A new physical mechanism of formation of runaway electron (RE) beams during plasma disruptions in tokamaks is proposed. The plasma disruption is caused by a strong stochastic magnetic field formed due to nonlinearly excited low-mode number magnetohydrodynamic (MHD) modes. It is conjectured that the runaway electron beam is formed in the central plasma region confined inside the intact magnetic surface located between q = 1 and the closest low-order rational magnetic surfaces [q = 5/4 or q = 4/3, . . . ]. It results in that runaway electron beam current has a helical nature with a predominant m/n = 1/1 component. The thermal quench and current quench times are estimated using the collisional models for electron diffusion and ambipolar particle transport in a stochastic magnetic field, respectively. Possible mechanisms for the decay of the runaway electron current owing to an outward drift electron orbits and resonance interaction of high-energy electrons with the m/n = 1/1 MHD mode are discussed.The runaway electrons (REs) generated during the disruptions of tokamak plasmas may reach a several tens of MeV and may contribute to the significant part of postdisruption plasma current. The prevention of such RE beams is of a paramount importance in future tokamaks, especially in the ITER operation, since it may severely damage a device wall [1][2][3][4][5].The mitigation of REs by massive gas injections (MGI) and externally applied resonant magnetic perturbations (RMPs) have been extensively discussed in literature (see, e.g., Refs. [6-8] and references therein). However, no regular strategy to solve this problem has been developed because up to now the physical mechanisms of the formation of REs during plasma disruptions are not well understood. In spite of the numerous dedicated experiments to study the problem of runaway current generation during plasma disruptions in different tokamaks (see, e.g., [7][8][9][10][11][12][13][14][15]) no clear dependence of RE formation on plasma parameters has been established. These numerous experiments show the complex nature of plasma disruption process especially the formation of RE beams.One of the important features of the formation of RE beams is the irregularity and variability of the beam parameters from one discharge to another one. This is an indication of the sensitivity of RE beam formations on initial conditions which is the characteristic feature of nonlinear processes, particularly, the chaotic system. Therefore one expects that ab initio numerical simulations of the RE formation process may not be quite productive to explain it because of complexity of computer simulations of nonlinear processes [16]. The problems of numerical simulations of plasma disruptions is comprehensively discussed in [17].In this work we propose a new physical mechanism of formation of RE beams during plasma disruptions in tokamaks. It is based on the analysis of numerous experimental results, mainly obtained in the TEXTOR tokamak and the ideas of magnetic field stochasticity [18]. The mecha...