Abstract
In metals and plasmas the Coulomb interaction between mobile charged particles is screened. The main long-range interaction between the particles is then the magnetic interaction. When radiation is negligible the simplest way to study this interaction is to use the Darwin approximation. In this way one retains a conservative finite degree of freedom problem. We review the derivation of the Darwin Lagrangian and present careful derivations of the corresponding Hamiltonian in various limits. Our results go beyond those of previous authors in several respects. We point out some consequences of the magnetic interaction energy for the dynamics of charged particles with screened Coulomb interaction. Applications to metallic conduction electrons and to plasmas are considered. \textcopyright{} 1996 The American Physical Society.
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