Presented here are results of simulations of neutron background performed fora time projection chamber acting as a particle dark matter detector in anunderground laboratory. The investigated background includes neutrons from rockand detector components, generated via spontaneous fission and (alpha, n)reactions, as well as those due to cosmic-ray muons. Neutrons were propagatedto the sensitive volume of the detector and the nuclear recoil spectra werecalculated. Methods of neutron background suppression were also examined andlimitations to the sensitivity of a gaseous dark matter detector are discussed.Results indicate that neutrons should not limit sensitivity to WIMP-nucleoninteractions down to a level of (1 - 3) x 10^{-8} pb in a 10 kg detector.
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