Millimeter-Wave Beam Scattering by Field-Aligned Blobs in Simple Magnetized Toroidal Plasmas

The first direct experimental measurements of the scattering of a millimeter-wave beam by plasma blobs in a simple magnetized torus are reported. The wavelength of the beam is comparable to the characteristic size of the blob. In situ Langmuir probe measurements show that fluctuations of the electron density induce correlated fluctuations of the transmitted power. A first-principles full-wave model, using conditionally sampled 2D electron density profiles, predicts fluctuations of the millimeter-wave power that are in agreement with experiments.

Figure 1

TORPEX illustration and raw data. (a) Illustration of the experimental setup in TORPEX with a helical magnetic field line (in blue) in a simple magnetized torus configuration. A mmw beam is injected in $X$ mode from the top of the vessel and detected at the bottom through dielectric windows. In situ 2D measurements of density fluctuations associated with blobs are obtained from the HEXTIP array of 95 Langmuir probes at the positions indicated in black. (b)–(d) Snapshots of density fluctuations showing (b) blob formation, (c) detachment, and (d) radial propagation (in the vicinity of the white cross). The shaded area represents the mmw beam at the full width at half maximum of the mmw power from comsol simulations in vacuum. (e) Time evolution of the electron density normalized to the $X$-mode cutoff electron density as measured at the location in white in (b).

Figure 2

Statistical properties of the detected mmw-power signal. (a) Time-averaged detected mmw power with and without plasma. (b) Comparison of the time evolution of the detected mmw power, normalized to its mean value, with (black) and without (green) plasma. (c) Standard deviation of the detected mmw-power signal. (d) Cross-correlation between the mmw power measured at $x=5\mathrm{cm}$ and the electron density measured at each probe of HEXTIP.

Figure 3

Conditional sampling (CS) using two different probes to detect blobs. Note that, since $k_{\parallel }\approx 0$, a single blob would appear twice within the poloidal cross section of TORPEX. (a) Red (probe $A$) and blue (probe $B$) dashed lines show the result of CS using the probes identified in white in (b) and (c). (b),(c) Electron density fluctuations at $\tau =-20$ and $0\mu \mathrm{s}$, respectively. (d) Maximum amplitude of fluctuations of the normalized detected power $\delta {\tilde{P}}_{\max }/⟨P⟩$ as a function of the range of the CS threshold, taking probes $A$ and $B$ as references.

Figure 4

Full-wave simulation results. (a), (b) Fluctuations of the electric field amplitude associated with the blobs identified in Figs. 3 and 3 projected to the poloidal plane of the mmw system. The detected electric field is normalized to the electric field maximum of the launching horn $|E_{\mathrm{inj}}|$. (c), (d) Comparison of the time evolution of the mmw power at the two positions of detection identified by the blue and red horns in (a) and (b). The white arrows indicate a blob. The CS time evolution of the detected mmw power is obtained using probes $A$ and $B$ from Figs. 3 and 3 to detect blobs. Experimental results (the dashed lines) are compared to numerical simulations (the shaded areas).