The relation between the transport and the orbit models for a plasma

Starting with the Boltzmann equation and the dynamic equation of a charged particle, we develop a transport (particle) model for the plasma, as well as an orbit (guiding-center) model which is valid for arbitrarily large orbits. The development facilitates the interpretation of the difference between the two models, and sets the stage for the derivation of the conditions under which the two become interchangeable. These conditions include restrictions on the particle distribution and on the field gradients. The role of each model in the formulation of the self-consistent-field problem in the plasma is discussed.