  A kinetic model for studying the time evolution of the distribution function
for microwave start-up is presented. The model for the distribution function is
two dimensional in momentum space, but, for simplicity and rapid calculations,
has no spatial dependence. Experiments on the Mega Amp Spherical Tokamak have
shown that the plasma current is carried mainly by electrons with energies
greater than $70$ keV, and effects thought to be important in these experiments
are included, i.e. particle sources, orbital losses, the loop voltage and
microwave heating, with suitable volume averaging where necessary to give terms
independent of spatial dimensions. The model predicts current carried by
electrons with the same energies as inferred from the experiments, though the
current drive efficiency is smaller.
