and Taylor, T. D. 1983 Computational Methods for Fluid Flow, Springer.Google Scholar
Pezzi, O., Valentini, F., Perrone, D. and Veltri, P. 2013a Eulerian simulations of collisional effects on electrostatic plasma waves. Phys. Plasmas 20, 092 111.Google Scholar
Pezzi, O., Valentini, F., Perrone, D. and Veltri, P. 2013b Phys. Plasmas 20, 092 111.Google Scholar
Pezzi, O., Valentini, F., Perrone, D. and Veltri, P. 2014a Erratum: Eulerian simulations of collisional effects on electrostatic plasma waves. Phys. Plasmas 21, 019 901.Google Scholar
Pezzi, O., Valentini, F. and Veltri, P. 2014b Kinetic ion-acoustic solitary waves in collisional plasmas. Eur. Phys. J. D 68, 128.Google Scholar
Spitzer, L. Jr, 1956 Physics of Fully Ionized Gases, Interscience Publishers.Google Scholar
Valentini, F., O'Neil, T. M. and Dubin, D. H. E. 2006 Excitation of nonlinear electron acoustic waves. Phys. Plasmas 13, 052 303.CrossRefGoogle Scholar
Vlasov, A. A. 1938 On vibration properties of electron gas. J. Exp. Theor. Phys. 8, 291.Google Scholar
Zakharov, V. E. and Karpman, V. I. 1963 On the nonlinear theory of the damping of plasma waves. Sov. Phys. JETP 16, 351–357.Google Scholar