Cascades of Parametric Instabilities in the Tokamak Plasma Edge during Electron Cyclotron Resonance Heating

We report observations of nonlinear two-plasmon decay instabilities (TPDIs) of a high-power microwave beam, a process similar to half-harmonic generation in optics, during electron cyclotron resonance heating in a tokamak. TPDIs are found to occur regularly in the plasma edge due to wave trapping in density fluctuations for various confinement modes, and the frequencies of both observed daughter waves agree with modeling. Emissions from a cascade of subsequent decays, which indicate a generation of ion Bernstein waves, are correlated with fast-ion generation. This emphasizes the limitations of standard linear microwave propagation models and possibly paves the way for novel microwave applications in plasmas.

Figure 1

(a) TCV cross section with global $(R,Z)$ and local slab $(x,y,z)$ coordinate systems where ${\mathbf{e}}_z\parallel {\mathbf{B}}^{(0)}$. (b) Example of the perpendicular wave number $k_{j,x}^{\pm }$ of two UH daughter waves with frequencies $f_1=41.27\mathrm{GHz}$, $f_2=41.43\mathrm{GHz}$ that are trapped inside a density perturbation in the edge of a plasma with TCV parameters. The pump wave interacts with the daughter waves in the region $x\in [x_l,x_r]$ (blue) where both daughter waves propagate. Parameters are $T_e=100\mathrm{eV}$ and $B^{(0)}=B_0{R}_0/R$ with $B_0=1.43\mathrm{T}$ and $R_0=0.88\mathrm{m}$. $x_{\mathrm{sep}}$ is positioned at $R=1.08\mathrm{m}$. An UH-PDI of $k_{1,x}^{\pm }$ creates the downshifted trapped UH wave $k_{3,x}^{\pm }$ and an IBW (not plotted). A further UH-PDI of $k_{3,x}^{\pm }$ creates the free UH wave $k_{4,x}^{\pm }$.

Figure 2

(a) Resonances, gyrotron ray trajectories, and line of sight of the radiometer mapped to the poloidal cross section of TCV in shot No. 77263 at $t=0.85\mathrm{s}$. (b),(c) Time traces of the injected power and $H_{\alpha }$ signal. (d) Frequency spectrum of the radiometer. The white dashed lines mark the time stamps $t_0$ in Fig. 3, and the red and green dashed lines mark bands around half gyrotron frequencies.

Figure 3

Time trace of the radiometer frequency spectrum at a time (a) during $L$ mode, and (b) during an ELM event in $H$ mode in shot No. 77263. The green line marks $f=f_{\mathrm{X}2\text{−}1}/2$.

Figure 4

Average PSD in each of the frequency bands marked in Fig. 2 vs the time difference between the acquisition and the closest peak in the $H_{\alpha }$ signal in shot No. 77263 during the $H$-mode period $t\in [0.98,1.11]\mathrm{s}$ with constant gyrotron power.

Figure 5

Edge density simulated by hesel at three time stamps around $t=0.85\mathrm{s}$ in No. 77263. The gray lines mark the 1D trapping regions that result in the largest instability growth rate within a gyrotron width (green lines). The corresponding trapped eigenmodes are plotted in the figures above.

Figure 6

Daughter wave frequencies and growth rates predicted by the 1D TPDI model in Eqs. (1)–(5) for the blob structure shown in Fig. 5. Only data from the four poloidal positions with highest instability growth rate are shown.

Figure 7

Time traces of (a) the injected power, (b) the NPA counts of high energy deuterium neutrals, and (c) a of the radiometer in shot No. 77585. (d) Smoothed average PSD in the spectrum for $t\in [1.4\mathrm{s},1.5\mathrm{s}]$.