Stability of the runaway electrons in tokamaks is analyzed. The distinction between high-density and low-density operation of tokamak discharges is interpreted in terms of the stability condition obtained. In the unstable case, the temporal evolution of the distribution function of the runaway electrons is obtained by solving the quasilinear equation. Time-dependent synchrotron emission from the runaway electrons is calculated.Recent measurements of cyclotron radiation from low-density tokamak plasmas have shown significantly nonthermal properties 1 " 3 : The radiation intensity is more than an order of magnitude above the thermal level expected from the measured temperature, with a broad frequency spectrum having minima at the gyroharmonics 4 ; the radiation level is nonsteady with sudden (% 10 jusec) increases in intensity, correlated with loop-voltage spikes, 4 with bursts of x rays and of radiation from oo pe to oo pi9 and with the ion heating. 5 In this Letter, we attempt to interpret this enhanced radiation as synchrotron emission by the runaway electrons. 6 A specific distribution function of the runaway electrons is obtained by solving the Fokker-Planck equation in the steady state, and this distribution is then used as the unperturbed runaway distribution for stability analysis. In the unstable region, the time-dependent quasilinear equation is solved analytically to obtain the nonlinear evolution of the runaway distribution. With this time-dependent distribution function of the runaway electrons, we calculate the time evolution of the spectrum of their synchrotron emission, including the effect of reabsorption by the background plasma.We solve the Fokker-Planck equation in the runaway region where v\\>v c = (E 0 /E) 1/2 v e , v e = (2T e /m) l/2 , E 0 =e lnA/A D 2 , and X D 2 = T e /Aune 2 . Included is a loss term of the form -v ]} f/v L T 0 , as a model to account for the loss of high-energy electrons caused by the imperfect magnetic surfaces, 7 where r 0 ml is the loss rate of particles with v n >v L . To have a steady state, a source at low energy is introduced to maintain a constant rate, y 0 , of runaway production given by 8 Y 0 = 0.35v 0 (E/E 0 )~3 /8 exp{-[(2E 0 /E) 1/2 +£ 0 /4E]}, where v Q is the electron-electron collision frequency. The Fokker-Planck equation in the runaway region 8 is then solved for v ]] »v c to obtain the following steady-state solutionThe normalization is so chosen that the loss of the runaways is balanced by the runaway production, i.e., An/r=n 0 y 0 , where An/n 0 is the density ratio of the runaways to the bulk thermal electrons, and r is the average life time of runaway electrons. Moreover, v ± and t>" are the velocity components perpendicular and parallel to the electric field, and v 0 = [Eu 0 r 0 /E 0 ] 1/2 v L is the effective cutoff velocity. Typically, for low-density discharges, the observed energy of the runaways is cut off at about 200 keV, corresponding to a value of v 0 /v e » 12 for a bulk electron temperature of 0.7 keV. Note that the effective perpendic...