Theory of Heating of a Nonreciprocal System of Particles

A simple theory, which describes a source of additional kinetic energy and its redistribution in systems of many particles with a nonreciprocal interaction (when Newton's third law is not valid), is presented. The theory yields the satisfactory results for a qualitative analysis of the features of dust dynamics in an anisotropic complex plasma. Unlike the theoretical models proposed earlier to explain the anomalous heating in the systems of particles with a nonreciprocal interaction, the model presented here allows to predict not only the kinetic energy growth for grains in laboratory RF discharges, but also an increase of their kinetic temperature in the direction of an ion flow as well as a difference in the energy distribution between the degrees of freedom. To verify the theory, we carried out numerical simulations of vertically aligned chains and extended-layered structures with a nonreciprocal model of interaction that is similar to interaction due to an effect of the ion focusing in a laboratory complex plasma.