First Direct Observation of Runaway-Electron-Driven Whistler Waves in Tokamaks

DIII-D experiments at low density ($n_e\sim {10}^{19}{\mathrm{m}}^{-3}$) have directly measured whistler waves in the 100–200 MHz range excited by multi-MeV runaway electrons. Whistler activity is correlated with runaway intensity (hard x-ray emission level), occurs in novel discrete frequency bands, and exhibits nonlinear limit-cycle-like behavior. The measured frequencies scale with the magnetic field strength and electron density as expected from the whistler dispersion relation. The modes are stabilized with increasing magnetic field, which is consistent with wave-particle resonance mechanisms. The mode amplitudes show intermittent time variations correlated with changes in the electron cyclotron emission that follow predator-prey cycles. These can be interpreted as wave-induced pitch angle scattering of moderate energy runaways. The tokamak runaway-whistler mechanisms have parallels to whistler phenomena in ionospheric plasmas. The observations also open new directions for the modeling and active control of runaway electrons in tokamaks.

Figure 1

Time evolution of (a) the magnetic fluctuation power spectra; (b) the electron temperature ($T_e$); electron density ($n_e$); and (c) the toroidal magnetic field (near the magnetic axis), and ECE—a measure of runaway perpendicular energy.

Figure 2

(a) Variation of mode frequency at constant density with ion cyclotron frequency; (b) variation of mode frequency with electron density and fits (dashed lines are based on $f\propto n_e^{-1/2}$).

Figure 3

(a) Wave electric field for toroidal mode number $n=35$ at 140 MHz; (b) power absorption as a function of frequency.

Figure 4

Cherenkov, normal, and anomalous Doppler resonances for $B=1\mathrm{T}$, $k=60{\mathrm{m}}^{-1}$, and $\theta =50°$ as a function of electron energy.

Figure 5

(a) Decreasing whistler activity with increasing magnetic field; and (b) threshold in averaged whistler emission power vs hard x-ray bremsstrahlung level.

Figure 6

Time evolution of runaway generated hard x-ray gamma energy spectrum for discharge No. 171089 of Fig. 5. Whistlers were present for $t=3.75$, 4.25, and absent for $t=4.75\sec$.

Figure 7

Time evolution of (a) 100–200 MHz magnetic fluctuation power spectra; (b) ECE intensity at 83.5, 92.5, 109.5, 111.5, and 113.5 GHz. Dashed arrows in (b) are times at which the ECE and whistler amplitudes peak; solid arrows in (a) are times at which whistler amplitudes drop. The gray shaded bars are intervals of $n=1$ sawtooth activity.