  Effects of collisions on conservation laws for toroidal plasmas are
investigated based on the gyrokinetic field theory. Associating the collisional
system with a corresponding collisionless system at a given time such that the
two systems have the same distribution functions and electromagnetic fields
instantaneously, it is shown how the collisionless conservation laws derived
from Noether's theorem are modified by the collision term. Effects of the
external source term added into the gyrokinetic equation can be formulated
similarly with the collisional effects. Particle, energy, and toroidal momentum
balance equations including collisional and turbulent transport fluxes are
systematically derived using a novel gyrokinetic collision operator, by which
the collisional change rates of energy and canonical toroidal angular momentum
per unit volume in the gyrocenter space can be given in the conservative forms.
The ensemble-averaged transport equations of particles, energy, and toroidal
momentum given in the present work are shown to include classical,
neoclassical, and turbulent transport fluxes which agree with those derived
from conventional recursive formulations.
