The portable nature of the Hall sensor set-up permits magnetic eld measurements across dierent experiments.
E.5.1 Quad gun and large welding cables strapping coil
Initial strapping elds are made with the welding cable strapping coils (Sec. D.5.2).
These coils are mounted on ports outside the vacuum chamber (Fig. E.6 (a)), so magnetic eld must diuse through the stainless steel chamber before reaching the plasma domain. The coils are in a bipole strapping conguration (Sec. D.5). The left
(b) Measured (c) Simulated (a) Set-up
Hall probe Strapping coil
Strapping coil
Figure E.6: (a) Set-up with placement of welding cable strapping coils, quad plasma gun, and Hall probe. (b) Measured magnetic eld from hall sensors. (c) Simulated magnetic eld.
(blue) coil produces bore eld oriented out of the vacuum chamber, whereas the right (red) coil produces bore eld oriented into the chamber. Magnetic measurements at a given time (t= 5 ms), along a plane (z = 14 cm) are visualized in Fig. E.6 (b). The measurements conrm uniform 200 G magnetic eld oriented in the −ˆx direction.
Simulations of the welding cable coils (Fig. E.6 (c)) match the measured prole to within 20%. The simulations use measured currents as input, but do not include magnetic diusion, nor account for distortions from eddy currents. The excellent match between measured and simulated data suggests that diusion eects do not play a signicant role over the time-scale of the strapping eld.
The Hall sensors can also be used to measure the bias eld from the quad plasma gun (Sec. D.3). Two bias coils located behind the cathode and anode (E.7 (a)) produce an arched magnetic structure. The lower coil produces a eld oriented into the vacuum chamber (zˆdirection) whereas the upper coil produces a eld oriented out of the vacuum chamber (−ˆz direction), similar to the magnetic eld of a horse-shoe
Hall probe Bias coil
(b) Bias only (c) Bias and strapping (a) Set-up
x y
Bias coil Cathode
Anode
Figure E.7: (a) Set-up highlight the activated bias coils and hall probe. (b) Measure- ment of magnetic eld due to bias coils (c) Measurement of magnetic eld including magnet.
Figure E.7 (b) visualizes magnetic eld measurements of the bias coils: the contour lines represent the Bz component of the magnetic eld and the arrows represent the Bx andBy component of the magnetic eld. A red-blue color table denotes magnetic eld amplitudes ranging from -350 G to 350 G. Figure E.7 (b) shows shows magnetic eld lines emerging from the bottom bias coil and curving upwards, before going down into the top bias coil, consistent with a ared magnetic tube structure [66].
The application of strapping eld super-imposes a strong Bx strapping component onto the bias eld. This is veried by measurements shown in Fig. E.7 (c). The magnetic eld in Fig. E.7 (c) no longer has the ared magnetic tube structure of Fig.
E.7 (a), consistent with the eld line visualizations in Fig. F.4.
z x
Strapping coils
Top view Isometric view
Figure E.8: Visualization of magnetic eld in region above strapping coils. Magnetic eld strength is in Teslas.
E.5.2 Single loop solar experiments
Later strapping elds are made with smaller coils inside the vacuum chamber. Figure E.8 shows measurements3 of magnetic eld in the region above the strapping coils.
The eld measurements include both the bias eld and strapping eld, but the bias coils (not shown) are so far from the measurement region, that the magnetic eld is strictly from the strapping coils. The bore strapping eld is approximately 0.025 Tesla but sharply drops o, eventually reaching a null point atz ≈30 cm.
These measurements are obtained using the set-up shown in Fig. E.5 (d). One disadvantage of this set-up, is that the polycarbonate board can collide with the strapping coils, which are also mounted inside the vacuum chamber. This prevents magnetic measurements at low heights, near the bias coils. Nevertheless, the modular nature of the 3-D Hall sensor carriages means that an alternate support structure can be adapted to the domain of interest. Such a support structure is shown in Fig. E.9 (a). Multiple 3-D Hall sensor carriages are mounted along a polycarbonate cut-out.
The cut-out is mounted to an angle-bracket which is attached along slots in the support structure. The entire assembly can be moved along the axis of the strapping coils, providing volumetric magnetic eld measurements.
Magnetic measurements along the plane of the plasma is shown in Figs. E.9 (b),
3These measurements are by Patricio Arrangoiz.
(a) Set-up (b) Bias only (c) Strapping only (d) Bias and strapping
Hall sensor
mount locations
Strapping coil
Polycarb cut-out
Cathode
Anode
Figure E.9: (a) Support structure for Hall sensors near the electrodes. The set-up permits the adjustments of Hall sensor placement along all three directions. (b) Measured bias eld along a single plane. (c) Measured strapping eld along a plane.
(d) Magnetic measurements of both bias and strapping eld.
(c), and (d). The magnetic eld produced by the bias coils is shown in Fig. E.9 (b). In Fig. E.9 (b), eld lines start from the cathode and arch towards the anode, consistent with a left-handed sigmoid conguration (see Fig. G.11). The strapping coils in coaxial conguration produce strapping eld oriented along the axis of the coils (Fig. E.9 (c)). When strapping eld and bias eld are combined, the result is an arched structure near the electrodes which transitions to primarily strapping eld by the strapping coil axis (Fig. E.9 (d)).