Self-mediation of runaway electrons via self-excited wave-wave and wave-particle interactions

Abstract

Nonlinear dynamics of runaway electron induced wave instabilities can significantly modify the runaway distribution critical to tokamak operations. Here we present the first-ever fully kinetic simulations of runaway-driven instabilities towards nonlinear saturation in a warm plasma where collisional damping is subdominant. It is found that the slow-X modes grow an order of magnitude faster than the whistler modes, and they parametrically decay to produce whistlers much faster than those directly driven by runaways. These parent-daughter waves, as well as secondary and tertiary wave instabilities, initiate a chain of wave-particle resonances that strongly diffuse runaways to the backward direction. This reduces almost half of the current carried by high-energy runaways, over a time scale orders of magnitude faster than experimental shot duration. These results beyond quasilinear analysis may impact anisotropic energetic electrons broadly in laboratory, space and astrophysics.

Figures (4)

• Figure 1: (a): the Fourier space of magnetic field $B_z$ where slow-X waves are strongly driven (red box). A schematic picture of a zoom-in window (green box) on the Fourier space from cold plasma dispersion Stix1992wavesbook illustrates different branches (especially the whistler and slow-X), and different waves on the branches. The strongly driven parent slow-X mode (blue star) can parametrically decay into two pairs of daughter wave groups (red or green triangles), both including whistler waves. (b): in the momentum space distribution, the slow-X waves diffuse the high-energy tail over pitch and momentum at this early time, as shown by the resonance lines (dashed lines) and diffusion directions (red arrows).
• Figure 2: The momentum space at moderate energy at different times. The strong slow-x waves initiate a chain of wave-particle resonances labeled as ABCD that diffuse runaways to the backward direction along their diffusion directions.
• Figure 3: (a): in the high-energy momentum space, the backward diffusion occurs sequentially along the diffusion directions of multiple resonances of forward whistler waves. (b) at later time the triggered backward whistlers diffuse electrons to higher pitch to encounter resonances of forward whistlers. Eventually the backward diffusion significantly fills the high pitch momentum space at high energy. (c): the integrated current distribution over momentum, where almost half of the integrated current at high energy is converted to lower energy during this process.
• Figure S1: Quasilinear diffusion coefficient $D_{\xi\xi}$ (arbitrary unit) in the momentum space calculated from the forward whistler branch ($kd_e\in [0,2]$) in the Fourier space, involving n=2 to -2 resonances for (a) $t\omega_{pe}=5000$ and (b) $t\omega_{pe}=250000$.