Stars as Laboratories for Fundamental Physics - MPP Theory Group

Characteristics of Stellar Plasmas 597
= Z k 2 D. Nu-
For only one species of ions with charge Ze one has ki
2
merically,
k D = 222 eV (Y e ρ/T 8 ) 1/2 ,
(D.15)
where ρ is in units of g cm −3 and T 8 = T/10 8 K. Contours in the ρ-T -
plane are shown in Fig. D.5.
Fig. D.5. Contours for the Debye scale k D in keV.
When the electrons are degenerate they cannot form a Debye-Hückel
cloud around a test charge. Rather, their distribution is characterized
by a Thomas-Fermi model which results in the screening scale k 2 TF =
4αp F E F /π. Because k TF ≪ k D the electron screening can be neglected
relative to the ions whence k S ≈ k i .
Degenerate electrons form an essentially inert background of negative
charge in which the ions move, subject to their mutual Coulomb
interaction. They can be treated as a weakly coupled Boltzmann gas as
long as a typical thermal energy exceeds a typical Coulomb interaction
energy. As a quantitative measure one uses the plasma parameter
Γ = Z 2 α/a i T,
(D.16)
where Ze is the nuclear charge and a i the ion-sphere radius defined by
= 4πa 3 i /3 with the ion density n i . Numerically this is
n −1
i
Γ = 1.806×10 −3 T −1
8 (Z 5 2Y e ρ) 1/3 , (D.17)