Page 4 - Internal magnetic field measurements of translated and merged field-reversed configuration plasmas in the FAT-CM device

10J114-4 Gota et al.
Rev. Sci. Instrum. 89, 10J114 (2018)
FIG. 4. (a) Contour maps of magnetic-field (Bz and Bt ) radial profiles as a function of time in the single-sided/translated FRC plasma, measured by the internal magnetic probe array in the FAT-CM mid-plane, and (b) time slice of the radial magnetic field profiles at t = 46 μs (during FRC translation through the probe array).
the probe array. Similar toroidal magnetic field features in translated FRCs were previously observed in TCS13 and C-27 experiments.
Figure 5 shows internal magnetic field profiles for the collisional-merging FRC case. Contour maps of the poloidal and toroidal magnetic field evolution are shown in Fig. 5(a), while two time slices of the radial profiles at t = 46 and 80 μs are shown in Fig. 5(b). Those time slices correspond to the times when the two FRCs collide and a quiescent phase of the merged FRC, respectively. In both cases, clear field- reversed structures of the Bz profiles are successfully observed. However, FRC performance and lifetime are evidently affected by the presence of the inserted magnetic probe array. Plasma lifetimes were shortened to ∼150 μs compared with ∼300 μs in the longer-lived FRC case without the internal magnetic probe array inserted (see Fig. 3). In this collisional-merging FRC case, each of the two-translated FRCs appears to carry significant toroidal magnetic fields with opposite helicity, and the strong Bt observed during the FRC collision still remains at the quiescent phase of the merged FRC, as seen in Fig. 5. One interesting observation in this double-sided collisional- merging plasma discharge is that the signs/polarities of the measured Bt profile at +y and −y locations (strictly speak- ing, in the positive and negative vertical locations relative to the plasma axis, rplasma = 0) appear to be opposite, which is also seen in the single-sided FRC translation case (Fig. 4). The characteristics of opposite Bt polarities and its profile (including Bt = 0 location) vary in time, as seen in the Bt contour map of Fig. 5(a). This Bt profile evolution and change in sign may indicate a plasma motion/shift in the axial direction, as observed in the single-sided/translated FRC case.
FIG. 5. (a) Contour maps of magnetic-field (Bz and Bt ) radial profiles as a function of time in the collisional-merging FRC plasma, measured by the internal magnetic probe array in the FAT-CM mid-plane, and (b) time slices of the radial magnetic field profiles at t = 46 and 80 μs (around FRC collision and quiescent phase, respectively).
IV. DISCUSSION
An RR model is a well-known and adequate profile model for the magnetic field and density of FRCs in the equilib- rium phase8,9 as well as for the translated FRC/plasmoid.13 The poloidal flux (φp) of the FRC can be approximately estimated from the excluded-flux measurement with the RR model, expressed as Eq. (2). By contrast, a direct measure- ment of the magnetic field profile yields a relatively simple poloidal flux estimation as
φp =−
􏰀 R 􏰀 rs 2πrBzdr= 0R
2πrBzdr, (3)
where R is the radius of magnetic field null point (Bz = 0)
and rs is the separatrix radius of FRC that is approximately
equal to the excluded-flux radius r ∆φ . In the ideal FRC, the
poloidal flux amounts inside and outside R are equal to each
other. Figure 6 shows the position adjusted/shifted Bz profile
of collisional-merging FRC [t = 80 μs of Fig. 5(b)], in which
the radial position is adjusted based on the following relation:
√
R = r∆φ/ 2. Using Eqs. (2) and (3), the poloidal flux inside the FRC can be estimated as follows: φp RR ∼ 1.5 mWb and φp ∼ 0.6 mWb. The discrepancy between the two estimates