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Two-Component Plasmas in Two and Three Dimensions

  • Jean-Pierre Hansen
Part of the NATO ASI Series book series (volume 154)

Abstract

The two-component plasma (TCP) is a model system made up of N1 positive charges q1 and N2 negative charges q2 in a d-dimensional volume Ω. The corresponding number densities nα = Nα/Ω satisfy the charge neutrality requirement
$$ {{\rm{n}}_1}{{\rm{q}}_{\rm{1}}} + {{\rm{n}}_2}{{\rm{q}}_{\rm{2}}} = 0 $$
(1.1)
We shall be mostly concerned with point charges, and more specifically with fully stripped ions (q1 = + ze) and electrons (q2 = - e, where e is the elementary charge); the interaction is then purely Coulombic and the total Hamiltonian of the system can be cast in the form:
$$ {\rm{H = }}{{\rm{H}}_{{\rm{11}}}} + {{\rm{H}}_{{\rm{22}}}} + {{\rm{V}}_{{\rm{12}}}} $$
(1.2a)
where
$$ {{\rm{H}}_{{\rm{\alpha \alpha }}}} = \sum\limits_{{\rm{i = 1}}}^{{\rm{N\alpha }}} {{{{\rm{p}}_{\rm{i}}^2} \over {2{{\rm{m}}_{\rm{\alpha }}}}}} \sum\nolimits_{\rm{i}} {{}_ < \sum {_{_{_{\rm{j}}}}{\rm{v\alpha \alpha }}} } (|{{{\rm{\vec r}}}_{\rm{i}}} - {{{\rm{\vec r}}}_{\rm{j}}}|) $$
(1.2b)
$$ {{\rm{V}}_{{\rm{12}}}} = \sum\limits_{{\rm{i}} = 1}^{{{\rm{N}}_1}} {\sum\limits_{{\rm{j}} = 1}^{{{\rm{N}}_2}} {{{\rm{v}}_{{\rm{12}}}}(|{{{\rm{\vec r}}}_{\rm{i}}} - {{{\rm{\vec r}}}_{\rm{j}}}|)} } $$
(1.2c)
$$ {{\rm{v}}_{{\rm{\alpha \beta }}}}({\rm{r}}) = {{\rm{q}}_{\rm{\alpha }}}{{\rm{q}}_{\rm{\beta }}}\Phi ({\rm{r}}) $$
(1.2d)
and Φ(r) is the solution of the d-dimensional Poisson equation, i.e. Φ(r) = 1/r in 3d and Φ(r) = -ln(r/L) (with L an arbitrary scaling length) in 2d. Partially stripped ions (of well-defined valence Z) have a finite core, so that the ion-ion potential v11(r) must then include a short-range Born-Mayer repulsion, while the ion-electron interaction can be described by a pseudo-potential for distances shorter than the core radius. However, except at very high temperatures, the Coulomb repulsion between ions is sufficiently strong to prevent the cores (of diameter σ say) to come into contact (i.e. Z2e2/σ>>kBT in 3d) so that a point ion description is generally adequate.

Keywords

Hydrogen Plasma Plasma Phase Pauli Repulsion Coulomb Coupling Coulomb Coupling Parameter 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Plenum Press, New York 1987

Authors and Affiliations

  • Jean-Pierre Hansen
    • 1
  1. 1.Laboratoire de Physique Théorique des LiquidesUniversité Pierre et Marie CurieParis Cedex 05France

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