Model for Collision Processes in Gases: Small-Amplitude Oscillations of Charged Two-Component Systems

Gross, Eugene P.; Krook, Max

doi:10.1103/physrev.102.593

Cited by 270 publications

(135 citation statements)

References 5 publications

Supporting

Mentioning

133

Contrasting

Unclassified

Order By: Relevance

“…The first term of 'flbtl collision determines the loss rate of f f prom velocities v', vi ' The differential scattering cross section is given by For purposes of the estimates in this paper we shall approximate the collision term in the Boltzmann equation in the form proposed by Gross-and Krook (1956); this approach is also known as the relaxation time approximation (c.f., e.g., Reif, 1965); the approximation is mathematically exceptionally simple and physically not only instructive but has been shoran to be quite satisfactory in other comparable physical situations.…”

Section: Y Formulationmentioning

confidence: 99%

A theory of local and global processes which affect solar wind electrons, 1. The origin of typical 1 AU velocity distribution functions—Steady state theory

Scudder¹,

Olbert²

1979

J. Geophys. Res.

213

103

View full text Add to dashboard Cite

A new detailed first principle kinetic theory for electrons is presented which is neither a classical fluid treatment nor an expospheric calculation. This new theory illustrates the global and local properties of the solar wind expansion that shape the observed features of the electron distribution function fe, such as its bifurcation, its skewness, and the ‘differential’ temperatures of the thermal and suprathermal subpopulations. Our approach starts with the Boltzmann equation and retains the effects of Coulomb collisions via a Krook collision operator without recourse to wave‐particle effects. We conclude that Coulomb collisions determine the population and shape of fe in both the thermal (E kT) energy regimes. We find that electrons with E >7kT constitute a special subpopulation of the suprathermals, insofar as Coulomb collisions are concerned; these we call ‘extrathermals.’ The electrons in the thermal portion of fe have undergone ∼10‐20 Coulomb collisions for cumulative momentum transfer en route to the observer at 1 AU; this population is thus more removed from the properties of coronal electrons than the suprathermal population. This latter group retains a strong memory of coronal conditions, since they have undergone only a few momentum transfer collisions. The thermal population is most nearly in collisional contact with the local dynamics (compressions, rarefactions, etc.) of the solar wind. The suprathermal portion of fe is determined by Coulomb collisional interactions with the distribution of solar wind material on radial scale of the heliopause itself. In this respect the suprathermal portion of fe is found to be responsive to the consequences of the global dynamics of the solar wind expansion. We find that this subpopulation is an attenuated vestige of collisional populations deep in the corona (1.03–10 Rs) which has been redistributed via Coulomb multiple pitch angle scattering on magnetically open field lines. The suprathermal particles moving toward the sun are computed to be observed as a result of Coulomb‐collision‐induced backscattering at larger (1–10 AU) heliocentric distances than that of the observer. Based on this theoretical picture, quantitative estimates for the partition of thermal and suprathermal phase density, the break in the velocity distribution, and the magnitude of the skewness (heat flux density) agree well with those typically observed near 1 AU. These calculations predict that the extrathermal fraction of the phase density, the extrathermal temperature, and the net heat flux density carried by electrons should be anticorrelated with the local bulk speed in quasi‐steady‐state flows and that the radial variation of extrathermal temperature inside 1 AU should be essentially independent of heliocentric distance. Our work also shows that the observation of suprathermal particles cannot be taken as a priori evidence for in situ wave particle interaction(s), since we can theoretically calculate a suprathermal population of solar wind electrons at 1 AU b...

show abstract

Section: Y Formulationmentioning

confidence: 99%

A theory of local and global processes which affect solar wind electrons, 1. The origin of typical 1 AU velocity distribution functions—Steady state theory

Scudder¹,

Olbert²

1979

J. Geophys. Res.

213

103

View full text Add to dashboard Cite

show abstract

“…First, a simplified Boltzmann equation with the Krook operator 40 is solved to determine the electron distribution function f e , and then the heat flux q x (in the x direction) is calculated using the standard definition q x ¼ ðm=2Þ Ð d 3 tt 2 t x f e where m is the electron mass.…”

Section: Appendix: the Radiation-hydrodynamic Code Lilacmentioning

confidence: 99%

Multiple spherically converging shock waves in liquid deuterium

et al. 2011

View full text Add to dashboard Cite

“…Assuming for simplicity altitudes below 110 km where ions are practically fully unmagnetized, we will use a kinetic equation with the BGK collision term (Bhatnagar et al, 1954;Gross and Krook, 1956;Morse, 1964):…”

Section: Electron Fluid Modelmentioning

confidence: 99%

Modeling of the Farley-Buneman instability in the E-region ionosphere: a new hybrid approach

2008

View full text Add to dashboard Cite

Abstract.A novel approach to nonlinear simulations of the Farley-Buneman (FB) instability in the E-region ionosphere is developed. The mathematical model includes a fluid description of electrons and a simplified kinetic description of ions based on a kinetic equation with the Bhatnagar-GrossCrook (BGK) collision term. This hybrid model takes into account all major factors crucial for development and nonlinear stabilization of the instability (collisional drag forces, ion inertia and Landau damping, dominant electron nonlinearity, etc.). At the same time, these simulations are free of noises caused by the finite number of particles and may require less computer resources than particle-in-cell (PIC) or hybridsemi-fluid semi-PIC -simulations. First results of 2-D simulations are presented which agree reasonably well with those of previous 2-D PIC simulations. One of the potentially useful applications of the novel computational approach is modeling of the FB instability not far from its threshold.

show abstract

Model for Collision Processes in Gases: Small-Amplitude Oscillations of Charged Two-Component Systems

Cited by 270 publications

References 5 publications

A theory of local and global processes which affect solar wind electrons, 1. The origin of typical 1 AU velocity distribution functions—Steady state theory

A theory of local and global processes which affect solar wind electrons, 1. The origin of typical 1 AU velocity distribution functions—Steady state theory

Multiple spherically converging shock waves in liquid deuterium

Modeling of the Farley-Buneman instability in the E-region ionosphere: a new hybrid approach

Contact Info

Product

Resources

About