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FIG. 5. Measured density profile (a) and reconstructed Bz profile evolution (b). Field reversal lasts to nearly 8 ms as indicated by the Bz = 0 white colored contour line.
axis. Plotted in Fig. 6(a) is the time trace of plasma radius, averaged over 6 identical consecutive shots. The line integral density traces measured by the CO2/HeNe interferometer averaged over the same shots are plotted in Fig. 6(b). The first 4 in the sequence of 6 are polarimetry shots, and the last 2 are base line shots for measuring the polarimetry phase errors. The net Faraday rotation angle for the y = 0 cm chord averaged from this set of shots is shown in Fig. 6(c). The error bar is within ±0.1 , dominated by mechanical vibration e↵ect. The high frequency noise and plasma fluctuations in the data are smoothed to reveal the small equilibrium quantity.
As shown in Fig. 6, the measured Faraday rotation angle for the y = 0 cm chord is very small, (0.02 ± 0.1 ) during the plasma discharge. It agrees with the calculation based on the density profile and reconstructed Bz profile. The small Faraday rotation is due to the fact that as the laser beam crosses the field reversal radius, the Faraday rotation e↵ect cancels. If there were no field reversal, assuming the plasma is mirror confined with a uniform external axial field of 640 G, the Faraday rotation angle would be 0.7 . If the equilibrium near the end of the discharge when the field reversal radius is at r = 0 cm is used, the Faraday rotation angle is calculated to be 0.2 . For both non-reversed cases the expected Faraday
FIG. 6. Time traces of r (a), plasma density (b), and central FIR chord Faraday rotation angle (c) averaged from shots 46 271 to 46 276.
rotation angles are significantly larger than the small measured value. Therefore, Fig. 6(c) provides strong evidence for FRC field reversal.
V. SUMMARY
The HSFIR diagnostic system developed for the C-2U FRC experiment has superior interferometry and polarimetry resolutions and high bandwidth. The achieved extremely small instrument phase errors are due to the low noise FIR lasers. The resulting high quality density profile data allows for 1-dimentional equilibrium reconstruction, from which FRC field reversal is shown to last more than 5 ms. The high sensitivity plasma fluctuation data helped the understanding of newly discovered micro bursts which will be published in a separate paper.
In general FIR laser polarimetry for FRC plasmas are extremely challenging due to the intrinsic characteristic of high plasma beta, meaning high density high temperature plasmas are confined by weak magnetic field. On the one hand, weak magnetic field leads to small Faraday rotation angles to be measured. On the other hand, high plasma density limits the probe laser wavelength due to the refraction e↵ects, which further limits the Faraday rotation angles. Due to field reversal, Faraday rotation e↵ects in positive and negative field regions cancel each other, making the total Faraday rotation angle near zero. Despite the di culties, the HSFIR polarimetry successfully achieved the necessary resolution, measured the small (near zero) Faraday rotation angles due to poloidal field, which is a strong evidence indicating the FRC equilibrium magnetic field reversal.
ACKNOWLEDGMENTS
We thank our shareholders for their support and trust, and all fellow TAE sta↵ for their dedication, excellent work, and extra e↵orts.
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