Page 3 - Robustness of waves with a high phase velocity

the turbulence phase velocity in the plasma frame), and is the resonant toroidal density fluctuation wavenumber. The backscattered signal, received via the same beam optics (monostatic detection), is proportional to the density fluctuation amplitude at the resonant wavenumber. The probed radial wavenumber is ~ 0 as the beam propagates
FIGURE 1. (a) FRC cross section illustrating DBS launched/ backscattered beam trajectory and relation between launched and backscattered frequency and wavenumber; (b) density contours in the FRC axial midplane, as measured by CO2 interferometry (red: ne=3x1013 cm-3, purple: ne=0.5x1013 cm -3), illustrating a typical microwave beam path calculated via GENRAY ray tracing; the turning point is located just outside the cut-off layer; (c) plasma density profile and typical DBS probing locations (x,y are laboratory frame coordinates).
toroidally near the cut-off layer. The toroidal wavenumber , and the probed radii r in the laboratory frame are calculated using GENRAY [23] ray tracing based on high time resolution (10 μs) radial electron density profiles reconstructed from a six channel CO2 laser interferometer [24,25] located in the FRC axial midplane. A typical calculated microwave beam path is illustrated in Figure 2(b). Figure 2(c) shows the reconstructed density profile and typical DBS probing radii. All calculated DBS probing positions are mapped to the axial FRC midplane in laboratory (machine) coordinates and then mapped to plasma center coordinates.
A circular plasma cross section is assumed in the density profile reconstruction and validity of this approximation is checked via 2-D bolometry emission profile reconstruction at the FRC midplane, used also to determine the plasma center coordinates. The time-resolved E×B velocity is obtained from the instantaneous Doppler shift, . Neglecting the fluctuation phase velocity one obtains . The DBS diagnostic is described in more detail in [26].
DENSITY FLUCTUATIONS AND EXB FLOW
Figure 2(a) shows an example of a DBS quadrature spectrum ñ(f) obtained in an FRC plasma without plasma gun activation. The contours represent the density fluctuation level ñ(f) in arbitrary units, on a logarithmic scale. The probed radius varies between r~0.38-0.43m in the SOL. The width of the observed DBS spectrum is mainly due to toroidal curvature [26,27], limiting the toroidal wavenumber resolution to , with a median probed wavenumber ~2-4 ( ~6-9). In Fig. 2(b) the integrated density fluctuation level is shown. The large modulation in fluctuation envelope (and in the spectrum-averaged Doppler shift) is primarily due to strong n=1 MHD activity and the resulting elliptical plasma deformation. The time history of the excluded flux radius [Fig. 2(c)] indicates rapid FRC contraction. In contrast, Figs. 2(d-e) show the corresponding quantities for an FRC actively maintained via SOL biasing (plasma gun activated).
The quadrature spectrum (Fig. 2(d) shows predominant negative frequencies, in particular after t=0.8 ms. The toroidal E×B velocity can be extracted from the power-averaged Doppler-shifted spectrum, which here indicates flow in the ion diamagnetic direction (or positive Er) in the SOL. The contribution of the turbulence phase velocities to the measured Doppler shift/ is estimated to be less than 10%. Fig. 2(e) shows substantially lower integrated fluctuation levels. Most importantly, the integrated fluctuation level is substantially lower with plasma gun active,
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