The transport properties of ambipolar long-channel carbon-nanotube field-effect transistors are calculated in the framework of a diffusive-transport model. The effects associated with radiative and nonradiative recombinations of injected electrons and holes in the channel are considered, and the spatial dependence of the recombination profile on the gate and drain voltages is explored. Nonradiative recombination is shown to play a decisive role in the transport characteristics. The emitted light spot size is predicted to exhibit sensitive dependence on the nonradiative recombination mechanism. Moreover, the local electric field reaches a maximum but remains relatively small inside the recombination region.