Page 2 - Collisional merging formation of a field-reversed configuration in the FAT-CM device

Nucl. Fusion 59 (2019) 056024
causes a conversion of the kinetic energy to mostly thermal ion energy, which contrasts with the spheromak merging dominated by magnetic energy [9], resulting in an increase of the ion pressure that drastically expands the FRC radius and volume. This process has an important role in realizing an FRC based high-beta reactor core to capture high-energy beam ions while it is keeping its high-beta nature and simply- connected geometry.
During the collisional-merging process, the translated FRCs experience destructive perturbations on their separa- trix shape and internal magnetic structure. Indeed, the FRC expands several times in volume at the collisional merging. However, the merged magnetized plasmoid eventually set- tles in the quiescent equilibrium FRC state after the dynamic process. In this work, expanded radius and volume have been clearly observed by magnetic diagnostics of excluded flux and internal probe arrays in the confinement vessel. Other important plasma parameters, such as electron density and ion temperature have also been observed. The experimental results are compared with the numerical simulation results by two-dimensional (2D) resistive magnetohydrodynamics (MHD) code: Lamy Ridge [10] for better understanding of the dynamics of formation, translation and collisional merging processes.
2. Experimental device
Figure 1 shows a schematic diagram of the FAT-CM device and its external guide magnetic field profile. The device consists of the central confinement chamber and two FRTP formation sections, called ‘R-formation’ and ‘V-formation’. The forma- tion tubes are made of transparent quartz and the confinement chamber is made of stainless steel (inner bore is 0.78 m; skin time ~5ms) serving as a flux conserver in the timescale of the translation, collision and merging process. Quasi-static confinement magnetic field coils (inner diameter of 1.03 m) are placed along the confinement region. Initial FRCs are formed by the FRTP method in two formation sections with D2 gas-puffing.
In the typical FAT-CM operation, an FRC, which has ~1 × 1021 m−3 of electron density, is generated by the main compression field of ~0.40 T. The one-turn theta-pinch coil in each formation section consists of coil elements which have four different diameters of 36, 34, 32, and 30cm. The taper angle can be changed by the combination of coil elements. The maximum taper angle is about 1 degree. The initial FRCs, ~0.06 m in radius and ~1.0 m in length with 0.4–0.5 mWb of trapped magnetic flux, are accelerated by the gradient of the external guide magnetic field formed by the tapered theta- pinch coil and then injected into the confinement chamber with external magnetic field ~0.06 T. The translated FRCs collide in the middle of the confinement chamber at the rela- tive velocity in the range of 200–500 km s−1 at around t ~ 50 μs from the main reversal. To globally investigate and char- acterize the dynamics of the FRC formation, translation and collisional-merging process, a number of in-/ex-vessel magn- etic probes and optical measurements are installed along the device [11, 12].
T. Asai et al
A two-directional internal magnetic probe array is installed in the FAT-CM device. The two-axis probe array consists of 32 hand-wound pickup coils: 16 coils in each of the z and θ directions (for Bz and Bx measurements), spaced 3cm apart. Therefore, the probe array covers a total of 45 cm in space as shown in figure 2. The L/R penetration time for both Bz and Bx fields is less than 0.1 μs. As a plasma facing material and electrical insulation of the probe housing, AX05 grade boron- nitride jackets (outer diameter ~ 6.35mm) are mounted. Figure 2 illustrates the probe assembly installed in the mid- plane of the FAT-CM confinement vessel. With the long actu- ator and the probe housing, the probe array passes the center of the confinement vessel (r = 0) and can be fully retracted outside the vessel wall whose radius (rw) is ~0.4 m.
3. Experimental results
3.1. Global behavior
Figure 3 shows the time evolution of plasma parameters of both single and collisional merging FRCs in the FAT-CM device. The estimated excluded flux radius rΔφ at mid-plane, which is shown in figure 3(a),
r∆φ ∼ rw»1 − B0/Be (1)
is known to be comparable to the separatrix radius reflecting the poloidal flux for ideal FRC equilibrium with negligibly small plasma pressure in the scrape-off layer (SOL). Where, rw is the radius of the metal confinement chamber (r ~ 0.4 m), B0 is the magnetic field in vacuum, and Be is the external magnetic field. Figure 3(b) shows the estimated poloidal magnetic flux
φp_RR ∼ 0.31πBer∆3 φ/rw (2)
assuming the rigid-rotor (RR) equilibrium model [13] that is consistent with the internal field measurements for trans- lated FRCs [14]. Both plasma radius rΔφ and poloidal flux φp_RR are estimated using B-dot probes near the mid-plane, and line-integrated electron density is measured by a He–Ne laser interferometer system in the mid-plane of the confine- ment chamber. Figure 3 only shows one single-sided FRC case because the global behavior/performance of each FRC from the R- and V-formations are quite similar.
In the case of single-sided FRC formation/translation (red dashed lines in figure 3), the FRC is typically accelerated and ejected at a speed of 150–200 km s−1 into the confinement region; the FRC is then decelerated and bounced back-and- forth between the mirror regions. Note that the refection effi- ciency at the mirror is less than unity in the sigle translation case. In the case of collisional-merging FRCs (black solid lines in figure 3), radial expansion of the plasma is clearly observed and the separatrix radius, in the quasi-equilibrium phase, increases more than twofold compared with the single translation case as observed in the C-2/C-2U experiment at TAE [15]. The averaged electron density 〈ne〉 of the merged FRC, ~2.5 × 1020 m−3, is ten times higher than the C-2U FRC (figure 3(c)). Table 1 lists principal plasma paramters of the merged and the single-translated FRC compared with an FRC
2