Consequences of Resistive Hose Modes in Tokamak Runaway Electron Beams

A beam of runaway electrons (REs) within a cold background plasma can be unstable to resistive hose modes. Helical deflection of the current centroid of the beam away from its initial position is imperfectly canceled by eddy currents in the cold background plasma. The resulting over-stable, kink-like oscillations grow on a time scale determined by the resistivity of the cold plasma. Using a fluid model for the RE beam, we find that these high frequency modes are faster growing than resistive MHD instabilities when resistivity is large [PoP 31, 010701 (2024)]. This is relevant to post-disruption tokamak plasmas during the current plateau phase, where it is observed that a beam-like population of REs carries a large fraction of the total current, usually with a minimum safety factor greater than one. The hose mode in the fluid model is driven by gradients in the RE current density profile, and scales linearly with the ratio of the RE transit time to the resistive decay time. Nonlinear evolution of the instability in cylindrical geometry flattens the parallel current profile near the magnetic axis. Simulations of an unstable beam-plasma equilibrium in a circular cross-section tokamak show the formation of magnetic islands at the onset of saturation, indicating coupling to resonant perturbations. Later in time, the magnetic field lines are stochastic throughout much of the core. Simulations including a region of open field lines assess whether the change in magnetic topology results in substantial loss of REs.