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Nucl. Fusion 59 (2019) 112009 H. Gota et al
Figure 8. Effect of edge biasing on FRC plasma stability. From the top panel to the bottom: excluded-flux radius, line-integrated electron density from midplane FIR interferometer, and n = 2 mode amplitude estimated by SVD analysis using Mirnov probe array.
the case of no edge biasing a large amplitude of n = 2 MHD perturbation (elliptical distortion) appears and grows early in the discharge (t < 0.5 ms: signals on both line-integrated density and n = 2 mode amplitude) which leads to a loss of internal energy, particles, and ultimately to the FRC lifetime much shorter than that of −Er applied edge biasing case. The MHD perturbation amplitude is determined using singular value decomposition (SVD) analysis [44] of an azimuthal array of eight Mirnov probes located near the central region of the CV [28]. In the case without edge biasing the peak of the n = 2 mode amplitude correlates well with the time when the excluded-flux radius is abruptly dropped as shown in figure 8; while, with effective edge biasing FRC plasma is globally sta- bilized and no strong n = 2 mode activity is observed, thus extending plasma lifetime/duration. This edge biasing effect on FRC stability, together with NBI, is consistent with C-2/2U experiments [7, 9, 10].
As the second example of edge biasing scheme and its effect, an electrical potential of the central electrode inside outer divertors changed to be positive, meaning +Er applied, at which ion Doppler spectroscopy located near the midplane has indicated a clear edge biasing effect on plasma rotation and its velocity [45], as shown in figure 9. The instrument has a fan array of 15 viewing chords that covers about a half of the CV cross-section; an impact parameter of the outer-most viewing chord is ~0.39 m and the system measures oxygen 4 + line emission at 278.1 nm. In a typical FRC without edge biasing, impurity ions start to rotate in the electron diamagnetic direction and then reverse the direction/rotation gradually into the ion diamagnetic direction as can be seen in figure 9(a); while, in the positively-biased edge control case (i.e. applying +Er), impurity ions are accelerated to rotate in
the ion diamagnetic direction thus reaching to the maximum velocity earlier in time as compared to non-biasing case. Note that an instrumental error of this ion rotation measurement is quite small, only a few km s−1. Based on the impurity ion velocity distribution and its angular velocity, it is found that core region of the plasma exhibits a rigid-rotor profile with no velocity shear while the shear is observed near the edge inside the FRC separatrix. The peak velocity of the plasma rota- tion as well as shear flow can be controlled by edge-biasing systems as can be seen in figure 9(b), where the total biasing current is estimated from power supplies on both sides of the device. The more biasing current is driven/applied to open- field-line plasmas, the higher rotation velocity and shear flow can be obtained. However, it is also found that applying too high biasing current could cause/excite global MHD instabili- ties such as n = 1 wobble and n = 2 rotational modes, which is dependent on the applied radial electric field amplitude as well as its polarity. This FRC rotation and its velocity can be discussed using momentum equation, as equation (1) of [7].
Magnetic fields in both inner and outer divertors can also be varied by squeezing or flaring flux bundles to change the radial electric field (i.e. varying Er/r), which is also important to generate the sufficient E × B shear flow for FRC stability control, and perhaps contributes to some auxiliary heating on SOL/open-field-line plasmas. In fact, it was observed in C-2U that flaring magnetic field at end divertor regions has produced ~20%–30% hotter core plasma temperatures of FRC’s as compared to non-flaring case [5, 6]. Changing magnetic field configuration inside the inner divertors is the key to estab- lishing a new operating regime that can provide more effective control on SOL/edge plasmas, much closer to the core FRC inside the CV as compared with that from outer divertors, as
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