Short-range Collision Research Articles

Stabilizing effects of short-range collisions on longitudinal plasma waves

The paper deals with the problem of linear stability of longitudinal plane waves in a partially ionized plasma. The investigation is carried out, both analytically and numerically, by adding a short range collision term to the Vlasov equation. It is shown that electrically unstable plasmas are stabilized if the collision frequency for binary encounters is large enough. An illustrative example is discussed in detail.

The influence of short-range collisions on the Vlasov equation for plasmas

Abstract The linearized Vlasov-Maxwell equations, describing longitudinal plasma waves, are studied with the addition of a simple short-range collision term and for a given equilibrium distribution. The problem of stability, and of existence and location of isolated eigenvalues determining the asymptotic time behavior of the plasma following a small plane wave initial perturbation with given arbitrary wave number are investigated.

Damping of collective modes in liquid metals. II

For pt.I see ibid., vol.8, p.89 (1975). Calculations are reported of the memory function associated with the longitudinal current correlations along with some results for the density fluctuation spectrum for a model of liquid rubidium. The latter are compared with the information about the dynamics of density fluctuations obtained from molecular dynamics computations and neutron scattering experiments on the liquid near its melting point. The fourth frequency moment has played an essential role in generalized hydrodynamic or viscoelastic theories of the dynamic structure factor. However, the fourth moment is infinite for the rigid core potential and yet the rigid sphere fluid is frequently used as a model for real liquids. It is argued that a theory of the density fluctuation spectrum of a liquid should accurately describe the short-range collision processes, so that the rigid core limit can be recovered, even if this can only be achieved, as with the present approach, at the expense of the fourth moment condition.

Damping of collective modes in liquid metals

For pt.I see ibid., vol.8, p.89 (1975). Calculations are reported of the memory function associated with the longitudinal current correlations along with some results for the density fluctuation spectrum for a model of liquid rubidium. The latter are compared with the information about the dynamics of density fluctuations obtained from molecular dynamics computations and neutron scattering experiments on the liquid near its melting point. The fourth frequency moment has played an essential role in generalized hydrodynamic or viscoelastic theories of the dynamic structure factor. However, the fourth moment is infinite for the rigid core potential and yet the rigid sphere fluid is frequently used as a model for real liquids. It is argued that a theory of the density fluctuation spectrum of a liquid should accurately describe the short-range collision processes, so that the rigid core limit can be recovered, even if this can only be achieved, as with the present approach, at the expense of the fourth moment condition.

Thermodynamic Properties of an Electron Plasma

The thermodynamic properties of an electron plasma are investigated on the basis of the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy equation. The correlation energy has been calculated up to the ${\ensuremath{\epsilon}}^{2}$ term ($\ensuremath{\epsilon}$ is the standard plasma parameter) in terms of an exact solution of the binary correlation function taking into account the short-range collision effect. The contribution of ternary correlations to the correlation energy has been determined in lowest order, which turns out to be of the second order in $\ensuremath{\epsilon}$. The total sum of the corrections due to the short-range collision effect and the ternary correlation effect is found to be in agreement with the result obtained by Abe, Bowers, and Salpeter within the regime of Gibbs' statistical thermodynamics. Although the appearance of the binary correlation function obtained in the present studies differs from those derived by Bowers-Salpeter and by O'Neil-Rostoker, it is shown that all of these expressions are essentially equivalent. According to the present analysis, however, it is proven that these expressions do not describe correctly the way in which correlation effects diminish at large distances and therefore the statement made by DeWitt saying that $g(x)\ensuremath{\sim}\frac{1}{8}(\mathrm{ln}3){\ensuremath{\epsilon}}^{2}\mathrm{exp}(\ensuremath{-}{k}_{D}r)$ as $r\ensuremath{\rightarrow}\ensuremath{\infty}$ is not correct.