184 THERMODYNAMICS OF PLASMAS WITH DEVELOPED IONIZATION
MC k
|
Γ |
|
. |
. |
GDH DH GDH |
. |
|
. |
DH |
|
LDH
. |
MN LDH |
. |
MN |
|
|
. |
LDH |
.
ΓD
Coulomb interaction energy, UMC, from the Monte Carlo method of expansion over Γ (Brush et al. 1966; Hansen 1973): LDH – first order (Debye–H¨uckel approximation); Γ2 – second order (Abe 1959); Γ3 – third order (Cohen and Murphy 1969). Simplest models: DH – nonlinearized form of Debye–H¨uckel approximation; GDH – Debye approximation in a grand canonical ensemble (Likal’ter 1969; Ebeling et al. 1991); MN – (Mitchell and Ninham 1968; Guttman et al. 1968); LDH*, LDH**, DH*, GDH*, MN* – the same approximations after correction with the local quasineutrality condition (5.25)–(5.27). More complex approximations: 1 – HMC (Carley 1974); 2 – HMC (Springer et al. 1973); 3 – solution of the BBGKY hierarchy equations (Hirt 1967); 4 – MSA (Gillan 1974). (After Gryaznov and Iosilevskii 1976).
with numerical and analytical techniques. For instance, the failure of Carley (1974) to satisfy condition (5.27) a ected the results (see Fig. 5.6), and pointed to their considerable incorrectness.
5.1.10OCP ion mixture
A mixture of charges Z1 and Z2 is interesting for astrophysics. In the ion–sphere model, the static energy of the binary mixture is given by the expression
5/3 |
5/3 |
¯1/3 |
2 |
/rskT ) |
uex/(nkT ) = −0.9[x1Z1 |
+ (1 − x1)Z2 |
]Z |
(e |
−
5/3 ¯ 1/3
= 0.9Z (Z) γ ,
¯
where n = n1 + n2, x1 = n1/n, Z = (Z1n1
γ = e2/rskT .
(5.36)
+ Z2n2)/n, rs = (4πn/3)−1/3, and