Theory of two threshold fields for relativistic runaway electrons

This Letter presents a rigorous kinetic theory for relativistic runaway electrons in the near critical electric field in tokamaks. The theory provides a distribution function of the runaway electrons, reveals the presence of two different threshold electric fields, and describes a mechanism for hysteresis in the runaway electron avalanche. Two different threshold electric fields characterize a minimal field required for sustainment of the existing runaway population and a higher field required for the avalanche onset. The near-threshold regime for runaway electrons determines the time scale of toroidal current decay during runaway mitigation in tokamaks.