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Narrowband electrostatic noise (NEN) is frequently observed in the Earth‧s distant magnetotail. NEN exhibits a spectral peak between 100 and 316 Hz and is very impulsive, having a peak amplitude in the range 10−4−10−3V/mHz. It has been suggested that NEN represents a plasma wave mode which results from a hole in the low energy electron velocity distribution. In this paper, it is shown by means of numerical simulation that a wave mode is excited in the presence of a modest sized electron hole. In the simulations the mode saturates at low amplitudes, in agreement with observations, without destroying the hole. It is suggested that the burst-like behavior of NEN is due to the persistence of these nonstandard modes and their ability to be excited by a variety of weak free energy sources.