It is proposed that ac voltage (^a c ) oscillations observed in sliding charge-density-wave systems are caused by phase vortices at the sample ends. The model's prediction that v ac is length independent is verified experimentally. The long-range phase coherence implied by thermal-gradient experiments is consistent with the vortex model but not with models based on impurities.PACS numbers: 72.15.Nj, 72.20.Ht,One of the most puzzling features of electronic transport in the series of compounds that demonstrate charge-density-wave (CDW) conduction is the appearance of well defined voltage oscillations 1 when the dc electric field exceeds a threshold value E T . The fundamental frequency of this oscillation has been shown 2 to be proportional to the current carried by the moving CDW. This phenomenon has been seen 3 in NbSe 3 , TaS 3 , (TaSe 4 ) 2 I, (NbSe 4 ) 10 / 3 I, and the bronzes K 0 . 3 MoO 3 and Rb 0 . 3 MoO 3 , all of which display nonlinear I-V curves associated with CDW depinning. Most of the theories 4 ' 6 proposed for the ac voltage invoke the impurities as the source of the current oscillations through their interaction with the moving CDW. The simplest such model is the impurity washboard model of Gruner, Zawadowski, and Chaikin. 4 In the static situation the weakly pinned condensate distorts its phase to maximize the pinning energy gained from the impurities. The average length of the domains within which the phase is roughly uniform is the Fukuyama-Lee-Rice (FLR) 7 length X FLR (10-50 Mm in NbSe 3 ). It is well established experimentally that the threshold field is determined by the impurity concentration. However, the situation when the CDW moves is less clear. In particular we shall present evidence showing that the phase coherence length (when sliding) is much longer than A FLR and infer that the impurities play no major role in the (narrow-band) noise generation. (A perplexing problem with domain structures in the sliding CDW is the question of how oscillations in adjacent domains couple to provide the sharp spectra seen. Also the question of what happens at walls separating domains with different velocities is unresolved.)We propose a model for the CDW noise based on the following assumptions: (I) An array of vortices is created when the CDW phase undergoes an abrupt change such as at the sample ends. (II) Regardless of the phase configuration in the static (pinned) condensate, when sliding occurs the phase coherence may extend over macroscopic distances approaching the sample length in pure samples. The creation and annihilation of the phase vortices at the sample ends leads to a modulation of the current which is observed as the ac noise. Various theories 8 ' 9 have explored the effect of internal degrees on the dynamics of the moving CDW. In our model we may regard the conduction noise as a manifestation of the internal degrees of freedom expressed as phase dislocations in inhomogeneous situations. The vortex array insofar as it is an energetically favorable way for the system to overcome ph...