The problem of helium ash removal from a fusion reactor is treated with spatially varying plasma parameters, and the allowance of variations is found to strongly influence the necessary conditions for sustained deuterium-tritium (DT) ignition. In particular, a one dimensional (1-D) particle transport model is used to calculate the core helium concentration on the basis of a suitably parametrized source profile. It is estimated that the necessary exhaust efficiency for sustained DT ignition is of the order of 2%, rather than the familiar 10% figure deduced from uniform plasma calculations. This is due to: (1) the fact that tau P and tau E are not equal; and (2) the fact that fusion alphas are produced only in a fraction of the plasma volume. It is also shown that, in order for the ash concentration to be effectively controllable by pumping, it is necessary that the particle diffusion coefficient be sufficiently high and that the reactor's power density not be excessive. In order to determine the exact pumping requirements for a machine such as ITER, a more detailed and self-consistent model is needed