Oscillatory behaviors in wave-particle interactions of runaway electrons*

Runaway electrons generated in tokamaks can excite whistler waves in a wide frequency range. The excited whistler waves can cause energy diffusion and pitch angle scattering of resonant electrons, and alter the distribution function. In this study, we find that the interaction of unstable whistler modes and resonant runaway electrons can be described using a predator-prey model. The modes driven by the inhomogeneity of the runaway electron distribution function can cause flattening of the distribution through quasilinear diffusion, which can stabilized the mode, and cause it to begin to decay. After some time, the inhomogeneous distribution function is recovered, and the mode can begin growing again. This periodic process can cause several oscillatory phenomena associated with runaway electrons, including the oscillations of low-frequency whistler waves and high-frequency extraordinary electron waves, and sawtooth-like behavior of ECE signals. In addition, we also study the oscillatory behavior of the synchrotron radiation pattern that has been found in experiments, which is also connected to the excitation and damping of whistler modes.