The time-dependent photoconductive current response of semi-insulating GaAs is probed based on one-dimensional simulations, with a focus on the lock-on phenomenon. Our results capture most of the experimental observations. It is shown that trap-to-band impact ionization fuels local field enhancements, and photon recycling also plays an important role in pushing the device towards lock-on above a 3.5 kV/cm threshold field. The results compare well with actual data in terms of the magnitudes, the rise times, and the oscillatory behavior seen at higher currents. Moving multiple domains are predicted, and the response shown depended on the location of the photoexcitation spot relative to the electrodes.