This paper examines the formal structure of the Boltzmann equation (BE) theory
of charged particle transport in neutral gases. The initial value problem of
the BE is studied by using perturbation theory generalised to non-Hermitian
operators. The method developed by R�sibois was generalised in order to
be applied for the derivation of the transport coecients of swarms of charged
particles in gases. We reveal which intrinsic properties of the operators
occurring in the kinetic equation are sucient for the generalised diffusion
equation (GDE) and the density gradient expansion to be valid. Explicit
expressions for transport coecients from the (asymmetric) eigenvalue problem
are also deduced. We demonstrate the equivalence between these microscopic
expressions and the hierarchy of kinetic equations. The establishment of the
hydrodynamic regime is further analysed by using the time-dependent
perturbation theory. We prove that for times t ?
τ0
(τ0 is the relaxation time),
the one-particle distribution function of swarm particles can be transformed
into hydrodynamic form. Introducing time-dependent transport coecients
?
*(p)
(?q,t), which can be related
to various Fourier components of the initial distribution function, we also
show that for the long-time limit all ?
*(p)
(?q,t) become time and
?q independent in the same
characteristic time and achieve their hydrodynamic values.
PERIODIC FIRST INTEGRALS FOR HAMILTONIAN SYSTEMS OF LIE TYPE
