TRANSPORT-THEORY IN THE COLLISIONLESS LIMIT

Traditional transport theory provides a closure of fluid equations tha t is valid in the collisional, short mean-free-path limit. The possibi lity of extending an analogous closure to long mean-free path is exami ned here. An appropriate kinetic equation, using a model collision ope rator, is solved rigorously for arbitrary collisionality but weak, Max wellian source terms. The corresponding particle and heat flows are th en expressed in terms of the density and temperature profiles. The tra nsport matrix is found to be symmetric even at vanishing collision fre quency; in the collisionless limit it lakes the form of nonlocal opera tors. The operator corresponding to thermal conductivity agrees with o ne found previously by other authors. However particle diffusion, whic h turns out to satisfy a local Fick's law for any finite collision fre quency, becomes singular at vanishing collisionality, where the pressu re gradient vanishes, it is concluded that the fluxes can generally be expressed in terms of particle and energy sources, but not always in terms of pressure and temperature profiles. (C) 1998 American Institut e of Physics. [S1070-664X(98)01209-9]