Page 2 - Robustness of waves with a high phase velocity

electromagnetic drift waves have been predicted at finite (where μ0 is the free space permeability and Be is the external magnetic field) for a large toroidal wavenumber ( range (1 ≤ ≤ 10 or higher, where with is the ion sound gyroradius), with growth rates peaking for 0.2 ≤ ≤ 0.6 [12]. The growth rate has been predicted to depend strongly on the ratio of density and temperature gradient scale lengths, and , where and . According to analytical calculations presented in [11], ion mode instability is expected only for , a criterion which is not satisfied in the C-2 plasma investigated here. Unstable electron mode may exist for < 1 and ~1, conditions which are satisfied in C-2. Experimentally, density fluctuations with toroidal wavelength in between the ion and electron gyroradius scale have indeed been observed in the C-2 FRC via Doppler Backscattering, as discussed in detail below. Extremely short wavelength electron temperature gradient (ETG) instabilities (linearly most unstable for ≥ 1 and ≥ 2, where is the electron gyroradius,[13]) are expected to be only weakly unstable for the experimentally relevant range of β0 and ~1 in C-2, and are not observable by present FRC diagnostics.
The (closed flux surface) FRC plasma in C-2 [14] is surrounded by an (open fieldline) mirror-confined scrape- off layer (SOL) plasma with mirror ratio RM = 6-10. In addition to the instabilities discussed above, it is expected that the SOL plasma would be unstable to drift-interchange modes driven by density/temperature gradients and the (moderate) field line curvature, as observed experimentally in a tandem mirror experiment with very similar plasma parameters [15]. Also, at moderate/high β finite Larmor radius (FLR) effects do not always restrict interchange instability to < 1 as discussed in [16].
In this Letter we report the first systematic measurements of low frequency ( ) density turbulence and the turbulence decorrelation rate, the toroidal E× B flow velocity, and the radial E× B flow shear in the C-2 FRC plasma, both inside the FRC plasma and in the SOL. We present experimental evidence that (i) ion gyro-scale density fluctuations (0.5 40) peak in the SOL, and decrease substantially in amplitude inside the FRC separatrix; (ii) fluctuation levels increase when the E× B shearing rate decreases below the turbulence decorrelation rate, with concomitant onset of the n=2 rotational mode, increased FRC radial losses, and radial contraction of the FRC separatrix; (iii) substantial ExB flow shear just outside the FRC separatrix, and low fluctuation levels are sustained when an annular plasma gun is activated, resulting in substantially increased FRC lifetime.
DESCRIPTION OF THE C-2 FIELD-REVERSED CONFIGURATION
The C-2 FRC plasma is created via injecting and merging of two preformed, compact high-β plasmoids into a central confinement chamber with radius R=0.7m and length L=4.5m, with an external solenoidal field of 0.05- 0.14T, as described in detail elsewhere [14,17]. Typical line- averaged plasma densities in the experiments described here are 2.5-4 x 1019 m-3, and the ion and electron temperatures in the FRC core are ~400-600 eV and ~80-130 eV. The FRC core plasma is surrounded by an open field line, mirror-confined scrape-off layer (SOL) plasma, terminating axially on metallic end plates located in divertor chambers at a distance of 8.8 m from the machine axial midplane. An annular washer plasma gun [18,19] (inner diameter 0.11 m, outer diameter 0.13 m, located in the south divertor chamber) injects plasma along open field lines outside the FRC separatrix, mapping to a 3 cm wide annular region at the machine midplane. The local magnetic field at the gun location is ~0.5T. The washer guns have anode-cathode voltages of ~0.5-1.0 kV, with typical discharge current ~10 kA. The plasma guns are electrically floating with respect to the vacuum chamber, producing a negative (inwards pointing) radial electric field transmitted to the SOL region just outside the FRC separatrix [20].
THE DOPPLER BACKSCATTERING DIAGNOSTIC
The rms density fluctuation level (0.5 ≤ ≤ 4), toroidal ExB velocity, and turbulence decorrelation rate near the FRC midplane are evaluated via multi-channel Doppler backscattering (DBS [21,22]), using five co-linear diagnostic microwave beams focused into the plasma at an oblique angle ζ in the toroidal plane, via an adjustable parabolic stainless steel mirror (Figure 1a). Beam spot sizes of 2W0 ~ 3-4.5 cm are achieved depending on frequency (26 GHz ≤ f ≤ 66 GHz; W0 is the Gaussian 1/e2 power half width). Due to refraction in the plasma the microwave beams bend in the toroidal direction. Backscattering by plasma density fluctuations occurs preferentially near the cutoff layer [21], according to the selection rules and , where the indices I and S denote the incident and backscattered wave, is the toroidal turbulence advection velocity is
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