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The stability of non-relativistic runaway electron distributions with respect to the anomalous Doppler resonance is examined in a range of parameters of interest to Tokamaks, i.e. for Y Wpe/Rce 2 and for ohmic electric fields e = E/Ec 5 0.1. Distribution functions are calculated numerically within a region up to 35 ve (thermal velocities) using a finite-element 2-D Fokker-Planck code. Alternatively, an analytic approximation for the runaway distribution function is used, valid beyond the critical velocity vc ~ ve (Ec/E)I. Stability thresholds in (w, k 1 j) space are then determined. For example, for Y = 1 and e = 0.1, and providing that the runaway tail extends at least to 30 ve, unstable waves exist having w < 0.6 Rce and k 1 1 <0.03 Qce/ve.

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