Relation of the Plasma Kinetic Equation for the Darwin Hamiltonian to the Relativistic Landau Equation

The connection between the two-particle ring term for the kinetic equation with Darwin interaction and the ${\left(\frac{v}{c}\right)}^2$ approximation of the relativistic Landau equation is demonstrated. It is suggested that for practical calculations of ${\left(\frac{v}{c}\right)}^2$ corrections, an equation (with cutoffs) given might be used instead of the more complete kinetic equation (with ring-sum term and without cutoffs) derived recently.