Page 2 - Characterization of compact-toroid injection during formation, translation, and field-penetration

11D409-2 Roche et al.
Rev. Sci. Instrum. 87, 11D409 (2016)
FIG.1. Cartoonofmagneticfieldandcurrentmeasuringcoilpositionsatone of many locations along axis of C-2U. New components in red.
two additional diagnostics: more B-dot probes4 and Rogowski coils.5 These will be detailed in Sec. III
III. MAGNETIC FIELD MEASUREMENT UPGRADES
The excluded flux radius, r ,6 is defined as the di↵erence between the total enclosed flux at the wall and flux that would be enclosed if the magnetic field measured at the wall was constant across the entire cross section. That is, for a vessel of radius rw,
r = rwp1 B0/ (B0 + Bin), (1)
where B0 and Bin are the magnetic field strength measured at the wall without plasma and the field perturbation due to plasma respectively. This relation assumes that the plasma is centered and that the wall is a perfect flux conserver. Since both of these are not valid assumptions in C-2U, additional field measurements are required. Thompson et al.2 described using an array of Mirnov probes and external field measurements to account for these perturbations. To deal with the fringing fields of the external flux conservers 8 new external Bz probes were installed and 8 Rogowski coils were also installed to measured the currents in both the 6 ExFCs and DC Magnet coils as shown in Fig. 1.
A. External B-Dots
Eight new magnetic field probes (B-Dots) were installed to measure the total flux leakage of C-2U. The probes are constructed using a small ceramic core chip inductor (Coilcraft, Inc., part 1812CS-333XGLBa). They have 33 μH of inductance and a↵ective area of 8.1 cm2 (See Fig. 2). This is su cient to measure the ⇠50 G fields. In fact, the probes are sensitive to signals ⇠0.1 G when actively integrated with RC time constant RC = 100 μs. The probes are fixed to the ID of the DC magnet coils: 8 coils, 8 probes.
B. Rogowski coils
Rogowski coils measure changing current passing through the loop of the coil. A Rogowski coil is essentially a solenoid that has been bent into a torus with a return wire running down the center to eliminate pickup from external fields. Two sizes were constructed (See Fig. 2) to fit the various applications The DC Magnet and ExFC Rogowski
FIG.2. Imageofnewlyinstalleddiagnostics:(a)FCRogowskicoil,(b)Chip inductor B-Dot, (c) DC magnet Rogowski coil.
have 2.4 nH and 1.4 nH of inductance respectively. Both Rogowski coils are shielded with a split conductor. This increases the response time of the coils by avoiding the skin e↵ect that a fully enclosing shield would generate.
IV. ANALYSIS MODEL
The ExFCs generated two issues that were dealt with in our analysis: the distortion of axial magnetic field at the external wall of the vessel, Bex, and the loss of total flux conservation with active currents. The former is solved by the new array of probes and the latter is resolved by performing a vacuum shot (no plasma) with currents driven in the ExFCs.
In the past the assumption was made that Bex was constant between the DC magnets and vessel wall when calculating flux loss. This is an underestimate of the total loss of flux and therefore r . Since the DC field coils represent a sparse solenoid the field strength increases with proximity to the coils. However, it is only a small correction. By taking the ratio of the DC fields (before plasma) of Bex1 and Bex2 we can maintain consistency in the data between C-2 and C-2U
FIG. 3. E↵ectiveness of scaling external Bz measurements based on DC field measurement: (a) DC fields and ratio for scaling, (b) Time resolved traces with and without scaling applied.