⁸An alternative expression of Z_eff is also found in the litterature, which arises from the definition of the electron-ion collision time τ_ss^′. Indeed, since

1 τess′ ~ n-′Z2-q4ln-Λ--′ ss ss′ e ess

for each species in the plasma, where ln Λ_ess^′ is the Coulomb logarithm for species s in the ionization state s^′, the mean electron collision time τ_e is given by the relation

1 ∑ 1 4∑ ∑ 2 τe = ′τess′ ∝ qe ′ nss′(ψ)Zss′lnΛess′ ss s s

which leads to introduce a pseudo-effective charge Z_eff as

1 4 τe ∝ neqeZeff lnΛee

so that

Zeff = ∑ ∑ nss′Z2ss′lnΛ† ′∕(neln Λee) s s′ ess

which differs from the well known standard expression. However, it can be shown from Coulomb collision theory that the Landau operator scales like (1∕Zeff) , as indicated in Ref.[?]. It is therefore reasonable to neglect differences between ln Λ_ess^′≃ ln Λ_ee and consequently both definitions of the effective charge merges within this assumption.