Dynamic local field, sum rules, and dynamic structure factor of a classical plasma with a logarithmic potential in two dimensions atΓ=2

For a classical one-component plasma gas with a logarithmic potential in two dimensions at {Γ}==e²/kBT=2, we have constructed a dynamic local-field term which satisfies the third-moment and compressibility sum rules exactly. Using it, we have obtained the dynamic structure factor, the plasmon dispersion relation, and the static structure sum rule. We have also compared the asymptotic behavior of our dynamic local field with the well-known relations due to Niklasson and Shaw.